Spin-dependent quark beam function at NNLO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boughezal, Radja; Petriello, Frank; Schubert, Ulrich

2017-08-01

We calculate the beam function for longitudinally polarized quarks through next-to-next-to-leading order (NNLO) in QCD perturbation theory. This is the last missing ingredient needed to apply the factorization theorem for the N-jettiness event-shape variable in a variety of polarized collisions through the NNLO level. We present all technical details of our derivation. As a by-product of our calculation we provide the first independent check of the previously obtained unpolarized quark beam function. We anticipate that our result will have phenomenological applications in describing data from polarized collisions.

Final-state interaction and B-->KK decays in perturbative QCD

NASA Astrophysics Data System (ADS)

Chen, Chuan-Hung; Li, Hsiang-Nan

2001-01-01

We predict the branching ratios and CP asymmetries of the B-->KK decays using the perturbative QCD factorization theorem, in which tree, penguin, and annihilation contributions, including both factorizable and nonfactorizable ones, are expressed as convolutions of hard six-quark amplitudes with universal meson wave functions. The unitarity angle φ3=90° and the B and K meson wave functions extracted from experimental data of the B-->Kπ and ππ decays are employed. Since the B-->KK decays are sensitive to final-state interaction effects, the comparision of our predictions with future data can test the neglect of these effects in the above formalism. The CP asymmetry in the B+/--->K+/-K0 modes and the B0d-->K+/-K-/+ branching ratios depend on annihilation and nonfactorizable amplitudes. The B-->KK data can also verify the evaluation of these contributions.

Poincare recurrence theorem and the strong CP problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalloniatis, Alex C.; Nedelko, Sergei N.; Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna

2006-02-01

The existence in the physical QCD vacuum of nonzero gluon condensates, such as , requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit 'topological charge' q characterizing the fields approximating the gluon configurations which should dominate the QCD partition function. If q is an irrational number then the critical values of the {theta} parameter for which CP is spontaneously broken are dense in R, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of U{sub A}(1) symmetry. We present anmore » explicit realization of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.« less

The pion: an enigma within the Standard Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horn, Tanja; Roberts, Craig D.

2016-05-27

Almost 50 years after the discovery of gluons & quarks, we are only just beginning to understand how QCD builds the basic bricks for nuclei: neutrons, protons, and the pions that bind them. QCD is characterised by two emergent phenomena: confinement & dynamical chiral symmetry breaking (DCSB). They are expressed with great force in the character of the pion. In turn, pion properties suggest that confinement & DCSB are closely connected. As both a Nambu-Goldstone boson and a quark-antiquark bound-state, the pion is unique in Nature. Developing an understanding of its properties is thus critical to revealing basic features ofmore » the Standard Model. We describe experimental progress in this direction, made using electromagnetic probes, highlighting both improvements in the precision of charged-pion form factor data, achieved in the past decade, and new results on the neutral-pion transition form factor. Both challenge existing notions of pion structure. We also provide a theoretical context for these empirical advances, first explaining how DCSB works to guarantee that the pion is unnaturally light; but also, nevertheless, ensures the pion is key to revealing the mechanisms that generate nearly all the mass of hadrons. Our discussion unifies the charged-pion elastic and neutral-pion transition form factors, and the pion's twist-2 parton distribution amplitude. It also indicates how studies of the charged-kaon form factor can provide significant contributions. Importantly, recent predictions for the large-$Q^2$ behaviour of the pion form factor can be tested by experiments planned at JLab 12. Those experiments will extend precise charged-pion form factor data to momenta that can potentially serve in validating factorisation theorems in QCD, exposing the transition between the nonperturbative and perturbative domains, and thereby reaching a goal that has long driven hadro-particle physics.« less

Transverse momentum dependent (TMD) parton distribution functions: Status and prospects*

DOE PAGES

Angeles-Martinez, R.; Bacchetta, A.; Balitsky, Ian I.; ...

2015-01-01

In this study, we review transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q T spectra of Higgs and vector bosons for low q T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present the application of a new tool, TMD LIB, to parton density fits andmore » parameterizations.« less

Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.

PubMed

Fodor, Z; Hoelbling, C; Krieg, S; Lellouch, L; Lippert, Th; Portelli, A; Sastre, A; Szabo, K K; Varnhorst, L

2016-08-19

In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4)  MeV in the modified minimal subtraction scheme at 2  GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Uensal, Mithat

In recent work, we derived the long-distance confining dynamics of certain QCD-like gauge theories formulated on small S{sup 1}xR{sup 3} based on symmetries, an index theorem, and Abelian duality. Here, we give the microscopic derivation. The solution reveals a new mechanism of confinement in QCD(adj) in the regime where we have control over both perturbative and nonperturbative aspects. In particular, consider SU(2) QCD(adj) theory with 1{<=}n{sub f}{<=}4 Majorana fermions, a theory which undergoes gauge symmetry breaking at small S{sup 1}. If the magnetic charge of the Bogomol'nyi-Prasad-Sommerfield (BPS) monopole is normalized to unity, we show that confinement occurs due tomore » condensation of objects with magnetic charge 2, not 1. Because of index theorems, we know that such an object cannot be a two identical monopole configuration. Its net topological charge must vanish, and hence it must be topologically indistinguishable from the perturbative vacuum. We construct such non-self-dual topological excitations, the magnetically charged, topologically null molecules of a BPS monopole and KK antimonopole, which we refer to as magnetic bions. An immediate puzzle with this proposal is the apparent Coulomb repulsion between the BPS-KK pair. An attraction which overcomes the Coulomb repulsion between the two is induced by 2n{sub f}-fermion exchange. Bion condensation is also the mechanism of confinement in N=1 SYM on the same four-manifold. The SU(N) generalization hints a possible hidden integrability behind nonsupersymmetric QCD of affine Toda type, and allows us to analytically compute the mass gap in the gauge sector. We currently do not know the extension to R{sup 4}.« less

Parton distributions in the LHC era

NASA Astrophysics Data System (ADS)

Del Debbio, Luigi

2018-03-01

Analyses of LHC (and other!) experiments require robust and statistically accurate determinations of the structure of the proton, encoded in the parton distribution functions (PDFs). The standard description of hadronic processes relies on factorization theorems, which allow a separation of process-dependent short-distance physics from the universal long-distance structure of the proton. Traditionally the PDFs are obtained from fits to experimental data. However, understanding the long-distance properties of hadrons is a nonperturbative problem, and lattice QCD can play a role in providing useful results from first principles. In this talk we compare the different approaches used to determine PDFs, and try to assess the impact of existing, and future, lattice calculations.

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation.

PubMed

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-04

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the ΔI=1 channel with the parity-odd pion-nucleon coupling constant h_{π}^{1}. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating h_{π}^{1} and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the ΔI=1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of h_{π}^{1} by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of h_{π}^{1}, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation

NASA Astrophysics Data System (ADS)

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-01

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the Δ I =1 channel with the parity-odd pion-nucleon coupling constant hπ1 . Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating hπ1 and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the Δ I =1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of hπ1 by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of hπ1, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Lattice fermions

NASA Technical Reports Server (NTRS)

Wilczek, Frank

1987-01-01

A simple heuristic proof of the Nielsen-Ninomaya theorem is given. A method is proposed whereby the multiplication of fermion species on a lattice is reduced to the minimal doubling, in any dimension, with retention of appropriate chiral symmetries. Also, it is suggested that use of spatially thinned fermion fields is likely to be a useful and appropriate approximation in QCD - in any case, it is a self-checking one.

The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable

NASA Astrophysics Data System (ADS)

Bochicchio, Marco

2017-03-01

Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

Quantum Chromodynamics and Color Confinement (confinement 2000) - Proceedings of the International Symposium

NASA Astrophysics Data System (ADS)

Suganuma, H.; Fukushima, M.; Toki, H.

The Table of Contents for the book is as follows: * Preface * Opening Address * Monopole Condensation and Quark Confinement * Dual QCD, Effective String Theory, and Regge Trajectories * Abelian Dominance and Monopole Condensation * Non-Abelian Stokes Theorem and Quark Confinement in QCD * Infrared Region of QCD and Confining Configurations * BRS Quartet Mechanism for Color Confinement * Color Confinement and Quartet Mechanism * Numerical Tests of the Kugo-Ojima Color Confinement Criterion * Monopoles and Confinement in Lattice QCD * SU(2) Lattice Gauge Theory at T > 0 in a Finite Box with Fixed Holonomy * Confining and Dirac Strings in Gluodynamics * Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory * Quark Confinement Physics from Lattice QCD * An (Almost) Perfect Lattice Action for SU(2) and SU(3) Gluodynamics * Vortices and Confinement in Lattice QCD * P-Vortices, Nexuses and Effects of Gribov Copies in the Center Gauges * Laplacian Center Vortices * Center Vortices at Strong Couplings and All Couplings * Simulations in SO(3) × Z(2) Lattice Gauge Theory * Exciting a Vortex - the Cost of Confinement * Instantons in QCD * Deformation of Instanton in External Color Fields * Field Strength Correlators in the Instanton Liquid * Instanton and Meron Physics in Lattice QCD * The Dual Ginzburg-Landau Theory for Confinement and the Role of Instantons * Lattice QCD for Quarks, Gluons and Hadrons * Hadronic Spectral Functions in QCD * Universality and Chaos in Quantum Field Theories * Lattice QCD Study of Three Quark Potential * Probing the QCD Vacuum with Flavour Singlet Objects : η' on the Lattice * Lattice Studies of Quarks and Gluons * Quarks and Hadrons in QCD * Supersymmetric Nonlinear Sigma Models * Chiral Transition and Baryon-number Susceptibility * Light Quark Masses in QCD * Chiral Symmetry of Baryons and Baryon Resonances * Confinement and Bound States in QCD * Parallel Session * Off-diagonal Gluon Mass Generation and Strong Randomness of Off-diagonal Gluon Phase in the Maximally Abelian Gauge * On the Colour Confinement and the Minimal Surface * Glueball Mass and String Tension of SU(2) Gluodynamics from Abelian Monopoles and Strings * Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio Model at Finite Temperature and Density * Confining Flux-Tube and Hadrons in QCD * Gauge Symmetry Breakdown due to Dynamical Higgs Scalar * Spatial Structure of Quark Cooper Pairs * New Approach to Axial Coupling Constants in the QCD Sum Rule and Instanton Effects * String Breaking on a Lattice * Bethe-Salpeter Approach for Mesons within the Dual Ginzburg-Landau Theory * Gauge Dependence and Matching Procedure of a Nonrelativistic QCD Boundstate Formalism * A Mathematical Approach to the SU(2)-Quark Confinement * Simulations of Odd Flavors QCD by Hybrid Monte Carlo * Non-Perturbative Renormalization Group Analysis of Dynamical Chiral Symmetry Breaking with Beyond Ladder Contributions * Charmonium Physics in Finite Temperature Lattice QCD * From Meson-Nucleon Scattering to Vector Mesons in Nuclear Matter * Symposium Program * List of Participants

Further Comments on a Vanishing Singlet Axial Vector Charge

NASA Astrophysics Data System (ADS)

Cheng, T. P.; Kochelev, N. I.; Vento, Vicente

The recent suggestion of a vanishing flavor-singlet axial-charge of nucleon due to a nontrivial vacuum structure is further amplified. A perturbative QCD discussion, applicable for the heavy quark contributions, relates it to the physics of the decoupling theorem. It is also shown that gA0˜= 0 leads to a negative η‧-meson-quark coupling, which has been found to be compatible with the chiral quark model phenomenology.

Vafa-Witten theorem and Lee-Yang singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2009-12-15

We prove the analyticity of the finite volume QCD partition function for complex values of the {theta}-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at {theta}=0 and has an important consequence: the absence of a first order phase transition at {theta}=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, andmore » existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP{sup N} sigma model.« less

Secondary production of massive quarks in thrust

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoang, André H.; Erwin Schrödinger International Institute for Mathematical Physics, University of Vienna, Boltzmanngasse 9, A-1090 Vienna; Mateu, Vicent

2016-01-22

We present a factorization framework that takes into account the production of heavy quarks through gluon splitting in the thrust distribution for e{sup +}e{sup −} → hadrons. The explicit factorization theorems and some numerical results are displayed in the dijet region where the kinematic scales are widely separated, which can be extended systematically to the whole spectrum. We account for the necessary two-loop matrix elements, threshold corrections, and include resummation up to N{sup 3}LL order. We include nonperturbative power corrections through a field theoretical shape function, and remove the O(Λ{sub QCD}) renormalon in the partonic soft function by appropriate mass-dependentmore » subtractions. Our results hold for any value of the quark mass, from an infinitesimally small (merging to the known massless result) to an infinitely large one (achieving the decoupling limit). This is the first example of an application of a variable flavor number scheme to final state jets.« less

Mrst '96: Current Ideas in Theoretical Physics - Proceedings of the Eighteenth Annual Montréal-Rochester-Syracuse-Toronto Meeting

NASA Astrophysics Data System (ADS)

O'Donnell, Patrick J.; Smith, Brian Hendee

1996-11-01

The Table of Contents for the full book PDF is as follows: * Preface * Roberto Mendel, An Appreciaton * The Infamous Coulomb Gauge * Renormalized Path Integral in Quantum Mechanics * New Analysis of the Divergence of Perturbation Theory * The Last of the Soluble Two Dimensional Field Theories? * Rb and Heavy Quark Mixing * Rb Problem: Loop Contributions and Supersymmetry * QCD Radiative Effects in Inclusive Hadronic B Decays * CP-Violating Dipole Moments of Quarks in the Kobayashi-Maskawa Model * Hints of Dynamical Symmetry Breaking? * Pi Pi Scattering in an Effective Chiral Lagrangian * Pion-Resonance Parameters from QCD Sum Rules * Higgs Theorem, Effective Action, and its Gauge Invariance * SUSY and the Decay H_2^0 to gg * Effective Higgs-to-Light Quark Coupling Induced by Heavy Quark Loops * Heavy Charged Lepton Production in Superstring Inspired E6 Models * The Elastic Properties of a Flat Crystalline Membrane * Gauge Dependence of Topological Observables in Chern-Simons Theory * Entanglement Entropy From Edge States * A Simple General Treatment of Flavor Oscillations * From Schrödinger to Maupertuis: Least Action Principles from Quantum Mechanics * The Matrix Method for Multi-Loop Feynman Integrals * Simplification in QCD and Electroweak Calculations * Programme * List of Participants

Next-to-leading-logarithmic power corrections for N -jettiness subtraction in color-singlet production

NASA Astrophysics Data System (ADS)

Boughezal, Radja; Isgrò, Andrea; Petriello, Frank

2018-04-01

We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable T . Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small T at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections to a particular definition of 0-jettiness. We present a numerical study of the power corrections in the context of their application to the N -jettiness subtraction method for higher-order calculations, using gluon-fusion Higgs production as an example. The inclusion of the next-to-leading-logarithmic power corrections further improves the numerical efficiency of the approach beyond the improvement obtained from the leading-logarithmic power corrections.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horn, Tanja; Roberts, Craig D.

Quantum chromodynamics (QCDs) is the strongly interacting part of the Standard Model. It is supposed to describe all of nuclear physics; and yet, almost 50 years after the discovery of gluons and quarks, we are only just beginning to understand how QCD builds the basic bricks for nuclei: neutrons and protons, and the pions that bind them together. QCD is characterised by two emergent phenomena: confinement and dynamical chiral symmetry breaking (DCSB). They have far-reaching consequences, expressed with great force in the character of the pion; and pion properties, in turn, suggest that confinement and DCSB are intimately connected. Indeed,more » since the pion is both a Nambu–Goldstone boson and a quark–antiquark bound-state, it holds a unique position in nature and, consequently, developing an understanding of its properties is critical to revealing some very basic features of the Standard Model. We describe experimental progress toward meeting this challenge that has been made using electromagnetic probes, highlighting both dramatic improvements in the precision of charged-pion form factor data that have been achieved in the past decade and new results on the neutral-pion transition form factor, both of which challenge existing notions of pion structure. We also provide a theoretical context for these empirical advances, which begins with an explanation of how DCSB works to guarantee that the pion is un-naturally light; but also, nevertheless, ensures that the pion is the best object to study in order to reveal the mechanisms that generate nearly all the mass of hadrons. In canvassing advances in these areas, our discussion unifies many aspects of pion structure and interactions, connecting the charged-pion elastic form factor, the neutral-pion transition form factor and the pion's leading-twist parton distribution amplitude. It also sketches novel ways in which experimental and theoretical studies of the charged-kaon electromagnetic form factor can provide significant contributions. Importantly, it appears that recent predictions for the large-Q 2 behaviour of the charged-pion form factor can be tested by experiments planned at the upgraded 12 GeV Jefferson Laboratory. Those experiments will extend precise charged-pion form factor data up to momentum transfers that it now appears may be large enough to serve in validating factorisation theorems in QCD. If so, they may expose the transition between the non-perturbative and perturbative domains and thereby reach a goal that has driven hadro-particle physics for around 35 years.« less

The pion: an enigma within the Standard Model

NASA Astrophysics Data System (ADS)

Horn, Tanja; Roberts, Craig D.

2016-07-01

Quantum chromodynamics (QCDs) is the strongly interacting part of the Standard Model. It is supposed to describe all of nuclear physics; and yet, almost 50 years after the discovery of gluons and quarks, we are only just beginning to understand how QCD builds the basic bricks for nuclei: neutrons and protons, and the pions that bind them together. QCD is characterised by two emergent phenomena: confinement and dynamical chiral symmetry breaking (DCSB). They have far-reaching consequences, expressed with great force in the character of the pion; and pion properties, in turn, suggest that confinement and DCSB are intimately connected. Indeed, since the pion is both a Nambu-Goldstone boson and a quark-antiquark bound-state, it holds a unique position in nature and, consequently, developing an understanding of its properties is critical to revealing some very basic features of the Standard Model. We describe experimental progress toward meeting this challenge that has been made using electromagnetic probes, highlighting both dramatic improvements in the precision of charged-pion form factor data that have been achieved in the past decade and new results on the neutral-pion transition form factor, both of which challenge existing notions of pion structure. We also provide a theoretical context for these empirical advances, which begins with an explanation of how DCSB works to guarantee that the pion is un-naturally light; but also, nevertheless, ensures that the pion is the best object to study in order to reveal the mechanisms that generate nearly all the mass of hadrons. In canvassing advances in these areas, our discussion unifies many aspects of pion structure and interactions, connecting the charged-pion elastic form factor, the neutral-pion transition form factor and the pion's leading-twist parton distribution amplitude. It also sketches novel ways in which experimental and theoretical studies of the charged-kaon electromagnetic form factor can provide significant contributions. Importantly, it appears that recent predictions for the large-Q 2 behaviour of the charged-pion form factor can be tested by experiments planned at the upgraded 12 GeV Jefferson Laboratory. Those experiments will extend precise charged-pion form factor data up to momentum transfers that it now appears may be large enough to serve in validating factorisation theorems in QCD. If so, they may expose the transition between the non-perturbative and perturbative domains and thereby reach a goal that has driven hadro-particle physics for around 35 years.

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations.

PubMed

Ma, Yan-Qing; Qiu, Jian-Wei

2018-01-12

Following our previous proposal, we construct a class of good "lattice cross sections" (LCSs), from which we can study the partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that the proposed functions for lattice QCD calculation of PDFs in the literature are special cases of these good LCSs.

Finite-volume effects and the electromagnetic contributions to kaon and pion masses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benic, Sanjin; Fukushima, Kenji; Garcia-Montero, Oscar

Here, we compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations inmore » the gluon saturation regime of QCD. We demonstrate that k ⊥ and collinear factorized expressions for inclusive photon production are obtained as leading twist approximations to our result. In particular, the collinearly factorized expression is directly sensitive to the nuclear gluon distribution at small x. Other results of interest include the realization of the Low-Burnett-Kroll soft photon theorem in the CGC framework and a comparative study of how the photon amplitude is obtained in Lorenz and light-cone gauges.« less

QCD topological susceptibility from the nonlocal chiral quark model

NASA Astrophysics Data System (ADS)

Nam, Seung-Il; Kao, Chung-Wen

2017-06-01

We investigate the quantum chromodynamics (QCD) topological susceptibility χ by using the semi-bosonized nonlocal chiral-quark model (SB-NLχQM) for the leading large- N c contributions. This model is based on the liquid-instanton QCD-vacuum configuration, in which SU(3) flavor symmetry is explicitly broken by the finite current-quark mass ( m u,d, m s) ≈ (5, 135) MeV. To compute χ, we derive the local topological charge-density operator Q t( x) from the effective action of SB-NLχQM. We verify that the derived expression for χ in our model satisfies the Witten- Veneziano (WV) and the Leutwyler-Smilga (LS) formulae, and the Crewther theorem in the chiral limit by construction. Once the average instanton size and the inter-instanton distance are fixed with ρ¯ = 1/3 fm and R¯ = 1 fm, respectively, all the other parameters are determined self-consistently within the model. We obtain χ = (167.67MeV)4, which is comparable with the empirical value χ = (175±5MeV)4 whereas it turns out that χ QL = (194.30MeV)4 in the quenched limit. Thus, we conclude that the value of χ will be reduced around 10 20% by the dynamical-quark contribution.

The effective hyper-Kähler potential in the N = 2 supersymmetric QCD

NASA Astrophysics Data System (ADS)

Ketov, Sergei V.

1997-02-01

The effective low-energy hyper-Kähler potential for a massive N = 2 matter in N = 2 super-QCD is investigated. TheN = 2 extended supersymmetry severely restricts the N = 2 matter self-couplings so that their exact form can be fixed by a few parameters, which is apparent in the N = 2 harmonic superspace. In the N = 2 QED with a single matter hypermultiplet, the one-loop perturbative calculations lead to the Taub-NUT hyper-Kähler metric in the massive case, and a free metric in the massless case. It is remarkable that the naive non-renormalization `theorem' does not apply. There exists a manifestly N = 2 supersymmetric duality transformation converting the low-energy effective action for the N = 2 QED hypermultiplet into a sum of the quadratic and the improved (non-polynomial) actions for an N = 2 tensor multiplet. The duality transformation also gives a simple connection between the low-energy effective action in the N = 2 harmonic superspace and the component results.

Leading twist nuclear shadowing phenomena in hard processes with nuclei

DOE PAGES

L. Franfurt; Guzey, V.; Strikman, M.

2012-01-08

We present and discuss the theory and phenomenology of the leading twist theory of nuclear shadowing which is based on the combination of the generalization of Gribov-Glauber theory, QCD factorization theorems, and HERA QCD analysis of diffraction in lepton-proton deep inelastic scattering (DIS). We apply this technique for the analysis of a wide range of hard processes with nuclei-inclusive DIS on deuterons, medium-range and heavy nuclei, coherent and incoherent diffractive DIS with nuclei, and hard diffraction in proton-nucleus scattering - and make predictions for the effect of nuclear shadowing in the corresponding sea quark and gluon parton distributions. We alsomore » analyze the role of the leading twist nuclear shadowing in generalized parton distributions in nuclei and certain characteristics of final states in nuclear DIS. We discuss the limits of applicability of the leading twist approximation for small x scattering off nuclei and the onset of the black disk regime and methods of detecting it. It will be possible to check many of our predictions in the near future in the studies of the ultraperipheral collisions at the Large Hadron Collider (LHC). Further checks will be possible in pA collisions at the LHC and forward hadron production at Relativistic Heavy Ion Collider (RHIC). As a result, detailed tests will be possible at an Electon-Ion Collider (EIC) in USA and at the Large Hadron-Electron Collider (LHeC) at CERN.« less

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations

DOE PAGES

Ma, Yan-Qing; Qiu, Jian-Wei

2018-01-10

Following our previous proposal, we construct a class of good "lattice cross sections" (LCSs), from which we can study the partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. In conclusion, we also show that the proposed functions for lattice QCDmore » calculation of PDFs in the literature are special cases of these good LCSs.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Yan-Qing; Qiu, Jian-Wei

Following our previous proposal, we construct a class of good "lattice cross sections" (LCSs), from which we can study the partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. In conclusion, we also show that the proposed functions for lattice QCDmore » calculation of PDFs in the literature are special cases of these good LCSs.« less

Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions

DOE PAGES

Benic, Sanjin; Fukushima, Kenji; Garcia-Montero, Oscar; ...

2017-01-26

Here, we compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations inmore » the gluon saturation regime of QCD. We demonstrate that k ⊥ and collinear factorized expressions for inclusive photon production are obtained as leading twist approximations to our result. In particular, the collinearly factorized expression is directly sensitive to the nuclear gluon distribution at small x. Other results of interest include the realization of the Low-Burnett-Kroll soft photon theorem in the CGC framework and a comparative study of how the photon amplitude is obtained in Lorenz and light-cone gauges.« less

Studying the Puzzle of the Pion Nucleon Sigma Term

NASA Astrophysics Data System (ADS)

Kane, Christopher; Lin, Huey-Wen

2017-09-01

The pion nucleon sigma term (σπN) is a fundamental parameter of QCD and is integral in the experimental search for dark matter particles as it is used to calculate the cross section of interactions between potential dark matter candidates and nucleons. Recent calculations of this term from lattice-QCD data disagree with calculations done using phenomenological data. This disparity is large enough to cause concern in the dark matter community as it would change the constraints on their experiments. We investigate one potential source of this disparity by studying the flavor dependence on LQCD data used to calculate σπN. To calculate σπN, we study the nucleon mass dependence on the pion mass and implement the Hellmann-Feynman Theorem. Previous calculations only consider LQCD data that accounted for 2 and 3 of the lightest quarks in the quark sea. We extend this study by using new high statistic data that considers 2, 3, and 4 quarks in the quark sea to see if the exclusion of the heavier quarks can account for this disparity. National Science Foundation.

Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion

NASA Astrophysics Data System (ADS)

Bonetti, Marco; Melnikov, Kirill; Tancredi, Lorenzo

2018-03-01

We present an estimate of the next-to-leading-order (NLO) QCD corrections to mixed QCD-electroweak contributions to the Higgs boson production cross section in gluon fusion, combining the recently computed three-loop virtual corrections and the approximate treatment of real emission in the soft approximation. We find that the NLO QCD corrections to the mixed QCD-electroweak contributions are nearly identical to NLO QCD corrections to QCD Higgs production. Our result confirms an earlier estimate of these O (α αs2) effects by Anastasiou et al. [J. High Energy Phys. 04 (2009) 003, 10.1088/1126-6708/2009/04/003] and provides further support for the factorization approximation of QCD and electroweak corrections.

NLO cross sections in 4 dimensions without DREG

NASA Astrophysics Data System (ADS)

Hernández-Pinto, R. J.; Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, G. F. R.

2016-10-01

In this review, we present a new method for computing physical cross sections at NLO accuracy in QCD without using the standard Dimensional Regularisation. The algorithm is based on the Loop-Tree Duality theorem, which allow us to obtain loop integrals as a sum of phase-space integrals; in this way, transforming loop integrals into phase-space integrals, we propose a method to merge virtual and real contributions in order to find observables at NLO in d = 4 space-time dimensions. In addition, the strategy described is used for computing the γ* → qq̅(g) process. A more detailed discussion related on this topic can be found in Ref [1].

Zero-Bounded Limits as a Special Case of the Squeeze Theorem for Evaluating Single-Variable and Multivariable Limits

ERIC Educational Resources Information Center

Gkioulekas, Eleftherios

2013-01-01

Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…

Two-color QCD at high density

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boz, Tamer; Skullerud, Jon-Ivar; Centre for the Subatomic Structure of Matter, Adelaide University, Adelaide, SA 5005

2016-01-22

QCD at high chemical potential has interesting properties such as deconfinement of quarks. Two-color QCD, which enables numerical simulations on the lattice, constitutes a laboratory to study QCD at high chemical potential. Among the interesting properties of two-color QCD at high density is the diquark condensation, for which we present recent results obtained on a finer lattice compared to previous studies. The quark propagator in two-color QCD at non-zero chemical potential is referred to as the Gor’kov propagator. We express the Gor’kov propagator in terms of form factors and present recent lattice simulation results.

Calculation of neutral weak nucleon form factors with the AdS/QCD correspondence

NASA Astrophysics Data System (ADS)

Lohmann, Mark

The AdS/QCD (Anti-de Sitter/Quantum Chromodynamics) is a mathematical formalism applied to a theory based on the original AdS/CFT (Anti-de Sitter/ Conformal Field Theory) correspondence. The aim is to describe properties of the strong force in an essentially non-perturbative way. AdS/QCD theories break the conformal symmetry of the AdS metric (a sacrifice) to arrive at a boundary theory which is QCD-like (a payoff). This correspondence has been used to calculate well-known quantities in nucleon spectra and structure like Regge trajectories, form factors, and many others within an error of less than 20% from experiment. This is impressive considering that ordinary perturbation theory in QCD applied to the strongly interacting domain usually obtains an error of about 30%. In this thesis, the AdS/QCD correspondence method of light-front holography established by Brodsky and de Teramond is used in an attempt to calculate the Dirac and Pauli neutral weak form factors, FZ1 (Q2) and FZ2 (Q 2) respectively, for both the proton and the neutron. With this approach, we were able to determine the neutral weak Dirac form factor for both nucleons and the Pauli form factor for the proton, while the method did not succeed at determining the neutral weak Pauli form factor for the neutron. With these we were also able to extract the proton's strange electric and magnetic form factor, which addresses important questions in nucleon sub-structure that are currently being investigated through experiments at the Thomas Jefferson National Accelerator Facility.

Effective Lagrangians and Current Algebra in Three Dimensions

NASA Astrophysics Data System (ADS)

Ferretti, Gabriele

In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.

Iso-vector form factors of the delta and nucleon in QCD sum rules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ozpineci, A.

Form factors are important non-perturbative properties of hadrons. They give information about the internal structure of the hadrons. In this work, iso-vector axial-vector and iso-vector tensor form factors of the nucleon and the iso-vector axial-vector {Delta}{yields}N transition form factor calculations in QCD Sum Rules are presented.

Δ(1232) axial charge and form factors from lattice QCD.

PubMed

Alexandrou, Constantia; Gregory, Eric B; Korzec, Tomasz; Koutsou, Giannis; Negele, John W; Sato, Toru; Tsapalis, Antonios

2011-09-30

We present the first calculation on the Δ axial vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to Δ axial transition coupling constant and Δ axial charge.

The decay of Λ _b→ p~K^- in QCD factorization approach

NASA Astrophysics Data System (ADS)

Zhu, Jie; Ke, Hong-Wei; Wei, Zheng-Tao

2016-05-01

With only the tree-level operator, the decay of Λ _b→ pK is predicted to be one order smaller than the experimental data. The QCD penguin effects should be taken into account. In this paper, we explore the one-loop QCD corrections to the decay of Λ _b→ pK within the framework of QCD factorization approach. For the baryon system, the diquark approximation is adopted. The transition hadronic matrix elements between Λ _b and p are calculated in the light-front quark model. The branching ratio of Λ _b→ pK is predicted to be about 4.85× 10^{-6}, which is consistent with experimental data (4.9± 0.9)× 10^{-6}. The CP violation is about 5 % in theory.

Charmless two-body B decays: A global analysis with QCD factorization

NASA Astrophysics Data System (ADS)

Du, Dongsheng; Sun, Junfeng; Yang, Deshan; Zhu, Guohuai

2003-01-01

In this paper, we perform a global analysis of B→PP and PV decays with the QCD factorization approach. It is encouraging to observe that the predictions of QCD factorization are in good agreement with experiment. The best fit γ is around 79 °. The penguin-diagram to tree-diagram ratio |Pππ/Tππ| of π+π- decays is preferred to be larger than 0.3. We also show the confidence levels for some interesting channels: B0→π0π0, K+K-, and B+→ωπ+, ωK+. For B→πK* decays, they are expected to have smaller branching ratios with more precise measurements.

$$B\\to Kl^+l^-$$ decay form factors from three-flavor lattice QCD

DOE PAGES

Bailey, Jon A.

2016-01-27

We compute the form factors for the B → Kl +l - semileptonic decay process in lattice QCD using gauge-field ensembles with 2+1 flavors of sea quark, generated by the MILC Collaboration. The ensembles span lattice spacings from 0.12 to 0.045 fm and have multiple sea-quark masses to help control the chiral extrapolation. The asqtad improved staggered action is used for the light valence and sea quarks, and the clover action with the Fermilab interpretation is used for the heavy b quark. We present results for the form factors f+(q 2), f 0(q 2), and f T(q 2), where q 2more » is the momentum transfer, together with a comprehensive examination of systematic errors. Lattice QCD determines the form factors for a limited range of q 2, and we use the model-independent z expansion to cover the whole kinematically allowed range. We present our final form-factor results as coefficients of the z expansion and the correlations between them, where the errors on the coefficients include statistical and all systematic uncertainties. Lastly, we use this complete description of the form factors to test QCD predictions of the form factors at high and low q 2.« less

Form factors and differential branching ratio of B →K μ+μ- in AdS/QCD

NASA Astrophysics Data System (ADS)

Momeni, S.; Khosravi, R.

2018-03-01

The holographic distribution amplitudes (DAs) for the K pseudoscalar meson are derived. For this aim, the light-front wave function (LFWF) of the K meson is extracted within the framework of the anti-de Sitter/quantum chromodynamics (AdS/QCD) correspondence. We consider a momentum-dependent (dynamical) helicity wave function that contains the dynamical spin effects. We use the LFWF to predict the radius and the electromagnetic form factor of the kaon and compare them with the experimental values. Then, the holographic twist-2 DA of K meson ϕK(α ,μ ) is investigated and compared with the result of the light-cone sum rules (LCSR). The transition form factors of the semileptonic B →K ℓ+ℓ- decays are derived from the holographic DAs of the kaon. With the help of these form factors, the differential branching ratio of the B →K μ+μ- on q2 is plotted. A comparison is made between our prediction in AdS/QCD and the results obtained from two models including the LCSR and the lattice QCD as well as the experimental values.

Renormalization of composite operators in Yang-Mills theories using a general covariant gauge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, J.C.; Scalise, R.J.

Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear whenmore » gluonic matrix elements are taken on shell at zero momentum transfer.« less

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

NASA Astrophysics Data System (ADS)

Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

2018-02-01

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

Matching factorization theorems with an inverse-error weighting

NASA Astrophysics Data System (ADS)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

2018-06-01

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

Matching factorization theorems with an inverse-error weighting

DOE PAGES

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; ...

2018-04-03

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

Matching factorization theorems with an inverse-error weighting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

$$|V_{ub}|$$ from $$B\\to\\pi\\ell\

DOE PAGES

Bailey, Jon A.; et al.

2015-07-23

We present a lattice-QCD calculation of the B → πℓν semileptonic form factors and a new determination of the CKM matrix element |V ub|. We use the MILC asqtad (2+1)-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent z parametrization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolationmore » to the z expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain |V ub|, we simultaneously fit the experimental data for the B → πℓν differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find |V ub|=(3.72±0.16) × 10 –3, where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on |V ub| to the same level as the experimental error. We also provide results for the B → πℓν vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely determined than from our lattice-QCD calculation alone. Lastly, these results can be used in other phenomenological applications and to test other approaches to QCD.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, Jon A.; et al.

We present a lattice-QCD calculation of the B → πℓν semileptonic form factors and a new determination of the CKM matrix element |V ub|. We use the MILC asqtad (2+1)-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent z parametrization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolationmore » to the z expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain |V ub|, we simultaneously fit the experimental data for the B → πℓν differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find |V ub|=(3.72±0.16) × 10 –3, where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on |V ub| to the same level as the experimental error. We also provide results for the B → πℓν vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely determined than from our lattice-QCD calculation alone. Lastly, these results can be used in other phenomenological applications and to test other approaches to QCD.« less

D → Klv semileptonic decay using lattice QCD with HISQ at physical pion masses

NASA Astrophysics Data System (ADS)

Chakraborty, Bipasha; Davies, Christine; Koponen, Jonna; Lepage, G. Peter

2018-03-01

he quark flavor sector of the Standard Model is a fertile ground to look for new physics effects through a unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. We present a lattice QCD calculation of the scalar and the vector form factors (over a large q2 region including q2 = 0) associated with the D→ Klv semi-leptonic decay. This calculation will then allow us to determine the central CKM matrix element, Vcs in the Standard Model, by comparing the lattice QCD results for the form factors and the experimental decay rate. This form factor calculation has been performed on the Nf = 2 + 1 + 1 MILC HISQ ensembles with the physical light quark masses.

Proof of factorization of χ _{cJ} production in non-equilibrium QCD at RHIC and LHC in color singlet mechanism

NASA Astrophysics Data System (ADS)

Nayak, Gouranga C.

2017-12-01

Recently we have proved the factorization of NRQCD S-wave heavy quarkonium production at all orders in coupling constant. In this paper we extend this to prove the factorization of infrared divergences in χ _{cJ} production from color singlet c{\\bar{c}} pair in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This can be relevant to study the quark-gluon plasma at RHIC and LHC.

The singular behavior of massive QCD amplitudes

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Moch, Sven-Olaf

2007-05-01

We discuss the structure of infrared singularities in on-shell QCD amplitudes with massive partons and present a general factorization formula in the limit of small parton masses. The factorization formula gives rise to an all-order exponentiation of both, the soft poles in dimensional regularization and the large collinear logarithms of the parton masses. Moreover, it provides a universal relation between any on-shell amplitude with massive external partons and its corresponding massless amplitude. For the form factor of a heavy quark we present explicit results including the fixed-order expansion up to three loops in the small mass limit. For general scattering processes we show how our constructive method applies to the computation of all singularities as well as the constant (mass-independent) terms of a generic massive n-parton QCD amplitude up to the next-to-next-to-leading order corrections.

Calculation of the Nucleon Axial Form Factor Using Staggered Lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyer, Aaron S.; Hill, Richard J.; Kronfeld, Andreas S.

The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation ofmore » $$g_A$$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.« less

QCD Sum Rules and Models for Generalized Parton Distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anatoly Radyushkin

2004-10-01

I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ansaetze are briefly discussed.

Meson properties and phase diagrams in a SU(3) nonlocal PNJL model with lattice-QCD-inspired form factors

NASA Astrophysics Data System (ADS)

Carlomagno, J. P.

2018-05-01

We study the features of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model that includes wave-function renormalization. Model parameters are determined from vacuum phenomenology considering lattice-QCD-inspired nonlocal form factors. Within this framework, we analyze the properties of light scalar and pseudoscalar mesons at finite temperature and chemical potential determining characteristics of deconfinement and chiral restoration transitions.

Unique Factorization and the Fundamental Theorem of Arithmetic

ERIC Educational Resources Information Center

Sprows, David

2017-01-01

The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

NASA Astrophysics Data System (ADS)

Anupam, A. H.; Kundu, Arpan; Ray, Krishnendu

2018-05-01

It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

New methods for B meson decay constants and form factors from lattice NRQCD

NASA Astrophysics Data System (ADS)

Hughes, C.; Davies, C. T. H.; Monahan, C. J.; Hpqcd Collaboration

2018-03-01

We determine the normalization of scalar and pseudoscalar current operators made from nonrelativistic b quarks and highly improved staggered light quarks in lattice quantum chromodynamics (QCD) through O (αs) and ΛQCD/mb. We use matrix elements of these operators to extract B meson decay constants and form factors, and then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the B meson decay constants and form factors. We provide a new value for the B and Bs meson decay constants from lattice QCD calculations on ensembles that include u , d , s , and c quarks in the sea and those that have the u /d quark mass going down to its physical value. Our results are fB=0.196 (6 ) GeV , fBs=0.236(7 ) GeV , and fB s/fB=1.207 (7 ), agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of fB=0.190 (4 ) GeV , fBs=0.229(5 ) GeV , and fB s/fB=1.206 (5 ).

Improved perturbative QCD formalism for Bc meson decays

NASA Astrophysics Data System (ADS)

Liu, Xin; Li, Hsiang-nan; Xiao, Zhen-Jun

2018-06-01

We derive the kT resummation for doubly heavy-flavored Bc meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" Bc+→J /ψ π+. With a reasonable model for the Bc meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the Bc→J /ψ transition form factor appears to be power suppressed, and the Bc+→J /ψ π+ branching ratio is not lower than 10-3. The above improved perturbative QCD formalism is applicable to Bc meson decays to other charmonia and charmed mesons.

QCD Resummation for Single Spin Asymmetries

NASA Astrophysics Data System (ADS)

Kang, Zhong-Bo; Xiao, Bo-Wen; Yuan, Feng

2011-10-01

We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme-independent coefficients are calculated up to one-loop order.

QCD Resummation for Single Spin Asymmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang Z.; Xiao, Bo-Wen; Yuan, Feng

We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme-independent coefficients are calculated up to one-loop order.

Factorization of standard model cross sections at ultrahigh energy

NASA Astrophysics Data System (ADS)

Chien, Yang-Ting; Li, Hsiang-nan

2018-03-01

The factorization theorem for organizing multiple electroweak boson emissions at future colliders with energy far above the electroweak scale is formulated. Taking the inclusive muon-pair production in electron-positron collisions as an example, we argue that the summation over isospins is demanded for constructing the universal distributions of leptons and gauge bosons in an electron. These parton distributions are shown to have the same infrared structure in the phases of broken and unbroken electroweak symmetry, an observation consistent with the Goldstone equivalence theorem. The electroweak factorization of processes involving protons is sketched, with an emphasis on the subtlety of the scalar distributions. This formalism, in which electroweak shower effects are handled from the viewpoint of factorization theorem for the first time, is an adequate framework for collider physics at ultra high energy.

Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects

DOE PAGES

Bhattacharya, Atri; Enberg, Rikard; Jeong, Yu Seon; ...

2016-11-28

We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, k T factorization including low-x resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest datamore » on forward charm meson production from LHCb at 7 TeV and at 13 TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from 10% to 50% at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.« less

Scattering processes and resonances from lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briceno, Raul A.; Dudek, Jozef J.; Young, Ross D.

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lightermore » hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This paper reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. Finally, the challenges which currently limit the field are discussed along with the steps being taken to resolve them.« less

Scattering processes and resonances from lattice QCD

NASA Astrophysics Data System (ADS)

Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D.

2018-04-01

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This article reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

Scattering processes and resonances from lattice QCD

DOE PAGES

Briceno, Raul A.; Dudek, Jozef J.; Young, Ross D.

2018-04-18

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lightermore » hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This paper reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. Finally, the challenges which currently limit the field are discussed along with the steps being taken to resolve them.« less

Counting Heron Triangles with Constraints

DTIC Science & Technology

2013-01-25

Heron triangle is an integer, then b is even, say b = 2b1. By Pythagoras ’ theorem , a4 = h2 +4b21, and since in a Heron triangle, the heights are always...our first result, which follows an idea of [10, Theorem 2.3]. Theorem 4. Let a, b be two fixed integers, and let ab be factored as in (1). Then H(a, b...which we derive the result. Theorem 4 immediately offers us an interesting observation regarding a special class of fixed sides (a, b). Corollary 5. If

Twin Higgs Asymmetric Dark Matter.

PubMed

García García, Isabel; Lasenby, Robert; March-Russell, John

2015-09-18

We study asymmetric dark matter (ADM) in the context of the minimal (fraternal) twin Higgs solution to the little hierarchy problem, with a twin sector with gauged SU(3)^{'}×SU(2)^{'}, a twin Higgs doublet, and only third-generation twin fermions. Naturalness requires the QCD^{'} scale Λ_{QCD}^{'}≃0.5-20  GeV, and that t^{'} is heavy. We focus on the light b^{'} quark regime, m_{b^{'}}≲Λ_{QCD}^{'}, where QCD^{'} is characterized by a single scale Λ_{QCD}^{'} with no light pions. A twin baryon number asymmetry leads to a successful dark matter (DM) candidate: the spin-3/2 twin baryon, Δ^{'}∼b^{'}b^{'}b^{'}, with a dynamically determined mass (∼5Λ_{QCD}^{'}) in the preferred range for the DM-to-baryon ratio Ω_{DM}/Ω_{baryon}≃5. Gauging the U(1)^{'} group leads to twin atoms (Δ^{'}-τ^{'}[over ¯] bound states) that are successful ADM candidates in significant regions of parameter space, sometimes with observable changes to DM halo properties. Direct detection signatures satisfy current bounds, at times modified by dark form factors.

D meson semileptonic form factors in Nf = 3 QCD with Möbius domain-wall quarks

NASA Astrophysics Data System (ADS)

Kaneko, Takashi; Colquhoun, Brian; Fukaya, Hidenori; Hashimoto, Shoji

2018-03-01

e present our calculation of D → π and D → K semileptonic form factors in Nf = 2 + 1 lattice QCD. We simulate three lattice cutoffs a-1 ≃ 2.5, 3.6 and 4.5 GeV with pion masses as low as 230 MeV. The Möbius domain-wall action is employed for both light and charm quarks. We present our results for the vector and scalar form factors and discuss their dependence on the lattice spacing, light quark masses and momentum transfer.

QCD as a Theory of Hadrons

NASA Astrophysics Data System (ADS)

Narison, Stephan

2004-05-01

About Stephan Narison; Outline of the book; Preface; Acknowledgements; Part I. General Introduction: 1. A short flash on particle physics; 2. The pre-QCD era; 3. The QCD story; 4. Field theory ingredients; Part II. QCD Gauge Theory: 5. Lagrangian and gauge invariance; 6. Quantization using path integral; 7. QCD and its global invariance; Part III. MS scheme for QCD and QED: Introduction; 8. Dimensional regularization; 9. The MS renormalization scheme; 10. Renormalization of operators using the background field method; 11. The renormalization group; 12. Other renormalization schemes; 13. MS scheme for QED; 14. High-precision low-energy QED tests; Part IV. Deep Inelastic Scattering at Hadron Colliders: 15. OPE for deep inelastic scattering; 16. Unpolarized lepton-hadron scattering; 17. The Altarelli-Parisi equation; 18. More on unpolarized deep inelastic scatterings; 19. Polarized deep-inelastic processes; 20. Drell-Yan process; 21. One 'prompt photon' inclusive production; Part V. Hard Processes in e+e- Collisions: Introduction; 22. One hadron inclusive production; 23. gg scatterings and the 'spin' of the photon; 24. QCD jets; 25. Total inclusive hadron productions; Part VI. Summary of QCD Tests and as Measurements; Part VII. Power Corrections in QCD: 26. Introduction; 27. The SVZ expansion; 28. Technologies for evaluating Wilson coefficients; 29. Renormalons; 30. Beyond the SVZ expansion; Part VIII. QCD Two-Point Functions: 31. References guide to original works; 32. (Pseudo)scalar correlators; 33. (Axial-)vector two-point functions; 34. Tensor-quark correlator; 35. Baryonic correlators; 36. Four-quark correlators; 37. Gluonia correlators; 38. Hybrid correlators; 39. Correlators in x-space; Part IX. QCD Non-Perturbative Methods: 40. Introduction; 41. Lattice gauge theory; 42. Chiral perturbation theory; 43. Models of the QCD effective action; 44. Heavy quark effective theory; 45. Potential approaches to quarkonia; 46. On monopole and confinement; Part X. QCD Spectral Sum Rules: 47. Introduction; 48. Theoretical foundations; 49. Survey of QCD spectral sum rules; 50. Weinberg and DMO sum rules; 51. The QCD coupling as; 52. The QCD condensates; 53. Light and heavy quark masses, etc.; 54. Hadron spectroscopy; 55. D, B and Bc exclusive weak decays; 56. B0(s)-B0(s) mixing, kaon CP violation; 57. Thermal behaviour of QCD; 58. More on spectral sum rules; Part XI. Appendix A: physical constants and unites; Appendix B: weight factors for SU(N)c; Appendix C: coordinates and momenta; Appendix D: Dirac equation and matrices; Appendix E: Feynman rules; Appendix F: Feynman integrals; Appendix G: useful formulae for the sum rules; Bibliography; Index.

QCD as a Theory of Hadrons

NASA Astrophysics Data System (ADS)

Narison, Stephan

2007-07-01

About Stephan Narison; Outline of the book; Preface; Acknowledgements; Part I. General Introduction: 1. A short flash on particle physics; 2. The pre-QCD era; 3. The QCD story; 4. Field theory ingredients; Part II. QCD Gauge Theory: 5. Lagrangian and gauge invariance; 6. Quantization using path integral; 7. QCD and its global invariance; Part III. MS scheme for QCD and QED: Introduction; 8. Dimensional regularization; 9. The MS renormalization scheme; 10. Renormalization of operators using the background field method; 11. The renormalization group; 12. Other renormalization schemes; 13. MS scheme for QED; 14. High-precision low-energy QED tests; Part IV. Deep Inelastic Scattering at Hadron Colliders: 15. OPE for deep inelastic scattering; 16. Unpolarized lepton-hadron scattering; 17. The Altarelli-Parisi equation; 18. More on unpolarized deep inelastic scatterings; 19. Polarized deep-inelastic processes; 20. Drell-Yan process; 21. One 'prompt photon' inclusive production; Part V. Hard Processes in e+e- Collisions: Introduction; 22. One hadron inclusive production; 23. gg scatterings and the 'spin' of the photon; 24. QCD jets; 25. Total inclusive hadron productions; Part VI. Summary of QCD Tests and as Measurements; Part VII. Power Corrections in QCD: 26. Introduction; 27. The SVZ expansion; 28. Technologies for evaluating Wilson coefficients; 29. Renormalons; 30. Beyond the SVZ expansion; Part VIII. QCD Two-Point Functions: 31. References guide to original works; 32. (Pseudo)scalar correlators; 33. (Axial-)vector two-point functions; 34. Tensor-quark correlator; 35. Baryonic correlators; 36. Four-quark correlators; 37. Gluonia correlators; 38. Hybrid correlators; 39. Correlators in x-space; Part IX. QCD Non-Perturbative Methods: 40. Introduction; 41. Lattice gauge theory; 42. Chiral perturbation theory; 43. Models of the QCD effective action; 44. Heavy quark effective theory; 45. Potential approaches to quarkonia; 46. On monopole and confinement; Part X. QCD Spectral Sum Rules: 47. Introduction; 48. Theoretical foundations; 49. Survey of QCD spectral sum rules; 50. Weinberg and DMO sum rules; 51. The QCD coupling as; 52. The QCD condensates; 53. Light and heavy quark masses, etc.; 54. Hadron spectroscopy; 55. D, B and Bc exclusive weak decays; 56. B0(s)-B0(s) mixing, kaon CP violation; 57. Thermal behaviour of QCD; 58. More on spectral sum rules; Part XI. Appendix A: physical constants and unites; Appendix B: weight factors for SU(N)c; Appendix C: coordinates and momenta; Appendix D: Dirac equation and matrices; Appendix E: Feynman rules; Appendix F: Feynman integrals; Appendix G: useful formulae for the sum rules; Bibliography; Index.

Calculation of shear viscosity using Green-Kubo relations within a parton cascade

NASA Astrophysics Data System (ADS)

Wesp, C.; El, A.; Reining, F.; Xu, Z.; Bouras, I.; Greiner, C.

2011-11-01

The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the perturbation-QCD- (pQCD-) based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3 to 8 compared to elastic scatterings. The shear viscosity scales with the coupling as η˜1/[αs2log(1/αs)]. For constant αs the shear viscosity to entropy density ratio η/s has no dependence on temperature. Replacing the pQCD-based collision angle distribution of binary scatterings by an isotropic form decreases the shear viscosity by a factor of 3.

Higgs boson gluon-fusion production in QCD at three loops.

PubMed

Anastasiou, Charalampos; Duhr, Claude; Dulat, Falko; Herzog, Franz; Mistlberger, Bernhard

2015-05-29

We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.

Structure of rapidity divergences in multi-parton scattering soft factors

NASA Astrophysics Data System (ADS)

Vladimirov, Alexey

2018-04-01

We discuss the structure of rapidity divergences that are presented in the soft factors of transverse momentum dependent (TMD) factorization theorems. To provide the discussion on the most general level we consider soft factors for multi-parton scattering. We show that the rapidity divergences are result of the gluon exchanges with the distant transverse plane, and are structurally equivalent to the ultraviolet divergences. It allows to formulate and to prove the renormalization theorem for rapidity divergences. The proof is made with the help the conformal transformation which maps rapidity divergences to ultraviolet divergences. The theorem is the systematic form of the factorization of rapidity divergences, which is required for the definition of TMD parton distributions. In particular, the definition of multi parton distributions is presented. The equivalence of ultraviolet and rapidity divergences leads to the exact relation between soft and rapidity anomalous dimensions. Using this relation we derive the rapidity anomalous dimension at the three-loop order.

QCD for Postgraduates (3/5)

ScienceCinema

Zanderighi, Giulia

2018-04-27

Modern QCD - Lecture 3 We will introduce processes with initial-state hadrons and discuss parton distributions, sum rules, as well as the need for a factorization scale once radiative corrections are taken into account. We will then discuss the DGLAP equation, the evolution of parton densities, as well as ways in which parton densities are extracted from data.

Electroweak Higgs production with HiggsPO at NLO QCD

NASA Astrophysics Data System (ADS)

Greljo, Admir; Isidori, Gino; Lindert, Jonas M.; Marzocca, David; Zhang, Hantian

2017-12-01

We present the HiggsPO UFO model for Monte Carlo event generation of electroweak VH and VBF Higgs production processes at NLO in QCD in the formalism of Higgs pseudo-observables (PO). We illustrate the use of this tool by studying the QCD corrections, matched to a parton shower, for several benchmark points in the Higgs PO parameter space. We find that, while being sizable and thus important to be considered in realistic experimental analyses, the QCD higher-order corrections largely factorize. As an additional finding, based on the NLO results, we advocate to consider 2D distributions of the two-jet azimuthal-angle difference and the leading jet p_T for new physics searches in VBF Higgs production. The HiggsPO UFO model is publicly available.

Exposing the QCD Splitting Function with CMS Open Data.

PubMed

Larkoski, Andrew; Marzani, Simone; Thaler, Jesse; Tripathee, Aashish; Xue, Wei

2017-09-29

The splitting function is a universal property of quantum chromodynamics (QCD) which describes how energy is shared between partons. Despite its ubiquitous appearance in many QCD calculations, the splitting function cannot be measured directly, since it always appears multiplied by a collinear singularity factor. Recently, however, a new jet substructure observable was introduced which asymptotes to the splitting function for sufficiently high jet energies. This provides a way to expose the splitting function through jet substructure measurements at the Large Hadron Collider. In this Letter, we use public data released by the CMS experiment to study the two-prong substructure of jets and test the 1→2 splitting function of QCD. To our knowledge, this is the first ever physics analysis based on the CMS Open Data.

Light meson form factors at high Q2 from lattice QCD

NASA Astrophysics Data System (ADS)

Koponen, Jonna; Zimermmane-Santos, André; Davies, Christine; Lepage, G. Peter; Lytle, Andrew

2018-03-01

Measurements and theoretical calculations of meson form factors are essential for our understanding of internal hadron structure and QCD, the dynamics that bind the quarks in hadrons. The pion electromagnetic form factor has been measured at small space-like momentum transfer |q2| < 0.3 GeV2 by pion scattering from atomic electrons and at values up to 2.5 GeV2 by scattering electrons from the pion cloud around a proton. On the other hand, in the limit of very large (or infinite) Q2 = -q2, perturbation theory is applicable. This leaves a gap in the intermediate Q2 where the form factors are not known. As a part of their 12 GeV upgrade Jefferson Lab will measure pion and kaon form factors in this intermediate region, up to Q2 of 6 GeV2. This is then an ideal opportunity for lattice QCD to make an accurate prediction ahead of the experimental results. Lattice QCD provides a from-first-principles approach to calculate form factors, and the challenge here is to control the statistical and systematic uncertainties as errors grow when going to higher Q2 values. Here we report on a calculation that tests the method using an ηs meson, a 'heavy pion' made of strange quarks, and also present preliminary results for kaon and pion form factors. We use the nf = 2 + 1 + 1 ensembles made by the MILC collaboration and Highly Improved Staggered Quarks, which allows us to obtain high statistics. The HISQ action is also designed to have small dicretisation errors. Using several light quark masses and lattice spacings allows us to control the chiral and continuum extrapolation and keep systematic errors in check. Warning, no authors found for 2018EPJWC.17506016.

Determination of $${{\\rm{\\Lambda }}}_{\\overline{{\\rm{MS}}}}$$ at five loops from holographic QCD

DOE PAGES

Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

2017-08-25

Here, the recent determination of themore » $$\\beta$$--function of the QCD running coupling $$\\alpha_{\\overline{MS}}(Q^2)$$ to five-loops, provides a verification of the convergence of a novel method for determining the fundamental QCD parameter $$\\Lambda_s$$ based on the Light-Front Holographic approach to nonperturbative QCD. The new 5-loop analysis, together with improvements in determining the holographic QCD nonperturbative scale parameter $$\\kappa$$ from hadronic spectroscopy, leads to an improved precision of the value of $$\\Lambda_s$$ in the $${\\overline{MS}}$$ scheme close to a factor of two; we find $$\\Lambda^{(3)}_{\\overline{MS}}=0.339\\pm0.019$$ GeV for $$n_{f}=3$$, in excellent agreement with the world average, $$\\Lambda_{\\overline{MS}}^{(3)}=0.332\\pm0.017$$ GeV. Lastly, we also discuss the constraints imposed on the scale dependence of the strong coupling in the nonperturbative domain by superconformal quantum mechanics and its holographic embedding in anti-de Sitter space.« less

QCD corrections to ZZ production in gluon fusion at the LHC

DOE PAGES

Caola, Fabrizio; Melnikov, Kirill; Rontsch, Raoul; ...

2015-11-23

We compute the next-to-leading-order QCD corrections to the production of two Z-bosons in the annihilation of two gluons at the LHC. Being enhanced by a large gluon flux, these corrections provide a distinct and, potentially, the dominant part of the N 3LO QCD contributions to Z-pair production in proton collisions. The gg → ZZ annihilation is a loop-induced process that receives the dominant contribution from loops of five light quarks, that are included in our computation in the massless approximation. We find that QCD corrections increase the gg → ZZ production cross section by O(50%–100%) depending on the values ofmore » the renormalization and factorization scales used in the leading-order computation and the collider energy. Furthermore, the large corrections to the gg → ZZ channel increase the pp → ZZ cross section by about 6% to 8%, exceeding the estimated theoretical uncertainty of the recent next-to-next-to-leading-order QCD calculation.« less

Lattice QCD and the timelike pion form factor.

PubMed

Meyer, Harvey B

2011-08-12

We present a formula that allows one to calculate the pion form factor in the timelike region 2m(π) ≤ √(s) ≤ 4m(π) in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.

Remarks on the Acceptance of Proofs: The Case of Some Recently Tackled Major Theorems.

ERIC Educational Resources Information Center

Neubrand, Michael

1989-01-01

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

Exclusive, hard diffraction in QCD

NASA Astrophysics Data System (ADS)

Freund, Andreas

In the first chapter we give an introduction to hard diffractive scattering in QCD to introduce basic concepts and terminology, thus setting the stage for the following chapters. In the second chapter we make predictions for nondiagonal parton distributions in a proton in the LLA. We calculate the DGLAP-type evolution kernels in the LLA, solve the nondiagonal GLAP evolution equations with a modified version of the CTEQ-package and comment on the range of applicability of the LLA in the asymmetric regime. We show that the nondiagonal gluon distribution g(x1,x2,t,μ2) can be well approximated at small x by the conventional gluon density xG(x,μ2). In the third chapter, we discuss the algorithms used in the LO evolution program for nondiagonal parton distributions in the DGLAP region and discuss the stability of the code. Furthermore, we demonstrate that we can reproduce the case of the LO diagonal evolution within less than 0.5% of the original code as developed by the CTEQ-collaboration. In chapter 4, we show that factorization holds for the deeply virtual Compton scattering amplitude in QCD, up to power suppressed terms, to all orders in perturbation theory. Furthermore, we show that the virtuality of the produced photon does not influence the general theorem. In chapter 5, we demonstrate that perturbative QCD allows one to calculate the absolute cross section of diffractive exclusive production of photons at large Q2 at HERA, while the aligned jet model allows one to estimate the cross section for intermediate Q2~2GeV2. Furthermore, we find that the imaginary part of the amplitude for the production of real photons is larger than the imaginary part of the corresponding DIS amplitude, leading to predictions of a significant counting rate for the current generation of experiments at HERA. We also find a large azimuthal angle asymmetry in ep scattering for HERA kinematics which allows one to directly measure the real part of the DVCS amplitude and hence the nondiagonal parton distributions. In the last chapter, we propose a new methodology of gaining shape fits to nondiagonal parton distributions and, for the first time, to determine the ratio η of the real to imaginary part of the DIS amplitude. We do this by using several recent fits to F2(x,Q2) to compute the asymmetry A for the combined DVCS and Bethe- Heitler cross section. The asymmetry A, isolates the interference term of DVCS and Bethe-Heitler in the total cross section, in other words, by isolating the real part of the DVCS amplitude through this asymmetry one has access to the nondiagonal parton distributions for the first time. Comparing the predictions for A against experiment would allow one to make a prediction of the shape, though not absolute value, of nondiagonal parton distributions. In the appendix, to illustrate an application of distributional methods as discussed in chapter 4, we will show, with the aid of simple examples, how to make simple estimates of the sizes of higher-order Feynman graphs. Our methods enable appropriate values of renormalization and factorization scales to be made. They allow the diagnosis of the source of unusually large corrections that are in need of resummation.

Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point.

PubMed

Durr, S; Fodor, Z; Hoelbling, C; Katz, S D; Krieg, S; Lellouch, L; Lippert, T; Metivet, T; Portelli, A; Szabo, K K; Torrero, C; Toth, B C; Varnhorst, L

2016-04-29

We present a QCD calculation of the u, d, and s scalar quark contents of nucleons based on 47 lattice ensembles with N_{f}=2+1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f_{ud}^{N}=0.0405(40)(35) and f_{s}^{N}=0.113(45)(40), which translates into σ_{πN}=38(3)(3)  MeV, σ_{sN}=105(41)(37)  MeV, and y_{N}=0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Chiu, Jui-Yu; Jain, Ambar; Neill, Duff; Rothstein, Ira Z.

2012-05-01

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at p T much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p ⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

Advances in QCD sum-rule calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Melikhov, Dmitri

2016-01-22

We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions: (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.

Collective Perspective on Advances in Dyson—Schwinger Equation QCD

NASA Astrophysics Data System (ADS)

Adnan, Bashir; Chang, Lei; Ian, C. Cloët; Bruno, El-Bennich; Liu, Yu-Xin; Craig, D. Roberts; Peter, C. Tandy

2012-07-01

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson—Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

QCD in heavy quark production and decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiss, J.

1997-06-01

The author discusses how QCD is used to understand the physics of heavy quark production and decay dynamics. His discussion of production dynamics primarily concentrates on charm photoproduction data which are compared to perturbative QCD calculations which incorporate fragmentation effects. He begins his discussion of heavy quark decay by reviewing data on charm and beauty lifetimes. Present data on fully leptonic and semileptonic charm decay are then reviewed. Measurements of the hadronic weak current form factors are compared to the nonperturbative QCD-based predictions of Lattice Gauge Theories. He next discusses polarization phenomena present in charmed baryon decay. Heavy Quark Effectivemore » Theory predicts that the daughter baryon will recoil from the charmed parent with nearly 100% left-handed polarization, which is in excellent agreement with present data. He concludes by discussing nonleptonic charm decay which is traditionally analyzed in a factorization framework applicable to two-body and quasi-two-body nonleptonic decays. This discussion emphasizes the important role of final state interactions in influencing both the observed decay width of various two-body final states as well as modifying the interference between interfering resonance channels which contribute to specific multibody decays. 50 refs., 77 figs.« less

{lambda}{sub b}{yields}p, {lambda} transition form factors from QCD light-cone sum rules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Yuming; Lue Caidian; Shen Yuelong

2009-10-01

Light-cone sum rules for the {lambda}{sub b}{yields}p, {lambda} transition form factors are derived from the correlation functions expanded by the twist of the distribution amplitudes of the {lambda}{sub b} baryon. In terms of the {lambda}{sub b} three-quark distribution amplitude models constrained by the QCD theory, we calculate the form factors at small momentum transfers and compare the results with those estimated in the conventional light-cone sum rules (LCSR) and perturbative QCD approaches. Our results indicate that the two different versions of sum rules can lead to the consistent numbers of form factors responsible for {lambda}{sub b}{yields}p transition. The {lambda}{sub b}{yields}{lambda}more » transition form factors from LCSR with the asymptotic {lambda} baryon distribution amplitudes are found to be almost 1 order larger than those obtained in the {lambda}{sub b}-baryon LCSR, implying that the preasymptotic corrections to the baryonic distribution amplitudes are of great importance. Moreover, the SU(3) symmetry breaking effects between the form factors f{sub 1}{sup {lambda}{sub b}}{sup {yields}}{sup p} and f{sub 1}{sup {lambda}{sub b}}{sup {yields}}{sup {lambda}} are computed as 28{sub -8}{sup +14}% in the framework of {lambda}{sub b}-baryon LCSR.« less

Cyclic Mario worlds — color-decomposition for one-loop QCD

NASA Astrophysics Data System (ADS)

Kälin, Gregor

2018-04-01

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons. [Figure not available: see fulltext.

A study of energy-energy correlations and measurement of {alpha}{sub s} at the Z{sup 0} resonance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

We present the energy-energy correlation (EEC) distribution and its asymmetry (AEEC) in hadronic decays of {Zeta}{sup 0} bosons measured by the SLD at SLAC. The data are found to be in good agreement with the predictions of perturbative QCD and fragmentation Monte Carlo models of hadron production. After correction for hadronization effects the data are compared with {Omicron}({alpha}{sub s}{sup 2}) perturbative QCD calculations from various authors. Fits to the central region of the EEC yield substantially different values of the QCD scale {lambda}{sub {ovr MS}} for each of the QCD calculations. There is also a sizeable dependence of the fittedmore » {lambda}{sub {ovr MS}} value on the QCD renormalization scale factor, f. Our preliminary results are {alpha}{sub s}(M {sub Z}) = 0.121 {plus_minus} 0.002(stat.) {plus_minus} 0.004(exp.sys.) {sub {minus}0.009}{sup +0.016} (theor.) for EEC and {alpha}{sub s}(M{sub Z}) = 0.108 {plus_minus} 0.003(stat.) {plus_minus} 0.005(exp.sys.){sub {minus}0.003}{sup +0.008}(theor.) for AEEC. The largest contribution to the error arises from the theoretical uncertainty in choosing the QCD renormalization scale.« less

Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

NASA Astrophysics Data System (ADS)

Haken, Hermann

2014-12-01

After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

Here, the recent determination of themore » $$\\beta$$--function of the QCD running coupling $$\\alpha_{\\overline{MS}}(Q^2)$$ to five-loops, provides a verification of the convergence of a novel method for determining the fundamental QCD parameter $$\\Lambda_s$$ based on the Light-Front Holographic approach to nonperturbative QCD. The new 5-loop analysis, together with improvements in determining the holographic QCD nonperturbative scale parameter $$\\kappa$$ from hadronic spectroscopy, leads to an improved precision of the value of $$\\Lambda_s$$ in the $${\\overline{MS}}$$ scheme close to a factor of two; we find $$\\Lambda^{(3)}_{\\overline{MS}}=0.339\\pm0.019$$ GeV for $$n_{f}=3$$, in excellent agreement with the world average, $$\\Lambda_{\\overline{MS}}^{(3)}=0.332\\pm0.017$$ GeV. Lastly, we also discuss the constraints imposed on the scale dependence of the strong coupling in the nonperturbative domain by superconformal quantum mechanics and its holographic embedding in anti-de Sitter space.« less

Solution of the two-dimensional spectral factorization problem

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1985-01-01

An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

The QCD form factor of heavy quarks at NNLO

NASA Astrophysics Data System (ADS)

Gluza, J.; Mitov, A.; Moch, S.; Riemann, T.

2009-07-01

We present an analytical calculation of the two-loop QCD corrections to the electromagnetic form factor of heavy quarks. The two-loop contributions to the form factor are reduced to linear combinations of master integrals, which are computed through higher orders in the parameter of dimensional regularization epsilon = (4-D)/2. Our result includes all terms of order epsilon at two loops and extends the previous literature. We apply the exponentiation of the heavy-quark form factor to derive new improved three-loop expansions in the high-energy limit. We also discuss the implications for predictions of massive n-parton amplitudes based on massless results in the limit, where the quark mass is small compared to all kinematical invariants.

Study of B c  → J/ψV and {B}_{c}^{* } \\rightarrow {\\eta }_{c}V decays within the QCD factorization

NASA Astrophysics Data System (ADS)

Chang, Qin; Chen, Li-Li; Xu, Shuai

2018-07-01

In this paper, we study the non-leptonic B c → J/ψV and {B}c* \\to {η }cV (V=ρ ,{K}* ) weak decays in the framework of QCD factorization. In the evaluation, the form factors are calculated using the Bauer–Stech–Wirbel model and the light-front quark model, respectively. Besides the longitudinal amplitude, the power-suppressed transverse contributions are also evaluated at next-to-leading order. The predictions for the observables of B c → J/ψV and {B}c* \\to {η }cV decays are presented. We find that the NLO QCD contribution presents about 8% correction to the branching ratios, and the longitudinal polarization fractions of these decays are at the level of (80 ∼ 90)%. In addition, we suggest direct measurements on some useful ratios, {R}{K* /ρ }(λ =0) and {\\widetilde{R}}{K* /ρ }(λ =0), which are very suitable to test the consistence between theoretical prediction and data because their theoretical uncertainties can be well controlled.

The B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

Inclusive prompt photon production in electron-nucleus scattering at small x

NASA Astrophysics Data System (ADS)

Roy, Kaushik; Venugopalan, Raju

2018-05-01

We compute the differential cross-section for inclusive prompt photon production in deeply inelastic scattering (DIS) of electrons on nuclei at small x in the framework of the Color Glass Condensate (CGC) effective theory. The leading order (LO) computation in this framework resums leading logarithms in x as well as power corrections to all orders in Q s, A 2 / Q 2, where Q s, A ( x) is the nuclear saturation scale. This LO result is proportional to universal dipole and quadrupole Wilson line correlators in the nucleus. In the soft photon limit, the Low-Burnett-Kroll theorem allows us to recover existing results on inclusive DIS dijet production. The k ⊥ and collinearly factorized expressions for prompt photon production in DIS are also recovered in a leading twist approximation to our result. In the latter case, our result corresponds to the dominant next-to-leading order (NLO) perturbative QCD contribution at small x. We next discuss the computation of the NLO corrections to inclusive prompt photon production in the CGC framework. In particular, we emphasize the advantages for higher order computations in inclusive photon production, and for fully inclusive DIS, arising from the simple momentum space structure of the dressed quark and gluon "shock wave" propagators in the "wrong" light cone gauge A - = 0 for a nucleus moving with P N + → ∞.

Accelerating lattice QCD simulations with 2 flavors of staggered fermions on multiple GPUs using OpenACC-A first attempt

NASA Astrophysics Data System (ADS)

Gupta, Sourendu; Majumdar, Pushan

2018-07-01

We present the results of an effort to accelerate a Rational Hybrid Monte Carlo (RHMC) program for lattice quantum chromodynamics (QCD) simulation for 2 flavors of staggered fermions on multiple Kepler K20X GPUs distributed on different nodes of a Cray XC30. We do not use CUDA but adopt a higher level directive based programming approach using the OpenACC platform. The lattice QCD algorithm is known to be bandwidth bound; our timing results illustrate this clearly, and we discuss how this limits the parallelization gains. We achieve more than a factor three speed-up compared to the CPU only MPI program.

Bounds and inequalities relating h-index, g-index, e-index and generalized impact factor: an improvement over existing models.

PubMed

Abbas, Ash Mohammad

2012-01-01

In this paper, we describe some bounds and inequalities relating h-index, g-index, e-index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower bound for h-index given by Theorem 2, [formula: see text], g ≥ 1, comes out to be more accurate as compared to Schubert-Glanzel relation h is proportional to C(2/3)P(-1/3) for a proportionality constant of 1, where C is the number of citations and P is the number of papers referenced. Also, the values of h-index obtained using Theorem 2 outperform those obtained using Egghe-Liang-Rousseau power law model for the given citation data of Price Medalists. Further, we computed the values of upper bound on g-index given by Theorem 3, g ≤ (h + e), where e denotes the value of e-index. We observe that the upper bound on g-index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.

Extra dimension searches at hadron colliders to next-to-leading order-QCD

NASA Astrophysics Data System (ADS)

Kumar, M. C.; Mathews, Prakash; Ravindran, V.

2007-11-01

The quantitative impact of NLO-QCD corrections for searches of large and warped extra dimensions at hadron colliders are investigated for the Drell-Yan process. The K-factor for various observables at hadron colliders are presented. Factorisation, renormalisation scale dependence and uncertainties due to various parton distribution functions are studied. Uncertainties arising from the error on experimental data are estimated using the MRST parton distribution functions.

Relating quark confinement and chiral symmetry breaking in QCD

NASA Astrophysics Data System (ADS)

Suganuma, Hideo; Doi, Takahiro M.; Redlich, Krzysztof; Sasaki, Chihiro

2017-12-01

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various ‘confinement indicators’, such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue {λ }n such as {λ }n{Nt-1}, which behaves as a reduction factor for small {λ }n. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities, while they are essential for chiral symmetry breaking. These relations indicate that there is no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, and find similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sufian, Raza Sabbir; de Teramond, Guy F.; Brodsky, Stanley J.

We present a comprehensive analysis of the space-like nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock componentsmore » $$|{qqqq\\bar{q}}$$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$$\\%$$ in the proton and about 40$$\\%$$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. As a result, the covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$$_5$$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.« less

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

DOE PAGES

Sufian, Raza Sabbir; de Teramond, Guy F.; Brodsky, Stanley J.; ...

2017-01-10

We present a comprehensive analysis of the space-like nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock componentsmore » $$|{qqqq\\bar{q}}$$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$$\\%$$ in the proton and about 40$$\\%$$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. As a result, the covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$$_5$$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.« less

Semi-NLO production of Higgs bosons in the framework of kt-factorization using KMR unintegrated parton distributions

NASA Astrophysics Data System (ADS)

Modarres, M.; Masouminia, M. R.; Aminzadeh Nik, R.; Hosseinkhani, H.; Olanj, N.

2018-01-01

The cross-section for the production of the Standard Model Higgs boson has been calculated using a mixture of LO and NLO partonic diagrams and the unintegrated parton distribution functions (UPDF) of the Kimber-Martin-Ryskin (KMR) from the kt-factorization framework. The UPDF are prepared using the phenomenological libraries of Martin-Motylinski-Harland Lang-Thorne (MMHT 2014). The results are compared against the existing experimental data from the CMS and the ATLAS collaborations and available pQCD calculation. It is shown that, while the present calculation is in agreement with the experimental data, it is comparable with the pQCD results. It is also concluded that the K-factor approximation is comparable with the semi-NLOkt-factorization predictions.

Holographic estimate of the meson cloud contribution to nucleon axial form factor

NASA Astrophysics Data System (ADS)

Ramalho, G.

2018-04-01

We use light-front holography to estimate the valence quark and the meson cloud contributions to the nucleon axial form factor. The free couplings of the holographic model are determined by the empirical data and by the information extracted from lattice QCD. The holographic model provides a good description of the empirical data when we consider a meson cloud mixture of about 30% in the physical nucleon state. The estimate of the valence quark contribution to the nucleon axial form factor compares well with the lattice QCD data for small pion masses. Our estimate of the meson cloud contribution to the nucleon axial form factor has a slower falloff with the square momentum transfer compared to typical estimates from quark models with meson cloud dressing.

Heavy quarkonium production at collider energies: Partonic cross section and polarization

DOE PAGES

Qiu, Jian -Wei; Kang, Zhong -Bo; Ma, Yan -Qing; ...

2015-01-27

We calculate the O(α³ s) short-distance, QCD collinear-factorized coefficient functions for all partonic channels that include the production of a heavy quark pair at short distances. Thus, this provides the first power correction to the collinear-factorized inclusive hadronic production of heavy quarkonia at large transverse momentum, pT, including the full leading-order perturbative contributions to the production of heavy quark pairs in all color and spin states employed in NRQCD treatments of this process. We discuss the role of the first power correction in the production rates and the polarizations of heavy quarkonia in high-energy hadronic collisions. The consistency of QCDmore » collinear factorization and nonrelativistic QCD factorization applied to heavy quarkonium production is also discussed.« less

Quality correction factors of composite IMRT beam deliveries: theoretical considerations.

PubMed

Bouchard, Hugo

2012-11-01

In the scope of intensity modulated radiation therapy (IMRT) dosimetry using ionization chambers, quality correction factors of plan-class-specific reference (PCSR) fields are theoretically investigated. The symmetry of the problem is studied to provide recommendable criteria for composite beam deliveries where correction factors are minimal and also to establish a theoretical limit for PCSR delivery k(Q) factors. The concept of virtual symmetric collapsed (VSC) beam, being associated to a given modulated composite delivery, is defined in the scope of this investigation. Under symmetrical measurement conditions, any composite delivery has the property of having a k(Q) factor identical to its associated VSC beam. Using this concept of VSC, a fundamental property of IMRT k(Q) factors is demonstrated in the form of a theorem. The sensitivity to the conditions required by the theorem is thoroughly examined. The theorem states that if a composite modulated beam delivery produces a uniform dose distribution in a volume V(cyl) which is symmetric with the cylindrical delivery and all beams fulfills two conditions in V(cyl): (1) the dose modulation function is unchanged along the beam axis, and (2) the dose gradient in the beam direction is constant for a given lateral position; then its associated VSC beam produces no lateral dose gradient in V(cyl), no matter what beam modulation or gantry angles are being used. The examination of the conditions required by the theorem lead to the following results. The effect of the depth-dose gradient not being perfectly constant with depth on the VSC beam lateral dose gradient is found negligible. The effect of the dose modulation function being degraded with depth on the VSC beam lateral dose gradient is found to be only related to scatter and beam hardening, as the theorem holds also for diverging beams. The use of the symmetry of the problem in the present paper leads to a valuable theorem showing that k(Q) factors of composite IMRT beam deliveries are close to unity under specific conditions. The theoretical limit k(Q(pcsr),Q(msr) ) (f(pcsr),f(msr) )=1 is determined based on the property of PCSR deliveries to provide a uniform dose in the target volume. The present approach explains recent experimental observations and proposes ideal conditions for IMRT reference dosimetry. The result of this study could potentially serve as a theoretical basis for reference dosimetry of composite IMRT beam deliveries or for routine IMRT quality assurance.

Wilson loops and QCD/string scattering amplitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makeenko, Yuri; Olesen, Poul; Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen O

2009-07-15

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in N=4 super Yang-Mills theory to large N QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson-loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum-dependent) poles can arise from the kernel. We show that the kernel becomes a constant whenmore » the number of external particles becomes large. The usual Veneziano amplitude then emerges in the kinematical regime, where the Wilson loop can be reliably approximated by the area behavior. In this case, we obtain a direct duality between Wilson loops and scattering amplitudes when spatial variables and momenta are interchanged, in analogy with the N=4 super Yang-Mills theory case.« less

Dual representation of lattice QCD with worldlines and worldsheets of Abelian color fluxes

NASA Astrophysics Data System (ADS)

Marchis, Carlotta; Gattringer, Christof

2018-02-01

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caola, Fabrizio; Melnikov, Kirill; Rontsch, Raoul

We compute the next-to-leading-order QCD corrections to the production of two Z-bosons in the annihilation of two gluons at the LHC. Being enhanced by a large gluon flux, these corrections provide a distinct and, potentially, the dominant part of the N 3LO QCD contributions to Z-pair production in proton collisions. The gg → ZZ annihilation is a loop-induced process that receives the dominant contribution from loops of five light quarks, that are included in our computation in the massless approximation. We find that QCD corrections increase the gg → ZZ production cross section by O(50%–100%) depending on the values ofmore » the renormalization and factorization scales used in the leading-order computation and the collider energy. Furthermore, the large corrections to the gg → ZZ channel increase the pp → ZZ cross section by about 6% to 8%, exceeding the estimated theoretical uncertainty of the recent next-to-next-to-leading-order QCD calculation.« less

High-precision QCD at hadron colliders:electroweak gauge boson rapidity distributions at NNLO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anastasiou, C.

2004-01-05

We compute the rapidity distributions of W and Z bosons produced at the Tevatron and the LHC through next-to-next-to leading order in QCD. Our results demonstrate remarkable stability with respect to variations of the factorization and renormalization scales for all values of rapidity accessible in current and future experiments. These processes are therefore ''gold-plated'': current theoretical knowledge yields QCD predictions accurate to better than one percent. These results strengthen the proposal to use $W$ and $Z$ production to determine parton-parton luminosities and constrain parton distribution functions at the LHC. For example, LHC data should easily be able to distinguish themore » central parton distribution fit obtained by MRST from that obtained by Alekhin.« less

Energy dependence of the transverse momentum distributions of charged particles in pp collisions measured by ALICE.

PubMed

Abelev, B; Adam, J; Adamová, D; Adare, A M; Aggarwal, M M; Aglieri Rinella, G; Agnello, M; Agocs, A G; Agostinelli, A; Ahammed, Z; Ahmad, N; Ahmad Masoodi, A; Ahmed, I; Ahn, S A; Ahn, S U; Aimo, I; Aiola, S; Ajaz, M; Akindinov, A; Aleksandrov, D; Alessandro, B; Alexandre, D; Alici, A; Alkin, A; Alme, J; Alt, T; Altini, V; Altinpinar, S; Altsybeev, I; Alves Garcia Prado, C; Andrei, C; Andronic, A; Anguelov, V; Anielski, J; Antičić, T; Antinori, F; Antonioli, P; Aphecetche, L; Appelshäuser, H; Arbor, N; Arcelli, S; Armesto, N; Arnaldi, R; Aronsson, T; Arsene, I C; Arslandok, M; Augustinus, A; Averbeck, R; Awes, T C; Äystö, J; Azmi, M D; Bach, M; Badalà, A; Baek, Y W; Bailhache, R; Bala, R; Baldisseri, A; Baltasar Dos Santos Pedrosa, F; Bán, J; Baral, R C; Barbera, R; Barile, F; Barnaföldi, G G; Barnby, L S; Barret, V; Bartke, J; Basile, M; Bastid, N; Basu, S; Bathen, B; Batigne, G; Batyunya, B; Batzing, P C; Baumann, C; Bearden, I G; Beck, H; Bedda, C; Behera, N K; Belikov, I; Bellini, F; Bellwied, R; Belmont-Moreno, E; Bencedi, G; Beole, S; Berceanu, I; Bercuci, A; Berdnikov, Y; Berenyi, D; Bergognon, A A E; Bertens, R A; Berzano, D; Betev, L; Bhasin, A; Bhati, A K; Bhom, J; Bianchi, L; Bianchi, N; Bianchin, C; Bielčík, J; Bielčíková, J; Bilandzic, A; Bjelogrlic, S; Blanco, F; Blanco, F; Blau, D; Blume, C; Bock, F; Bogdanov, A; Bøggild, H; Bogolyubsky, M; Boldizsár, L; Bombara, M; Book, J; Borel, H; Borissov, A; Bornschein, J; Botje, M; Botta, E; Böttger, S; Braidot, E; Braun-Munzinger, P; Bregant, M; Breitner, T; Broker, T A; Browning, T A; Broz, M; Brun, R; Bruna, E; Bruno, G E; Budnikov, D; Buesching, H; Bufalino, S; Buncic, P; Busch, O; Buthelezi, Z; Caffarri, D; Cai, X; Caines, H; Caliva, A; Calvo Villar, E; Camerini, P; Canoa Roman, V; Cara Romeo, G; Carena, F; Carena, W; Carminati, F; Casanova Díaz, A; Castillo Castellanos, J; Casula, E A R; Catanescu, V; Cavicchioli, C; Ceballos Sanchez, C; Cepila, J; Cerello, P; Chang, B; Chapeland, S; Charvet, J L; Chattopadhyay, S; 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Differential cross sections of charged particles in inelastic pp collisions as a function of p T have been measured at [Formula: see text] at the LHC. The p T spectra are compared to NLO-pQCD calculations. Though the differential cross section for an individual [Formula: see text] cannot be described by NLO-pQCD, the relative increase of cross section with [Formula: see text] is in agreement with NLO-pQCD. Based on these measurements and observations, procedures are discussed to construct pp reference spectra at [Formula: see text] up to p T =50 GeV/ c as required for the calculation of the nuclear modification factor in nucleus-nucleus and proton-nucleus collisions.

Introduction to the physics of the total cross section at LHC. A review of data and models

NASA Astrophysics Data System (ADS)

Pancheri, Giulia; Srivastava, Yogendra N.

2017-03-01

This review describes the development of the physics of hadronic cross sections up to recent LHC results and cosmic ray experiments. We present here a comprehensive review - written with a historical perspective - about total cross sections from medium to the highest energies explored experimentally and studied through a variety of methods and theoretical models for over 60 years. We begin by recalling the analytic properties of the elastic amplitude and the theorems about the asymptotic behavior of the total cross section. A discussion of how proton-proton cross sections are extracted from cosmic rays at higher than accelerator energies and help the study of these asymptotic limits, is presented. This is followed by a description of the advent of particle colliders, through which high energies and unmatched experimental precisions have been attained. Thus the measured hadronic elastic and total cross sections have become crucial instruments to probe the so called soft part of QCD physics, where quarks and gluons are confined, and have led to test and refine Regge behavior and a number of diffractive models. As the c.m. energy increases, the total cross section also probes the transition into hard scattering describable with perturbative QCD, the so-called mini-jet region. Further tests are provided by cross section measurements of γ p, γ ^* p and γ ^* γ ^* for models based on vector meson dominance, scaling limits of virtual photons at high Q^2 and the BFKL formalism. Models interpolating from virtual to real photons are also tested.

New Methods for B Decay Constants and Form Factors from Lattice NRQCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davies, Christine; Hughes, Ciaran; Monahan, Christopher

We determine the normalisation of scalar and pseudo scalar current operators made from NonRelativistic QCD (NRQCD) b quarks and Highly Improved Staggered (HISQ) light quarks through O(αs∧QCD/mb). We use matrix elements of these operators to extract B meson decay constants and form factors and compare to those obtained using the standard vector and axial vector operators. We work on MILC second-generation 2+1+1 gluon field configurations, including those with physical light quarks in the sea. This provides a test of systematic uncertainties in these calculations and we find agreement between the results to the 2% level of uncertainty previously quoted.

New methods for B decay constants and form factors from Lattice NRQCD

NASA Astrophysics Data System (ADS)

Davies, Christine; Hughes, Ciaran; Monahan, Christopher

2018-03-01

We determine the normalisation of scalar and pseudo scalar current operators made from NonRelativistic QCD (NRQCD) b quarks and Highly Improved Staggered (HISQ) light quarks through O(αs∧QCD/mb). We use matrix elements of these operators to extract B meson decay constants and form factors and compare to those obtained using the standard vector and axial vector operators. We work on MILC second-generation 2+1+1 gluon field configurations, including those with physical light quarks in the sea. This provides a test of systematic uncertainties in these calculations and we find agreement between the results to the 2% level of uncertainty previously quoted.

Hadronic decays of B →a1(1260 )b1(1235 ) in the perturbative QCD approach

NASA Astrophysics Data System (ADS)

Jing, Hao-Yang; Liu, Xin; Xiao, Zhen-Jun

2017-12-01

We calculate the branching ratios and polarization fractions of the B →a1b1 decays in the perturbative QCD(pQCD) approach at leading order, where a1(b1) stands for the axial-vector a1(1260 )[b1(1235 )] state. By combining the phenomenological analyses with the perturbative calculations, we find the following results: (a) the large decay rates around 10-5 to 10-6 of the B →a1b1 decays dominated by the longitudinal polarization(except for the B+→b1+a10 mode) are predicted and basically consistent with those in the QCD factorization(QCDF) within errors, which are expected to be tested by the Large Hadron Collider and Belle-II experiments. The large B0→a10b10 branching ratio could provide hints to help explore the mechanism of the color-suppressed decays. (b) the rather different QCD behaviors between the a1 and b1 mesons result in the destructive(constructive) contributions in the nonfactorizable spectator diagrams with a1(b1) emission. Therefore, an interesting pattern of the branching ratios appears for the color-suppressed B0→a10a10,a10b10, and b10b10 modes in the pQCD approach, BR (B0→b10b10)>BR (B0→a10b10)≳BR (B0→a10a10), which is different from BR (B0→b10b10)˜BR (B0→a10b10)≳BR (B0→a10a10) in the QCDF and would be verified at future experiments. (c) the large naive factorization breaking effects are observed in these B →a1b1 decays. Specifically, the large nonfactorizable spectator(weak annihilation) amplitudes contribute to the B0→b1+a1-(B+→a1+b10andB+→b1+a10) mode(s), which demand confirmations via the precise measurements. Furthermore, the different phenomenologies shown among B →a1b1, B →a1a1, and B →b1b1 decays are also expected to be tested stringently, which could shed light on the typical QCD dynamics involved in these modes, even further distinguish those two popular pQCD and QCDF approaches.

Anatomy of the ρ resonance from lattice QCD at the physical point

NASA Astrophysics Data System (ADS)

Sun, Wei; Alexandru, Andrei; Chen, Ying; Draper, Terrence; Liu, Zhaofeng; Yang, Yi-Bo; χQCD Collaboration

2018-05-01

We propose a strategy to access the q\\bar{q} component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the q\\bar{q} component is derived at different valence quark masses, and shows a linear dependence on {m}{{π }}2. The slope is determined to be {c}1=0.505(3) {{{GeV}}}-1, from which the valence {{π }}{{ρ }} sigma term is extracted to be {σ }{{π }{{ρ }}}({val)}=9.82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the q\\bar{q} component is interpolated to be {m}{{ρ }}=775.9+/- 6.0+/- 1.8 {{MeV}}, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the q\\bar{q} component to be {f}{{{ρ }}-}=208.5+/- 5.5+/- 0.9 {{MeV}}, which can be compared with the experimental value {f}{{ρ }}{{\\exp }}≈ 221 {{MeV}} through the relation {f}{{ρ }}{{\\exp }}=\\sqrt{{Z}{{ρ }}}{f}{{{ρ }}+/- }, with {Z}{{ρ }}≈ 1.13 being the on-shell wavefunction renormalization of ρ owing to the {{ρ }}-{{π }} interaction. We emphasize that {m}{{ρ }} and {f}{{ρ }} of the q\\bar{q} component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom. Supported in part by the U.S. DOE Grant No. DE-SC0013065, the National Nature Science Foundation of China (NSFC) (11335001, 11575196, 11575197, 11621131001) (CRC110 by DFG and NSFC), A. A. is supported in part by the National Science Foundation CAREER (PHY-1151648) and by U.S. DOE (DE-FG02-95ER40907), Y. C. thanks the CAS Center for Excellence in Particle Physics (CCEPP) for their support, this research used the resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy (DE-AC05-00OR22725)

Limit Theorems for Dispersing Billiards with Cusps

NASA Astrophysics Data System (ADS)

Bálint, P.; Chernov, N.; Dolgopyat, D.

2011-12-01

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.

A heat kernel proof of the index theorem for deformation quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2017-11-01

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the index formula for which this formula contains no extra constant factors.

Constraints on the [Formula: see text] form factor from analyticity and unitarity.

PubMed

Ananthanarayan, B; Caprini, I; Kubis, B

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic [Formula: see text] form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the [Formula: see text] form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around [Formula: see text].

High-mass diffraction in the QCD dipole picture

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

1998-05-01

Using the QCD dipole picture of the BFKL pomeron, the cross-section of single diffractive dissociation of virtual photons at high energy and large diffractively excited masses is calculated. The calculation takes into account the full impact-parameter phase-space and thus allows to obtain an exact value of the triple BFKL Pomeron vertex. It appears large enough to compensate the perturbative 6-gluon coupling factor (α/π)3 thus suggesting a rather appreciable diffractive cross-section.

Total γ ⋆ }γ {⋆ cross section and the QCD dipole picture

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.; Florkowski, W.

1998-05-01

In the framework of the dipole picture of the BFKL pomeron we discuss two possibilities of calculating the total γ^{star}γ^{star} cross section of the virtual photons. It is shown that the dipole model reproduces the results obtained earlier from k_T-factorization up to the selection of the scale determining the length of the QCD cascade. The choice of scale turns out to be important for the numerical outcome of the calculations.

Leading isospin-breaking corrections to meson masses on the lattice

NASA Astrophysics Data System (ADS)

Giusti, Davide; Lubicz, Vittorio; Martinelli, Guido; Sanfilippo, Francesco; Simula, Silvano; Tantalo, Nazario; Tarantino, Cecilia

2018-03-01

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with Nf = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters (m⌢d-m⌢u)/ΛQCD and αem, where m⌢f is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen's theorem violation parameters εγ(MM, 2 GeV), επ0 εK0(MS, 2 GeV) for the light quark masses (m⌢d-m⌢u)(MS¯,2 GeV),(m⌢u/m⌢d)(MS¯,2 GeV); for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.

Elastic and Diffractive Scattering - Proceedings of the International Conference on Vth Blois Workshop

NASA Astrophysics Data System (ADS)

Kang, K.; Fried, H. M.; Tan, C.-I.

1994-02-01

The Table of Contents for the book is as follows: * Preface * `Overview' on Elastic Scattering and Total Cross-Sections * A Precise Measurement of the Real Part of the Elastic Scattering Amplitude at the {S bar{p}pS} * Luminosity Dependent Measurement of the p bar{p} Total Cross Section at √{s} = 541 GeV * Status of Fermilab E-710 * Luminosity-Independent Measurement of bar{p}p Elastic Scattering, Single Diffraction, Dissociation and Total Cross Section at √{s} = 546 and 1800 GeV * Phase Relations Revisited: A Challenge for SSC and LHC * Status of Near-Forward Elastic Scattering * bar{p}p Collisions at √{s} = 1.8 TeV: p, σt and B * p bar{p} Forward Scattering Parameters Results from Fermilab E760 * Photoproduction Results from H1 at HERA * Total and Jet Photoproduction Cross Sections at HERA and Fermilab * Minijet Model for High Energy γp Cross Sections * The Pomeron as Massive Gluons * Large N Theories with Glueball-like Spectra * Unitarity Relations for Gluonic Pomeron * The Donnachie-Landshoff Pomeron vs. QCD * The Odderon Intercept in Perturbative QCD * Theoret. and Phenomenol. Aspects of the Odderon * First Theorist's Gaze at HERA Data at Low xB * H1 Results for Structure Functions at Small x * Partial Photoproduction Cross Sections at √{s} ≈prox 180 GeV and First Results on F2 of the Proton from the ZEUS Experiment * Observation of a New Class of Events in Deep Inelastic Scattering * Jet Production in Muon-Proton and Muon-Nuclei Scattering at Fermilab-E665 * D0 Studies of Perturbative QCD * Large Rapidity Gaps and Single Diffraction Dissociation in High Energy pp and bar{p}p Collisions * Hadron and Reggeon Structure in High Energy Collisions * Monte Carlo Studies of Diffractive Processes in Deep Inelastic Scattering * Elastic Parton-Parton Amplitudes in Geometrical Models * Non-Perturbative QCD Calculations of High-Energy Observables * Effective Field Theory for Diffractive QCD Processes * High Energy Behavior of σtot, ρ, and B - Asymptotic Amplitude Analysis and a QCD-Inspired Analysis * Rapidity Gaps and Multiplicity Fluctuations * Branching Processes and Multi-Particle Production * High Energy Elastic Scattering and Nucleon as a Topological Soliton * The Behavior of Cross Sections at Very High Energies * The Pomeron and QCD with Many Light Quarks * Heterotic Pomeron: High Energy Hadronic Collisions in QCD * CDF Results on Electroweak Physics * DØ Results on Electroweak Physics * Search for the Top Quark and Other New Particles at DØ * Rapidity Gaps and Forward Physics at DØ * High Energy Asymptotics of Perturbative Multi-Color QCD * Rapidity Gaps in e+e- Collisions * Large Rapidity Gap, Jet Events at HERA: a PQCD Approach * High Energy Parton-Parton Elastic Scattering in QCD * Parton-Parton Elastic Scattering and Rapidity Gaps at Tevatron Energies * Hard Elastic Scattering * Hard Diffractive Processes * Three Successful Tests of Color Transparency and Nuclear Filtering * New KNO in QCD * A Chiral Condensate Search at the Tevatron * Cosmic Ray Evidences for Aligned High Energy Jets at Supertevatron Energy and Hard DDD * "New Hadronic State" Observed in Extremely High Energy Cosmic-Ray Interactions * Meson and Nucleon Form Factors in PQCD * Elastic Charge Form Factors for Pseudoscalar Mesons * The Ultimate Experiment * Search for Coherent Charm Production in 800 GeV/c Proton-Silicon Interactions * Chiral Quark Model and Hadron Scattering * Elastic Spin Experiments at UNK, Fermilab and SSC * Spin-Flip in Elastic and Diffractive Scattering * FNAL Polarized Beams and Spin Dependence at RHIC * Particle Tracking in the Close-to-Forward Region (η > 5.5) * Blois V: Experimental Summary * Blois V: Summary Talk * List of Participants

Analysis of the strong coupling form factors of ΣbNB and ΣcND in QCD sum rules

NASA Astrophysics Data System (ADS)

Yu, Guo-Liang; Wang, Zhi-Gang; Li, Zhen-Yu

2017-08-01

In this article, we study the strong interaction of the vertices Σ b NB and Σ c ND using the three-point QCD sum rules under two different Dirac structures. Considering the contributions of the vacuum condensates up to dimension 5 in the operation product expansion, the form factors of these vertices are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which gives the coupling constants. Our analysis indicates that the coupling constants for these two vertices are G ΣbNB = 0.43±0.01 GeV-1 and G ΣcND = 3.76±0.05 GeV-1. Supported by Fundamental Research Funds for the Central Universities (2016MS133)

Hard diffraction in the QCD dipole picture

NASA Astrophysics Data System (ADS)

Bialas, A.; Peschanski, R.

1996-02-01

Using the QCD dipole picture of the BFKL pomeron, the gluon contribution to the cross-section for single diffractive dissociation in deep-inelastic high-energy scattering is calculated. The resulting contribution to the proton diffractive structure function integrated over t is given in terms of relevant variables, xP, Q2, and β = {x Bj}/{x P}. It factorizes into an explicit x P-dependent Hard Pomeron flux factor and structure function. The lux factor is found to have substantial logarithmic corrections which may account for the recent measurements of the Pomeron intercept in this process. The triple Pomeron coupling is shown to be strongly enhanced by the resummation of leading logs. The obtained pattern of scaling violation at small β is similar to that for F2 at small xBj.

Circuit filling factor (CFF) for multiply tuned probes, revisited

NASA Astrophysics Data System (ADS)

Conradi, Mark S.; Zens, Albert P.

2018-07-01

The concept of circuit filling factor (CFF) is re-examined for multi-tuned, multi-inductor probe circuits. The CFF is the fraction of magnetic stored energy residing in the NMR coil. The CFF theorem states that the CFF sums to unity across all the resonant normal modes. It dictates that improved performance from a large CFF in one mode comes at the expense of CFF (and performance) at the other mode(s). Simple analytical calculations of two-mode circuits are used to demonstrate and confirm the CFF theorem. A triple-resonance circuit is calculated to show the large trade-offs involved there. The theorem can provide guidance for choosing the best circuit and relative inductances in multi-nuclear probes. The CFF is directly accessible from ball frequency-shift measurements. We give experimental measures of the CFF from ball shifts and compare to calculated values of the CFF, with good agreement.

Nucleon structure from 2+1-flavor domain-wall QCD

NASA Astrophysics Data System (ADS)

Ohta, Shigemi

2018-03-01

Nucleon-structure calculations of isovector vector-and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki × dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.

Quality correction factors of composite IMRT beam deliveries: Theoretical considerations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouchard, Hugo

2012-11-15

Purpose: In the scope of intensity modulated radiation therapy (IMRT) dosimetry using ionization chambers, quality correction factors of plan-class-specific reference (PCSR) fields are theoretically investigated. The symmetry of the problem is studied to provide recommendable criteria for composite beam deliveries where correction factors are minimal and also to establish a theoretical limit for PCSR delivery k{sub Q} factors. Methods: The concept of virtual symmetric collapsed (VSC) beam, being associated to a given modulated composite delivery, is defined in the scope of this investigation. Under symmetrical measurement conditions, any composite delivery has the property of having a k{sub Q} factor identicalmore » to its associated VSC beam. Using this concept of VSC, a fundamental property of IMRT k{sub Q} factors is demonstrated in the form of a theorem. The sensitivity to the conditions required by the theorem is thoroughly examined. Results: The theorem states that if a composite modulated beam delivery produces a uniform dose distribution in a volume V{sub cyl} which is symmetric with the cylindrical delivery and all beams fulfills two conditions in V{sub cyl}: (1) the dose modulation function is unchanged along the beam axis, and (2) the dose gradient in the beam direction is constant for a given lateral position; then its associated VSC beam produces no lateral dose gradient in V{sub cyl}, no matter what beam modulation or gantry angles are being used. The examination of the conditions required by the theorem lead to the following results. The effect of the depth-dose gradient not being perfectly constant with depth on the VSC beam lateral dose gradient is found negligible. The effect of the dose modulation function being degraded with depth on the VSC beam lateral dose gradient is found to be only related to scatter and beam hardening, as the theorem holds also for diverging beams. Conclusions: The use of the symmetry of the problem in the present paper leads to a valuable theorem showing that k{sub Q} factors of composite IMRT beam deliveries are close to unity under specific conditions. The theoretical limit k{sub Q{sub p{sub c{sub s{sub r,Q{sub m{sub s{sub r}{sup f{sub p}{sub c}{sub s}{sub r},f{sub m}{sub s}{sub r}}}}}}}}}=1 is determined based on the property of PCSR deliveries to provide a uniform dose in the target volume. The present approach explains recent experimental observations and proposes ideal conditions for IMRT reference dosimetry. The result of this study could potentially serve as a theoretical basis for reference dosimetry of composite IMRT beam deliveries or for routine IMRT quality assurance.« less

Nonleptonic decays of B →(f1(1285 ),f1(1420 ))V in the perturbative QCD approach

NASA Astrophysics Data System (ADS)

Liu, Xin; Xiao, Zhen-Jun; Zou, Zhi-Tian

2016-12-01

We investigate the branching ratios, the polarization fractions, the direct C P -violating asymmetries, and the relative phases in 20 nonleptonic decay modes of B →f1V within the framework of the perturbative QCD approach at leading order with f1 including two 3P1-axial-vector states f1(1285 ) and f1(1420 ) . Here, B denotes B+, B0, and Bs0 mesons and V stands for the lightest vector mesons ρ , K*, ω , and ϕ , respectively. The Bs0→f1V decays are studied theoretically for the first time in the literature. Together with the angle ϕf1≈(24-2.7+3.2)∘ extracted from the measurement through Bd /s→J /ψ f1(1285 ) modes for the f1(1285 )-f1(1420 ) mixing system, it is of great interest to find phenomenologically some modes such as the tree-dominated B+→f1ρ+ and the penguin-dominated B+,0→f1K*+,0 , Bs0→f1ϕ with large branching ratios around O (10-6) or even O (10-5), which are expected to be measurable at the LHCb and/or the Belle-II experiments in the near future. The good agreement (sharp contrast) of branching ratios and decay pattern for B+→f1ρ+ , B+,0→f1(1285 )K*+,0[B+,0→f1(1420 )K*+,0] decays between QCD factorization and perturbative QCD factorization predictions can help us to distinguish these two rather different factorization approaches via precision measurements, which would also be helpful for us in exploring the annihilation decay mechanism through its important roles for the considered B →f1V decays.

Multi-boson block factorization of fermions

NASA Astrophysics Data System (ADS)

Giusti, Leonardo; Cè, Marco; Schaefer, Stefan

2018-03-01

The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g - 2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the gauge field and in the auxiliary boson fields. Once combined with the corresponding factorization of the quark propagator, it paves the way for multi-level Monte Carlo integration in the presence of fermions opening new perspectives in lattice QCD. Exploratory results on the impact on the above mentioned observables will be presented.

A Note on a Sampling Theorem for Functions over GF(q)n Domain

NASA Astrophysics Data System (ADS)

Ukita, Yoshifumi; Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi

In digital signal processing, the sampling theorem states that any real valued function ƒ can be reconstructed from a sequence of values of ƒ that are discretely sampled with a frequency at least twice as high as the maximum frequency of the spectrum of ƒ. This theorem can also be applied to functions over finite domain. Then, the range of frequencies of ƒ can be expressed in more detail by using a bounded set instead of the maximum frequency. A function whose range of frequencies is confined to a bounded set is referred to as bandlimited function. And a sampling theorem for bandlimited functions over Boolean domain has been obtained. Here, it is important to obtain a sampling theorem for bandlimited functions not only over Boolean domain (GF(q)n domain) but also over GF(q)n domain, where q is a prime power and GF(q) is Galois field of order q. For example, in experimental designs, although the model can be expressed as a linear combination of the Fourier basis functions and the levels of each factor can be represented by GF(q)n, the number of levels often take a value greater than two. However, the sampling theorem for bandlimited functions over GF(q)n domain has not been obtained. On the other hand, the sampling points are closely related to the codewords of a linear code. However, the relation between the parity check matrix of a linear code and any distinct error vectors has not been obtained, although it is necessary for understanding the meaning of the sampling theorem for bandlimited functions. In this paper, we generalize the sampling theorem for bandlimited functions over Boolean domain to a sampling theorem for bandlimited functions over GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over GF(q)n domain and linear codes.

New methods for B meson decay constants and form factors from lattice NRQCD

DOE PAGES

Hughes, C.; Davies, C. T.H.; Monahan, C. J.

2018-03-20

We determine the normalization of scalar and pseudoscalar current operators made from nonrelativistic b quarks and highly improved staggered light quarks in lattice quantum chromodynamics (QCD) through O(α s) and Λ QCD/m b. We use matrix elements of these operators to extract B meson decay constants and form factors, and then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the B meson decay constants and form factors. We provide a new value for the B and B s meson decay constants from lattice QCDmore » calculations on ensembles that include u, d, s, and c quarks in the sea and those that have the u/d quark mass going down to its physical value. Our results are f B=0.196(6) GeV, f Bs=0.236(7) GeV, and f Bs/f B=1.207(7), agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of f B=0.190(4) GeV, f Bs=0.229(5) GeV, and f Bs/f B=1.206(5).« less

New methods for B meson decay constants and form factors from lattice NRQCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hughes, C.; Davies, C. T.H.; Monahan, C. J.

We determine the normalization of scalar and pseudoscalar current operators made from nonrelativistic b quarks and highly improved staggered light quarks in lattice quantum chromodynamics (QCD) through O(α s) and Λ QCD/m b. We use matrix elements of these operators to extract B meson decay constants and form factors, and then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the B meson decay constants and form factors. We provide a new value for the B and B s meson decay constants from lattice QCDmore » calculations on ensembles that include u, d, s, and c quarks in the sea and those that have the u/d quark mass going down to its physical value. Our results are f B=0.196(6) GeV, f Bs=0.236(7) GeV, and f Bs/f B=1.207(7), agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of f B=0.190(4) GeV, f Bs=0.229(5) GeV, and f Bs/f B=1.206(5).« less

Perturbative corrections to B → D form factors in QCD

NASA Astrophysics Data System (ADS)

Wang, Yu-Ming; Wei, Yan-Bing; Shen, Yue-Long; Lü, Cai-Dian

2017-06-01

We compute perturbative QCD corrections to B → D form factors at leading power in Λ/ m b , at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to- B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme {m}_c˜ O(√{Λ {m}_b}) . The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale m c , compared to the counterparts entering the factorization formula of the vacuum-to- B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors f BD +,0 ( q 2) are explored by investigating the (differential) branching fractions and the R( D) ratio of B → Dℓν and by determining the CKM matrix element |V cb | from the total decay rate of B → Dμν μ .

Two-photon decay of the neutral pion in lattice QCD.

PubMed

Feng, Xu; Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Kaneko, Takashi; Noaki, Jun-Ichi; Shintani, Eigo

2012-11-02

We perform a nonperturbative calculation of the π(0) → γγ transition form factor and the associated decay width using lattice QCD. The amplitude for a two-photon final state, which is not an eigenstate of QCD, is extracted through a Euclidean time integral of the relevant three-point function. We utilize the all-to-all quark propagator technique to carry out this integration as well as to include the disconnected quark diagram contributions. The overlap fermion formulation is employed on the lattice to ensure exact chiral symmetry on the lattice. After examining various sources of systematic effects, except for a possible discretization effect, we obtain Γπ(0) → γγ = 7.83(31)(49) eV for the pion decay width, where the first error is statistical and the second is our estimate of the systematic error.

Virtual photon impact factors with exact gluon kinematics

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-06-01

An explicit analytic formula for the transverse and longitudinal impact factors ST, L( N, γ) of the photon using kT factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

J. J. Sakurai Prize for Theoretical Particle Physics Talk: Hard scattering factorization in QCD

NASA Astrophysics Data System (ADS)

Collins, John

2009-05-01

Many important cross sections in high-energy collisions are analyzed using factorization properties. I review the nature of factorization, how it arose from the parton model, and current issues in its development. This talk will be coordinated with the one by Soper.

Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.

2012-02-16

Light-Front Holography is one of the most remarkable features of the AdS/CFT correspondence. In spite of its present limitations it provides important physical insights into the nonperturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z inmore » AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound-state wavefunctions, and thus the fall-off as a function of the invariant mass of the constituents. The soft-wall holographic model modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics - a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions {Psi}{sub n/H} (x{sub i}, k{sub {perpendicular}i}, {lambda}{sub i}) which describe the hadron's momentum and spin distributions needed to compute the direct measures of hadron structure at the quark and gluon level, such as elastic and transition form factors, distribution amplitudes, structure functions, generalized parton distributions and transverse momentum distributions. The effective confining potential also creates quark-antiquark pairs from the amplitude q {yields} q{bar q}q. Thus in holographic QCD higher Fock states can have any number of extra q{bar q} pairs. We discuss the relevance of higher Fock-states for describing the detailed structure of space and time-like form factors. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also obtained.« less

Standard model predictions for B→Kℓ(+)ℓ- with form factors from lattice QCD.

PubMed

Bouchard, Chris; Lepage, G Peter; Monahan, Christopher; Na, Heechang; Shigemitsu, Junko

2013-10-18

We calculate, for the first time using unquenched lattice QCD form factors, the standard model differential branching fractions dB/dq2(B→Kℓ(+)ℓ(-)) for ℓ=e, μ, τ and compare with experimental measurements by Belle, BABAR, CDF, and LHCb. We report on B(B→Kℓ(+)ℓ(-)) in q2 bins used by experiment and predict B(B→Kτ(+)τ(-))=(1.41±0.15)×10(-7). We also calculate the ratio of branching fractions R(e)(μ)=1.00029(69) and predict R(ℓ)(τ)=1.176(40), for ℓ=e, μ. Finally, we calculate the "flat term" in the angular distribution of the differential decay rate F(H)(e,μ,τ) in experimentally motivated q2 bins.

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD

DOE PAGES

Blum, Thomas; Chowdhury, Saumitra; Hayakawa, Masashi; ...

2015-01-07

The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.

Higgs boson production via vector-boson fusion at next-to-next-to-leading order in QCD.

PubMed

Bolzoni, Paolo; Maltoni, Fabio; Moch, Sven-Olaf; Zaro, Marco

2010-07-02

We present the total cross sections at next-to-next-to-leading order in the strong coupling for Higgs boson production via weak-boson fusion. Our results are obtained via the structure function approach, which builds upon the approximate, though very accurate, factorization of the QCD corrections between the two quark lines. The theoretical uncertainty on the total cross sections at the LHC from higher order corrections and the parton distribution uncertainties are estimated at the 2% level each for a wide range of Higgs boson masses.

The order of the quantum chromodynamics transition predicted by the standard model of particle physics.

PubMed

Aoki, Y; Endrodi, G; Fodor, Z; Katz, S D; Szabó, K K

2006-10-12

Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.

AdS/QCD and Light Front Holography: A New Approximation to QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; de Teramond, Guy

2010-02-15

The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give themore » hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n+L+S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.« less

The gluon structure of hadrons and nuclei from lattice QCD

NASA Astrophysics Data System (ADS)

Shanahan, Phiala

2018-03-01

I discuss recent lattice QCD studies of the gluon structure of hadrons and light nuclei. After very briefly highlighting new determinations of the gluon contributions to the nucleon's momentum and spin, presented by several collaborations over the last year, I describe first calculations of gluon generalised form factors. The generalised transversity gluon distributions are of particular interest since they are purely gluonic; they do not mix with quark distributions at leading twist. In light nuclei they moreover provide a clean signature of non-nucleonic gluon degrees of freedom, and I present the first evidence for such effects, based on lattice QCD calculations. The planned Electron-Ion Collider, designed to access gluon structure quantities, will have the capability to test this prediction, and measure a range of gluon observables including generalised gluon distributions and transverse momentum dependent gluon distributions, within the next decade.

Light-cone distribution amplitudes of {xi} and their applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Yonglu; Huang Mingqiu

We present the light-cone distribution amplitudes of the {xi} baryons up to twist six on the basis of QCD conformal partial wave expansion to the leading order conformal spin accuracy. The nonperturbative parameters relevant to the DAs are determined in the framework of the QCD sum rule. The light-cone QCD sum rule approach is used to investigate both the electromagnetic form factors of {xi} and the exclusive semileptonic decay of {xi}{sub c} as applications. Our estimations on the magnetic moments are {mu}{sub {xi}{sup 0}}=-(1.92{+-}0.34){mu}{sub N} and {mu}{sub {xi}{sup -}}=-(1.19{+-}0.03){mu}{sub N}. The decay width of the process {xi}{sub c}{yields}{xi}e{sup +}{nu}{sub e}more » is evaluated to be {gamma}=8.73x10{sup -14} GeV, which is in accordance with the experimental measurements and other theoretical approaches.« less

Quasi-two-body decays B → Kρ → Kππ in perturbative QCD approach

NASA Astrophysics Data System (ADS)

Wang, Wen-Fei; Li, Hsiang-nan

2016-12-01

We analyze the quasi-two-body decays B → Kρ → Kππ in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the P-wave states ρ (770) and ρ‧ (1450) are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct CP asymmetries of the B → Kρ (770) , Kρ‧ (1450) → Kππ modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the P-wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the B → Kρ (770) → Kππ decays supports the PQCD factorization framework for exclusive hadronic B meson decays.

B→πll Form Factors for New Physics Searches from Lattice QCD.

PubMed

Bailey, Jon A; Bazavov, A; Bernard, C; Bouchard, C M; DeTar, C; Du, Daping; El-Khadra, A X; Freeland, E D; Gámiz, E; Gottlieb, Steven; Heller, U M; Kronfeld, A S; Laiho, J; Levkova, L; Liu, Yuzhi; Lunghi, E; Mackenzie, P B; Meurice, Y; Neil, E; Qiu, Si-Wei; Simone, J N; Sugar, R; Toussaint, D; Van de Water, R S; Zhou, Ran

2015-10-09

The rare decay B→πℓ^{+}ℓ^{-} arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B→π tensor form factor f_{T}. Together with the vector and scalar form factors f_{+} and f_{0} from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B^{+}→π^{+}μ^{+}μ^{-})=20.4(2.1)×10^{-9} in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].

$$B\\to\\pi\\ell\\ell$$ Form Factors for New-Physics Searches from Lattice QCD

DOE PAGES

Bailey, Jon A.

2015-10-07

The rare decay B→πℓ +ℓ - arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B→π tensor form factor f T. Together with the vector and scalar form factors f + and f 0 from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B +→π +μ +μ -)=20.4(2.1)×10 -9 in the standard model, whichmore » is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].« less

Lattice QCD in rotating frames.

PubMed

Yamamoto, Arata; Hirono, Yuji

2013-08-23

We formulate lattice QCD in rotating frames to study the physics of QCD matter under rotation. We construct the lattice QCD action with the rotational metric and apply it to the Monte Carlo simulation. As the first application, we calculate the angular momenta of gluons and quarks in the rotating QCD vacuum. This new framework is useful to analyze various rotation-related phenomena in QCD.

The Future of Hadrons: The Nexus of Subatomic Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quigg, Chris

2011-09-01

The author offers brief observations on matters discussed at the XIV International Conference on Hadron Spectroscopy and explore prospects for hadron physics. Quantum chromodynamics (QCD) has been validated as a new law of nature. It is internally consistent up to very high energies, and so could be a complete theory of the strong interactions. Whether QCD is the final answer for the strong interactions is a subject for continuing experimental tests, which are being extended in experimentation at the Large Hadron Collider. Beyond the comparison of perturbative calculations with experiment, it remains critically important to test the confinement hypothesis bymore » searching for free quarks, or for signatures of unconfined color. Sensitive negative searches for quarks continue to be interesting, and the definitive observation of free quarks would be revolutionary. Breakdowns of factorization would compromise the utility of perturbative QCD. Other discoveries that would require small or large revisions to QCD include the observation of new kinds of colored matter beyond quarks and gluons, the discovery that quarks are composite, or evidence that SU(3){sub c} gauge symmetry is the vestige of a larger, spontaneously broken, color symmetry. While probing our underlying theory for weakness or new openings, we have plenty to do to apply QCD to myriad experimental settings, to learn its implications for matter under unusual conditions, and to become more adept at calculating its consequences. New experimental tools provide the means for progress on a very broad front.« less

Continuous Advances in QCD 2008

NASA Astrophysics Data System (ADS)

Peloso, Marco M.

2008-12-01

1. High-order calculations in QCD and in general gauge theories. NLO evolution of color dipoles / I. Balitsky. Recent perturbative results on heavy quark decays / J. H. Piclum, M. Dowling, A. Pak. Leading and non-leading singularities in gauge theory hard scattering / G. Sterman. The space-cone gauge, Lorentz invariance and on-shell recursion for one-loop Yang-Mills amplitudes / D. Vaman, Y.-P. Yao -- 2. Heavy flavor physics. Exotic cc¯ mesons / E. Braaten. Search for new physics in B[symbol]-mixing / A. J. Lenz. Implications of D[symbol]-D[symbol] mixing for new physics / A. A. Petrov. Precise determinations of the charm quark mass / M. Steinhauser -- 3. Quark-gluon dynamics at high density and/or high temperature. Crystalline condensate in the chiral Gross-Neveu model / G. V. Dunne, G. Basar. The strong coupling constant at low and high energies / J. H. Kühn. Quarkyonic matter and the phase diagram of QCD / L. McLerran. Statistical QCD with non-positive measure / J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot. From equilibrium to transport properties of strongly correlated fermi liquids / T. Schäfer. Lessons from random matrix theory for QCD at finite density / K. Splittorff, J. J. M. Verbaarschot -- 4. Methods and models of holographic correspondence. Soft-wall dynamics in AdS/QCD / B. Batell. Holographic QCD / N. Evans, E. Threlfall. QCD glueball sum rules and vacuum topology / H. Forkel. The pion form factor in AdS/QCD / H. J. Kwee, R. F. Lebed. The fast life of holographic mesons / R. C. Myers, A. Sinha. Properties of Baryons from D-branes and instantons / S. Sugimoto. The master space of N = 1 quiver gauge theories: counting BPS operators / A. Zaffaroni. Topological field congurations. Skyrmions in theories with massless adjoint quarks / R. Auzzi. Domain walls, localization and confinement: what binds strings inside walls / S. Bolognesi. Static interactions of non-abelian vortices / M. Eto. Vortices which do not abelianize dynamically: semi-classical origin of non-abelian monopoles / K. Konishi. A generalized construction for lumps and non-abelian vortices / W. Vinci -- 6. Dynamics in supersymmetric theories. Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory / B. Basso. SO(2M) and USp(2M) (hyper)Kähler quotients and lumps / S. B. Gudnason -- 7. Other developments. Gluinos condensing at the CCNI: 4096 CPUs weigh in / J. Giedt ... [et al.]. Baryon Regge trajectories and the 1/N[symbol] expansion / J. L. Goity, N. Matagne. Infrared behavior of the fermion propagator in unquenched QED[symbol] with finite threshold effects / Y. Hoshino. Gauge fields in accelerated frames / F. Lenz. QCD at complex coupling, large order in perturbation theory and the gluon condensate / Y. Meurice. 511 KeV line and other diffuse emissions as a trace of the dark matter / A. R. Zhitnitsky -- 8. Glimpses of the conference.

Heavy quark form factors at two loops

NASA Astrophysics Data System (ADS)

Ablinger, J.; Behring, A.; Blümlein, J.; Falcioni, G.; De Freitas, A.; Marquard, P.; Rana, N.; Schneider, C.

2018-05-01

We compute the two-loop QCD corrections to the heavy quark form factors in the case of the vector, axial-vector, scalar and pseudoscalar currents up to second order in the dimensional parameter ɛ =(4 -D )/2 . These terms are required in the renormalization of the higher-order corrections to these form factors.

Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Sheng-Quan; Wu, Xing-Gang; Brodsky, Stanley J.

We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice overmore » the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.« less

Heavy quarkonium production at low P⊥ in nonrelativistic QCD with soft gluon resummation

NASA Astrophysics Data System (ADS)

Sun, Peng; Yuan, C.-P.; Yuan, Feng

2013-09-01

We extend the nonrelativistic QCD (NRQCD) prediction for the production of heavy quarkonium with low transverse momentum in hadronic collisions by taking into account effects from all-order soft gluon resummation. Following the Collins-Soper-Sterman formalism, we resum the most singular terms in the partonic subprocesses. The theoretical predictions of J/ψ and Υ productions are compared to the experimental data from the fixed target experiments (E866) and the collider experiments (RHIC, Tevatron, LHC). The associated nonperturbative Sudakov form factor for the gluon distributions is found to be different from the previous assumption of rescaling the quark form factor by the ratio of color factors. This conclusion should be further checked by future experiments on Higgs boson and/or diphoton production in pp collisions. We also comment on the implication of our results on determining the color-octet matrix elements associated with the J/ψ and Υ productions in the NRQCD factorization formalism.

CP violation in multibody B decays from QCD factorization

NASA Astrophysics Data System (ADS)

Klein, Rebecca; Mannel, Thomas; Virto, Javier; Vos, K. Keri

2017-10-01

We test a data-driven approach based on QCD factorization for charmless three-body B-decays by confronting it to measurements of CP violation in B - → π - π + π -. While some of the needed non-perturbative objects can be directly extracted from data, some others can, so far, only be modelled. Although this approach is currently model dependent, we comment on the perspectives to reduce this model dependence. While our model naturally accommodates the gross features of the Dalitz distribution, it cannot quantitatively explain the details seen in the current experimental data on local CP asymmetries. We comment on possible refinements of our simple model and conclude by briefly discussing a possible extension of the model to large invariant masses, where large local CP asymmetries have been measured.

Aspects of baryon structure in lattice QCD

NASA Astrophysics Data System (ADS)

Babich, Ronald

Despite the long success of Quantum Chromodynamics (QCD) as the theory of the strong interactions, there remains much to be understood about the structure of hadrons and the consequences of QCD in the nonperturbative regime. Lattice gauge theory, a framework nearly as old as QCD itself, makes calculations in this regime possible, starting from first principles. With advances in theoretical understanding, methods, and computer technology, the lattice has found application to an ever-widening range of problems. In this dissertation, I consider two such problems having to do with the structure of baryons. The first concerns the contribution of sea quarks, and the strange quark in particular, to form factors of the nucleon. This has been a long-standing challenge for the lattice, because such contributions involve the insertion of a current on a quark loop, demanding the full inversion of the discretized Dirac operator, conceptually a large sparse matrix. I discuss methods for addressing this challenge and present a calculation of the strange scalar form factor and the related parameter fTs. The latter is of great theoretical interest, since it enters into the cross section for the scattering of dark matter off nuclei in supersymmetric extensions of the standard model. As such, it represents a major uncertainty in the interpretation of direct detection experiments. I also present results for the strange quark contribution to the nucleon's axial and electromagnetic form factors, which are themselves the subject of active experimental programs. These calculations were performed using the Wilson fermion formulation on a 243 x 64 anisotropic lattice. In the second part of the dissertation, I turn to the valence sector and address the role of diquark correlations in the observed spectrum of hadrons and their properties. A diquark is a correlated pair of quarks, thought to play an important role in certain phenomenological models of hadrons. I present results for baryon wave functions, evaluated in both the Coulomb and Landau gauges. By comparing baryons that differ in their diquark content, I find evidence for enhanced correlation in the scalar diquark channel, as favored by QCD-inspired quark models. I also present results for diquark mass splittings, determined from diquark correlators in the Landau gauge. This second set of calculations was performed with the overlap Dirac operator on quenched gauge configurations at beta = 6.

Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

1976, 212-223. 110] M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. 1111 , A theorem on matchings in the plane, Graph Theory...in Memory of G.A. Dirac, Ann. Discrete Math . 41, North-Holland, Amsterdam, 1989, 347-354. 1121 N. Sbihi, Algorithme de recherche d’un stable de...cardinalitA maximum dans un graphe sans 6toile, Discrete Math . 29, 1980, 53-76. 1131 D. Sumner, On Tutte’s factorization theorem, Graphs and Combinatorics

B → Dℓν form factors at nonzero recoil and |V cb| from 2+1-flavor lattice QCD

DOE PAGES

Bailey, Jon A.

2015-08-10

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay B¯→Dℓν¯ at nonzero recoil. We carry out numerical simulations on 14 ensembles of gauge-field configurations generated with 2+1 flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the b and c valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate ourmore » results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parametrize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for f +(q 2) and f 0(q 2), including statistical and systematic errors, as coefficients of a series in the variable z and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, |V cb|=(39.6 ± 1.7 QCD+exp ± 0.2 QED) × 10 –3. As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. In conclusion, we use them to update our calculation of the ratio R(D) in the Standard Model, which yields R(D)=0.299(11).« less

QCD for Postgraduates (1/5)

ScienceCinema

Zanderighi, Giulia

2018-04-26

Modern QCD - Lecture 1 Starting from the QCD Lagrangian we will revisit some basic QCD concepts and derive fundamental properties like gauge invariance and isospin symmetry and will discuss the Feynman rules of the theory. We will then focus on the gauge group of QCD and derive the Casimirs CF and CA and some useful color identities.

Threshold resummation S factor in QCD: The case of unequal masses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solovtsova, O. P., E-mail: olsol@theor.jinr.r; Chernichenko, Yu. D., E-mail: chern@gstu.gomel.b

A new relativistic Coulomb-like threshold resummation S factor in quantum chromodynamics is obtained. The analysis in question is performed within the quantum-field-theory quasipotential approach formulated in the relativistic configuration representation for the case of interaction between two relativistic particles that have unequal masses.

Nonperturbative comparison of clover and highly improved staggered quarks in lattice QCD and the properties of the Φ meson

DOE PAGES

Chakraborty, Bipasha; Davies, C. T. H.; Donald, G. C.; ...

2017-10-02

Here, we compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggeredmore » $b$-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarisation. We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the $$\\phi$$ meson. Our final results for these parameters, using single-meson correlators and neglecting quark-line disconnected diagrams are: $$m_{\\phi} =$$ 1.023(5) GeV and $$f_{\\phi} = $$ 0.238(3) GeV in good agreement with experiment. These results come from calculations in the HISQ formalism using gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea with three lattice spacing values and $$m_{u/d}$$ values going down to the physical point.« less

A Proof of Factorization Theorem of Drell-Yan Process at Operator Level

NASA Astrophysics Data System (ADS)

Zhou, Gao-Liang

2016-02-01

An alternative proof of factorization theorem for Drell-Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines. Supported by the National Natural Science Foundation of China under Grant No. 11275242

On the interface between perturbative and nonperturbative QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.

2016-04-04

The QCD running couplingmore » $$\\alpha_s(Q^2)$$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $$\\alpha_s(Q^2)$$. The high-$Q^2$ dependence of the coupling $$\\alpha_s(Q^2)$$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $$\\alpha_s(Q^2)$$ then determines the scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $$Q_0$$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $$Q_0$$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $$\\bar{MS}$$, $$g_1$$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of $$\\alpha_s$$ at large distance seen in the literature can be explained by different choices of renormalization schemes. Lastly, we also provide the formulae to compute $$\\alpha_s(Q^2)$$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.« less

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

Li, Hui-Ran; Luo, Ming-Xing; Lai, Hong

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Role of QCD monopoles in jet quenching

NASA Astrophysics Data System (ADS)

Ramamurti, Adith; Shuryak, Edward

2018-01-01

QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at T Tc is responsible for the unusual kinetic properties of quark-gluon plasma. In this paper, we study the contribution of the monopoles to jet quenching phenomenon, using the Baier-Dokshitzer-Mueller-Peigne-Schiff framework and hydrodynamic backgrounds. In the lowest order for cross sections, we calculate the nuclear modification factor, RAA, and azimuthal anisotropy, v2, of jets, as well as the dijet asymmetry, Aj, and compare those to the available data. We find relatively good agreement with experiment when using realistic hydrodynamic backgrounds. In addition, we find that event-by-event fluctuations are not necessary to reproduce RAA and v2 data, but play a role in Aj. Since the monopole-induced effects are maximal at T ≈Tc, we predict that their role should be significantly larger, relative to quarks and gluons, at lower RHIC energies.

Top Quark Pair Production in Association with a Jet with Next-to-Leading-Order QCD Off-Shell Effects at the Large Hadron Collider.

PubMed

Bevilacqua, G; Hartanto, H B; Kraus, M; Worek, M

2016-02-05

We present a complete description of top quark pair production in association with a jet in the dilepton channel. Our calculation is accurate to next-to-leading order (NLO) in QCD and includes all nonresonant diagrams, interferences, and off-shell effects of the top quark. Moreover, nonresonant and off-shell effects due to the finite W gauge boson width are taken into account. This calculation constitutes the first fully realistic NLO computation for top quark pair production with a final state jet in hadronic collisions. Numerical results for differential distributions as well as total cross sections are presented for the Large Hadron Collider at 8 TeV. With our inclusive cuts, NLO predictions reduce the unphysical scale dependence by more than a factor of 3 and lower the total rate by about 13% compared to leading-order QCD predictions. In addition, the size of the top quark off-shell effects is estimated to be below 2%.

Exotic and excited-state radiative transitions in charmonium from lattice QCD

DOE PAGES

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.

2009-05-01

We compute, for the first time using lattice QCD methods, radiative transition rates involving excited charmonium states, states of high spin and exotics. Utilizing a large basis of interpolating fields we are able to project out various excited state contributions to three-point correlators computed on quenched anisotropic lattices. In the first lattice QCD calculation of the exoticmore » $$1^{-+}$$ $$\\eta_{c1}$$ radiative decay, we find a large partial width $$\\Gamma(\\eta_{c1} \\to J/\\psi \\gamma) \\sim 100 \\,\\mathrm{keV}$$. We find clear signals for electric dipole and magnetic quadrupole transition form factors in $$\\chi_{c2} \\to J/\\psi \\gamma$$, calculated for the first time in this framework, and study transitions involving excited $$\\psi$$ and $$\\chi_{c1,2}$$ states. We calculate hindered magnetic dipole transition widths without the sensitivity to assumptions made in model studies and find statistically significant signals, including a non-exotic vector hybrid candidate $Y_{\\mathrm{hyb?}} \\to \\et« less

Lattice QCD evidence that the Λ(1405) resonance is an antikaon-nucleon molecule.

PubMed

Hall, Jonathan M M; Kamleh, Waseem; Leinweber, Derek B; Menadue, Benjamin J; Owen, Benjamin J; Thomas, Anthony W; Young, Ross D

2015-04-03

For almost 50 years the structure of the Λ(1405) resonance has been a mystery. Even though it contains a heavy strange quark and has odd parity, its mass is lower than any other excited spin-1/2 baryon. Dalitz and co-workers speculated that it might be a molecular state of an antikaon bound to a nucleon. However, a standard quark-model structure is also admissible. Although the intervening years have seen considerable effort, there has been no convincing resolution. Here we present a new lattice QCD simulation showing that the strange magnetic form factor of the Λ(1405) vanishes, signaling the formation of an antikaon-nucleon molecule. Together with a Hamiltonian effective-field-theory model analysis of the lattice QCD energy levels, this strongly suggests that the structure is dominated by a bound antikaon-nucleon component. This result clarifies that not all states occurring in nature can be described within a simple quark model framework and points to the existence of exotic molecular meson-nucleon bound states.

Relativistic corrections to exclusive χc J+γ production from e+e- annihilation

NASA Astrophysics Data System (ADS)

Brambilla, Nora; Chen, Wen; Jia, Yu; Shtabovenko, Vladyslav; Vairo, Antonio

2018-05-01

We calculate in the nonrelativistic QCD (NRQCD) factorization framework all leading relativistic corrections to the exclusive production of χc J+γ in e+e- annihilation. In particular, we compute for the first time contributions induced by octet operators with a chromoelectric field. The matching coefficients multiplying production long distance matrix elements (LDMEs) are determined through perturbative matching between QCD and NRQCD at the amplitude level. Technical challenges encountered in the nonrelativistic expansion of the QCD amplitudes are discussed in detail. The main source of uncertainty comes from the not so well known LDMEs. Accounting for it, we provide the following estimates for the production cross sections at √{s }=10.6 GeV : σ (e+e-→χc 0+γ )=(1.4 ±0.3 ) fb , σ (e+e-→χc 1+γ )=(15.0 ±3.3 ) fb , and σ (e+e-→χc 2+γ )=(4.5 ±1.4 ) fb .

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

NASA Astrophysics Data System (ADS)

Feng, Feng; Jia, Yu; Sang, Wen-Long

2017-12-01

We compute the next-to-next-to-leading-order QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of nonrelativistic QCD (NRQCD) factorization for inclusive quarkonium decay process, for the first time, is verified to relative order αs2. As a by-product, the renormalization group equation of the leading NRQCD four-fermion operator O1(1S0 ) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured ηc hadronic width and, in particular, the branching fraction of ηc→γ γ . NRQCD appears to be capable of accounting for ηb hadronic decay to a satisfactory degree, and our most refined prediction is Br(ηb→γ γ )=(4.8 ±0.7 )×10-5.

Nuclear Modification of Neutral Pion Production at Low x in √s=200 GeV d+Au and p+p Collisions

NASA Astrophysics Data System (ADS)

Sedgwick, Kenneth Blair

Nuclear modification factors quantify suppression in particle production due to nuclear effects. They are defined as a ratio of invariant yields, with a numerator derived from a given species of nuclear collision and a denominator derived from a hypothetically equivalent ensemble of independent proton-proton collisions. At large momentum transfer Q 2 and low momentum fraction x, the neutral pion nuclear modification factor Rd+Au for d+Au collisions is useful for investigating initial state gluon saturation. The large initial state gluon multiplicity of the Au nucleus causes saturation effects to occur at lower energies in d+Au collisions, as compared to p+p collisions, resulting in a relative suppression. Measuring the relative suppression R d+Au can therefore test the validity of competing models describing saturation, including the framework of a color glass condensate (CGC). Measurements at low x are of particular interest because in this region linear pQCD evolution equations begin to break down. The Froissart theorem places a robust theoretical upper limit on the behavior of hadronic cross sections: a cross section can increase at most like ln2 E. Equivalently, an hadronic structure function can increase at most like ln2(1/x). Adherence to this theorem is necessary to preserve S-matrix unitarity; no physical system should exhibit behavior to the contrary. However linear evolution equations, which dictate structure function behavior, predict an unchecked growth of low-x gluons, in violation of the theorem. For this reason, it is expected that gluon saturation, via non-linear evolution, will take place at low x to steer the gluon distribution function back within the limitations of the Froissart bound. Greater suppression is expected at lower Q2; however, at low x, regions of high Q 2 are more difficult to access experimentally. Pushing out to higher Q2 is important for discriminating between competing theoretical models. In practice, regions of low x and high Q 2 translate to measurements at, respectively, high rapidity eta and high transverse momentum p⊥. The high rapidity 3.1 < eta < 3.9 Muon Piston Calorimeter (MPC) detector at PHENIX is ideally suited for measurements of neutral pion R d+Au probing regions of low x. At √s = 200 GeV, a combinatoric analysis of neutral pion decay products in the MPC can obtain measurements of Rd+Au up to a transverse momentum of p⊥ = 2 GeV/c. However, at p ⊥ greater than 2 GeV/c, photons from neutral pion decay have insufficient spatial separation to be independently resolved in the detector. In this analysis the transverse momentum range of the detector, measuring R d+Au at √s = 200 GeV, is extended to p⊥ = 3.5 GeV/c by studying photon pairs from neutral pions that resolve in the MPC as a single cluster. Increased suppression is reproduced at low p⊥, in agreement with previous data. For p⊥ > 2 GeV/c Cronin enhancement is not observed, as anticipated by the CGC framework. However, the data can not rule out the possibility that the observed suppression is the result of extreme nuclear shadowing. Also presented are invariant neutral pion yields for p+p and d+Au collisions and the invariant neutral pion cross section for p+p collisions at √s = 200 GeV.

Limit Theory for Panel Data Models with Cross Sectional Dependence and Sequential Exogeneity.

PubMed

Kuersteiner, Guido M; Prucha, Ingmar R

2013-06-01

The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n . The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Hedye (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

NASA Astrophysics Data System (ADS)

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

2018-04-01

We present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2-1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

Here, we present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2–1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

The Chiral Separation Effect in quenched finite-density QCD

NASA Astrophysics Data System (ADS)

Puhr, Matthias; Buividovich, Pavel

2018-03-01

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coeffcient for the CSE in the confining and deconfining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coeffcient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

DOE PAGES

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

2018-04-23

Here, we present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2–1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Counting the number of Feynman graphs in QCD

NASA Astrophysics Data System (ADS)

Kaneko, T.

2018-05-01

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

Importance of proper renormalization scale-setting for QCD testing at colliders

DOE PAGES

Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.

2015-12-22

A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.« less

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Zhu-Fang, E-mail: phycui@nju.edu.cn; State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190; Hou, Feng-Yao

2015-07-15

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.

Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities.

PubMed

Kaehler, G; Wagner, A J

2013-06-01

Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all k, which was done only for k=0 in previous derivations. The consistent derivation requires, in principle, locally velocity-dependent multirelaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.

An overview of transverse momentum dependent factorization and evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rogers, Ted C.

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.

An overview of transverse-momentum-dependent factorization and evolution

NASA Astrophysics Data System (ADS)

Rogers, T. C.

2016-06-01

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. I summarize basic results while attempting to trace their development over that past several decades.

An overview of transverse momentum dependent factorization and evolution

DOE PAGES

Rogers, Ted C.

2016-06-17

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.

QCD In Extreme Conditions

NASA Astrophysics Data System (ADS)

Wilczek, Frank

Introduction Symmetry and the Phenomena of QCD Apparent and Actual Symmetries Asymptotic Freedom Confinement Chiral Symmetry Breaking Chiral Anomalies and Instantons High Temperature QCD: Asymptotic Properties Significance of High Temperature QCD Numerical Indications for Quasi-Free Behavior Ideas About Quark-Gluon Plasma Screening Versus Confinement Models of Chiral Symmetry Breaking More Refined Numerical Experiments High-Temperature QCD: Phase Transitions Yoga of Phase Transitions and Order Parameters Application to Glue Theories Application to Chiral Transitions Close Up on Two Flavors A Genuine Critical Point! (?) High-Density QCD: Methods Hopes, Doubts, and Fruition Another Renormalization Group Pairing Theory Taming the Magnetic Singularity High-Density QCD: Color-Flavor Locking and Quark-Hadron Continuity Gauge Symmetry (Non)Breaking Symmetry Accounting Elementary Excitations A Modified Photon Quark-Hadron Continuity Remembrance of Things Past More Quarks Fewer Quarks and Reality

Recent development in lattice QCD studies for three-nucleon forces

NASA Astrophysics Data System (ADS)

Doi, Takumi; HAL QCD Collaboration

2014-09-01

The direct determination of nuclear forces from QCD has been one of the most desirable challenges in nuclear physics. Recently, a first-principles lattice QCD determination is becoming possible by a novel theoretical method, HAL QCD method, in which Nambu-Bethe-Salpeter (NBS) wave functions are utilized. In this talk, I will focus on the study of three-nucleon forces in HAL QCD method by presenting the recent theoretical/numerical development.

Electroexcitation of nucleon resonances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inna Aznauryan, Volker D. Burkert

2012-01-01

We review recent progress in the investigation of the electroexcitation of nucleon resonances, both in experiment and in theory. The most accurate results have been obtained for the electroexcitation amplitudes of the four lowest excited states, which have been measured in a range of Q2 up to 8 and 4.5 GeV2 for the Delta(1232)P33, N(1535)S11 and N(1440)P11, N(1520)D13, respectively. These results have been confronted with calculations based on lattice QCD, large-Nc relations, perturbative QCD (pQCD), and QCD-inspired models. The amplitudes for the Delta(1232) indicate large pion-cloud contributions at low Q2 and don't show any sign of approaching the pQCD regimemore » for Q2<7 GeV2. Measured for the first time, the electroexcitation amplitudes of the Roper resonance, N(1440)P11, provide strong evidence for this state as a predominantly radial excitation of a three-quark (3q) ground state, with additional non-3-quark contributions needed to describe the low Q2 behavior of the amplitudes. The longitudinal transition amplitude for the N(1535)S11 was determined and has become a challenge for quark models. Explanations may require large meson-cloud contributions or alternative representations of this state. The N(1520)D13 clearly shows the rapid changeover from helicity-3/2 dominance at the real photon point to helicity-1/2 dominance at Q2 > 0.5 GeV2, confirming a long-standing prediction of the constituent quark model. The interpretation of the moments of resonance transition form factors in terms of transition transverse charge distributions in infinite momentum frame is presented.« less

ηc Hadroproduction at Large Hadron Collider Challenges NRQCD Factorization

NASA Astrophysics Data System (ADS)

Butenschoen, Mathias; He, Zhi-Guo; Kniehl, Bernd A.

2017-03-01

We report on our analysis [1] of prompt ηc meson production, measured by the LHCb Collaboration at the Large Hadron Collider, within the framework of non-relativistic QCD (NRQCD) factorization up to the sub-leading order in both the QCD coupling constant αs and the relative velocity v of the bound heavy quarks. We thereby convert various sets of J/ψ and χc,J long-distance matrix elements (LDMEs), determined by different groups in J/ψ and χc,J yield and polarization fits, to ηc and hc production LDMEs making use of the NRQCD heavy quark spin symmetry. The resulting predictions for ηc hadroproduction in all cases greatly overshoot the LHCb data, while the color-singlet model contributions alone would indeed be sufficient. We investigate the consequences for the universality of the LDMEs, and show how the observed tensions remain in follow-up works by other groups.

MS overline -on-shell quark mass relation up to four loops in QCD and a general SU (N ) gauge group

NASA Astrophysics Data System (ADS)

Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias; Wellmann, David

2016-10-01

We compute the relation between heavy quark masses defined in the modified minimal subtraction and the on-shell schemes. Detailed results are presented for all coefficients of the SU (Nc) color factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Altogether there are about 380 master integrals. Some of them are computed analytically, others with high numerical precision using Mellin-Barnes representations, and the rest numerically with the help of FIESTA. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the MS ¯ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quarks. We discuss the dependence on the renormalization and factorization scale.

Double Parton Fragmentation Function and its Evolution in Quarkonium Production

NASA Astrophysics Data System (ADS)

Kang, Zhong-Bo

2014-01-01

We summarize the results of a recent study on a new perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum pT at collider energies. Such a new factorization formalism includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the mQ2/p_T^2 expansion for heavy quark mass mQ. For the NLP contribution, the so-called double parton fragmentation functions are involved, whose evolution equations have been derived. We estimate fragmentation functions in the non-relativistic QCD formalism, and found that their contribution reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization, in contrast to the single parton fragmentation function. This might shed some light on the heavy quarkonium polarization puzzle.

Diagrams for the Free Energy and Density Weight Factors of the Ising Models.

DTIC Science & Technology

1983-01-01

sum to zero . The associated R. A. Farrell, T. Morita, and P. H. E. Meijer, "Cluster Expan- also, "_ ratum: New Generating Functions and Results for the...given for the cubic lattices. We employ a theorem that states that a certain sum of diagrams is zero in order to obtain the density-dependent weight...these diagrams are given for the cubic lattices. We employ a theorem that states that a certain sum of diagrams is zero in order to obtain the density

The current matrix elements from HAL QCD method

NASA Astrophysics Data System (ADS)

Watanabe, Kai; Ishii, Noriyoshi

2018-03-01

HAL QCD method is a method to construct a potential (HAL QCD potential) that reproduces the NN scattering phase shift faithful to the QCD. The HAL QCD potential is obtained from QCD by eliminating the degrees of freedom of quarks and gluons and leaving only two particular hadrons. Therefor, in the effective quantum mechanics of two nucleons defined by HAL QCD potential, the conserved current consists not only of the nucleon current but also an extra current originating from the potential (two-body current). Though the form of the two-body current is closely related to the potential, it is not straight forward to extract the former from the latter. In this work, we derive the the current matrix element formula in the quantum mechanics defined by the HAL QCD potential. As a first step, we focus on the non-relativistic case. To give an explicit example, we consider a second quantized non-relativistic two-channel coupling model which we refer to as the original model. From the original model, the HAL QCD potential for the open channel is constructed by eliminating the closed channel in the elastic two-particle scattering region. The current matrix element formula is derived by demanding the effective quantum mechanics defined by the HAL QCD potential to respond to the external field in the same way as the original two-channel coupling model.

Disconnected-Sea Quarks Contribution to Nucleon Electromagnetic Form Factors

NASA Astrophysics Data System (ADS)

Sufian, Raza Sabbir

We present comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon electric and magnetic form factors. The lattice QCD estimates of strange quark magnetic moment GsM (0) = -0.064(14)(09) microN and the mean squared charge radius E = -0.0043(16)(14) fm2 are more precise than any existing experimental measurements and other lattice calculations. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light-sea and strange quarks contribution to the nucleon magnetic moment is -0.022(11)(09) microN and to the nucleon mean square charge radius is -0.019(05)(05) fm 2. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light-sea and strange quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of 0 ≤ Q2 ≤ 0.5 GeV2.

The static quark potential from the gauge independent Abelian decomposition

NASA Astrophysics Data System (ADS)

Cundy, Nigel; Cho, Y. M.; Lee, Weonjong; Leem, Jaehoon

2015-06-01

We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement.

Lattice analysis for the energy scale of QCD phenomena.

PubMed

Yamamoto, Arata; Suganuma, Hideo

2008-12-12

We formulate a new framework in lattice QCD to study the relevant energy scale of QCD phenomena. By considering the Fourier transformation of link variable, we can investigate the intrinsic energy scale of a physical quantity nonperturbatively. This framework is broadly available for all lattice QCD calculations. We apply this framework for the quark-antiquark potential and meson masses in quenched lattice QCD. The gluonic energy scale relevant for the confinement is found to be less than 1 GeV in the Landau or Coulomb gauge.

Strong Coupling Continuum QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pennington, M. R.

2011-05-23

The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.

Strong Coupling Continuum QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michael Pennington

2011-05-01

The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

Higgs Boson Production in Association with a Jet at Next-to-Next-to-Leading Order.

PubMed

Boughezal, Radja; Caola, Fabrizio; Melnikov, Kirill; Petriello, Frank; Schulze, Markus

2015-08-21

We present precise predictions for Higgs boson production in association with a jet. We work in the Higgs effective field theory framework and compute next-to-next-to-leading order QCD corrections to the gluon-gluon and quark-gluon channels, which is sufficient for reliable LHC phenomenology. We present fully differential results as well as total cross sections for the LHC. Our next-to-next-to-leading order predictions reduce the unphysical scale dependence by more than a factor of 2 and enhance the total rate by about twenty percent compared to next-to-leading order QCD predictions. Our results demonstrate for the first time satisfactory convergence of the perturbative series.

Limit Theory for Panel Data Models with Cross Sectional Dependence and Sequential Exogeneity

PubMed Central

Kuersteiner, Guido M.; Prucha, Ingmar R.

2013-01-01

The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Hedye (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT. PMID:23794781

The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larkoski, Andrew J.; Moult, Ian; Neill, Duff Austin

Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluonmore » expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α slog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α slog from the coefficients of the fixed order expansion.« less

QCD evolution of (un)polarized gluon TMDPDFs and the Higgs q T -distribution

NASA Astrophysics Data System (ADS)

Echevarria, Miguel G.; Kasemets, Tomas; Mulders, Piet J.; Pisano, Cristian

2015-07-01

We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them. We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy. Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unpolarized ( f {1/ g }), linearly polarized ( h {1/⊥ g }) and helicity ( g {1/L g }) gluon TMDPDFs, and show that, as expected, they are free from rapidity divergences. As a byproduct, we obtain the Wilson coefficients of the refactorization of these TMDPDFs at large transverse momentum. In particular, the coefficient of g {1/L g }, which has never been calculated before, constitutes a new and necessary ingredient for a reliable phenomenological extraction of this quantity, for instance at RHIC or the future AFTER@LHC or Electron-Ion Collider. The coefficients of f {1/ g } and h {1/⊥ g } have never been calculated in the present formalism, although they could be obtained by carefully collecting and recasting previous results in the new TMD formalism. We apply these results to analyze the contribution of linearly polarized gluons at different scales, relevant, for instance, for the inclusive production of the Higgs boson and the C-even pseudoscalar bottomonium state η b . Applying our resummation scheme we finally provide predictions for the Higgs boson q T -distribution at the LHC.

The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion

DOE PAGES

Larkoski, Andrew J.; Moult, Ian; Neill, Duff Austin

2016-11-15

Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluonmore » expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α slog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α slog from the coefficients of the fixed order expansion.« less

NLO QCD corrections to B c( B*c) production around the Z pole at an e + e - collider

NASA Astrophysics Data System (ADS)

Zheng, XuChang; Chang, ChaoHsi; Feng, TaiFu; Pan, Zan

2018-03-01

The production of B c and B*c mesons at a Z-factory (an e + e - collider operating at energies around the Z pole) is calculated up to the next-to-leading order (NLO) QCD accuracy. The results show that the dependence of the total cross sections on the renormalization scale μ is suppressed by the corrections, and the NLO corrections enhance the total cross sections of B c by 52% and of B*c by 33% when the renormalization scale is taken at μ = 2 m b . To observe the various behaviors of the production of the mesons B c and B*c, such as the differential cross section vs. the out-going angle, the forward-backward asymmetry, and the distribution vs. the energy fraction z up to NLO QCD accuracy as well as the relevant K-factor (NLO to LO) for the production, are calculated, and it is pointed out that some of the observables obtained in the present work may be used as a specific precision test of the standard model.

Chiral behavior of K →π l ν decay form factors in lattice QCD with exact chiral symmetry

NASA Astrophysics Data System (ADS)

Aoki, S.; Cossu, G.; Feng, X.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Noaki, J.; Onogi, T.; Jlqcd Collaboration

2017-08-01

We calculate the form factors of the K →π l ν semileptonic decays in three-flavor lattice QCD and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0.11 fm with four pion masses covering 290-540 MeV and a strange quark mass ms close to its physical value. By using the all-to-all quark propagator, we calculate the vector and scalar form factors with high precision. Their dependence on ms and the momentum transfer is studied by using the reweighting technique and the twisted boundary conditions for the quark fields. We compare the results for the semileptonic form factors with ChPT at next-to-next-to-leading order in detail. While many low-energy constants appear at this order, we make use of our data of the light meson electromagnetic form factors in order to control the chiral extrapolation. We determine the normalization of the form factors as f+(0 )=0.9636 (36 )(-35+57) and observe reasonable agreement of their shape with experiment.

QCD for Postgraduates (2/5)

ScienceCinema

Zanderighi, Giulia

2018-05-21

Modern QCD - Lecture 2 We will start discussing the matter content of the theory and revisit the experimental measurements that led to the discovery of quarks. We will then consider a classic QCD observable, the R-ratio, and use it to illustrate the appearance of UV divergences and the need to renormalize the coupling constant of QCD. We will then discuss asymptotic freedom and confinement. Finally, we will examine a case where soft and collinear infrared divergences appear, will discuss the soft approximation in QCD and will introduce the concept of infrared safe jets.

Nucleon-nucleon interactions via Lattice QCD: Methodology. HAL QCD approach to extract hadronic interactions in lattice QCD

NASA Astrophysics Data System (ADS)

Aoki, Sinya

2013-07-01

We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for nucleon-nucleon potentials.

Renormalization of Extended QCD2

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Yamamura, Ryo

2015-10-01

Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N_c, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region.

θ and the η ' in large N supersymmetric QCD

DOE PAGES

Dine, Michael; Draper, Patrick; Stephenson-Haskins, Laurel; ...

2017-05-22

Here, we study the large N θ dependence and the η' potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large N perturbation theory, including the presence of branches and the behavior of theories with matter (both with N f << N and N f ~ N ). But, there are also striking departures from ordinary QCD and the conventional large N description: instanton effects, when under control, are not exponentially suppressed at large N , and branched structure in supersymmetric QCD is always associatedmore » with approximate discrete symmetries. We suggest that these differences motivate further study of large N QCD on the lattice.« less

Matrix theory for baryons: an overview of holographic QCD for nuclear physics.

PubMed

Aoki, Sinya; Hashimoto, Koji; Iizuka, Norihiro

2013-10-01

We provide, for non-experts, a brief overview of holographic QCD (quantum chromodynamics) and a review of the recent proposal (Hashimoto et al 2010 (arXiv:1003.4988[hep-th])) of a matrix-like description of multi-baryon systems in holographic QCD. Based on the matrix model, we derive the baryon interaction at short distances in multi-flavor holographic QCD. We show that there is a very universal repulsive core of inter-baryon forces for a generic number of flavors. This is consistent with a recent lattice QCD analysis for Nf = 2, 3 where the repulsive core looks universal. We also provide a comparison of our results with the lattice QCD and the operator product expansion analysis.

Spin-1 Particles and Perturbative QCD

NASA Astrophysics Data System (ADS)

de Melo, J. P. B. C.; Frederico, T.; Ji, Chueng-Ryong

2018-07-01

Due to the angular condition in the light-front dynamics (LFD), the extraction of the electromagnetic form factors for spin-1 particles can be uniquely determined taking into account implicitly non-valence and/or the zero-mode contributions to the matrix elements of the electromagnetic current. No matter which matrix elements of the electromagnetic current is used to extract the electromagnetic form factors, the same unique result is obtained. As physical observables, the electromagnetic form factors obtained from matrix elements of the current in LFD must be equal to those obtained in the instant form calculations. Recently, the Babar collaboration (Phys Rev D 78:071103, 2008) has analyzed the reaction e^+ + e^-→ ρ ^+ + ρ ^- at √{s}=10.58 GeV to measure the cross section as well as the ratios of the helicity amplitudes F_{λ 'λ }. We present our recent analysis of the Babar data for the rho meson considering the angular condition in LFD to put a stringent test on the onset of asymptotic perturbative QCD and predict the energy regime where the subleading contributions are still considerable.

The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem

NASA Astrophysics Data System (ADS)

Avksentyev, E. A.

2015-11-01

The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.

Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory.

PubMed

Brandhuber, Andreas; Kostacińska, Martyna; Penante, Brenda; Travaglini, Gabriele

2017-10-20

Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF^{2}. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T_{2} in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF^{3}. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF^{3}. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T_{3}, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.

Up, down, and strange nucleon axial form factors from lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, Jeremy; Hasan, Nesreen; Meinel, Stefan

Here, we report a calculation of the nucleon axial form factorsmore » $$G_A^q(Q^2)$$ and $$G_P^q(Q^2)$$ for all three light quark flavors $$q\\in\\{u,d,s\\}$$ in the range $$0\\leq Q^2\\lesssim 1.2\\text{ GeV}^2$$ using lattice QCD. Our work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $$G_A^q(Q^2)$$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $$G_P^{u-d}(Q^2)$$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We also found that the disconnected contributions to $$G_P$$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.« less

Up, down, and strange nucleon axial form factors from lattice QCD

DOE PAGES

Green, Jeremy; Hasan, Nesreen; Meinel, Stefan; ...

2017-06-14

Here, we report a calculation of the nucleon axial form factorsmore » $$G_A^q(Q^2)$$ and $$G_P^q(Q^2)$$ for all three light quark flavors $$q\\in\\{u,d,s\\}$$ in the range $$0\\leq Q^2\\lesssim 1.2\\text{ GeV}^2$$ using lattice QCD. Our work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $$G_A^q(Q^2)$$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $$G_P^{u-d}(Q^2)$$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We also found that the disconnected contributions to $$G_P$$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.« less

Lung cancer diagnosis with quantitative DIC microscopy and support vector machine

NASA Astrophysics Data System (ADS)

Zheng, Longfei; Cai, Shuangshuang; Zeng, Bixin; Xu, Min

2017-01-01

We report the study of lung squamous cell carcinoma diagnosis using the TI-DIC microscopy and the scattering-phase theorem. The spatially resolved optical properties of tissue are computed from the 2D phase map via the scattering-phase theorem. The scattering coefficient, the reduced scattering coefficient, and the anisotropy factor are all found to increase with the grade of lung cancer. The retrieved optical parameters are shown to distinguish cancer cases from the normal cases with high accuracy. This label-free microscopic approach applicable to fresh tissues may be promising for in situ rapid cancer diagnosis.

Determination of the priority indexes for the oil refinery wastewater treatment process

NASA Astrophysics Data System (ADS)

Chesnokova, M. G.; Myshlyavtsev, A. V.; Kriga, A. S.; Shaporenko, A. P.; Markelov, V. V.

2017-08-01

The wastewater biological treatment intensity and effectiveness are influenced by many factors: temperature, pH, presence and concentration of toxic substances, the biomass concentration et al. Regulation of them allows controlling the biological treatment process. Using the Bayesian theorem the link between changes was determined and the wastewater indexes normative limits exceeding influence for activated sludge characteristics alteration probability was evaluated. The estimation of total, or aposterioric, priority index presence probability, which characterizes the wastewater treatment level, is an important way to use the Bayesian theorem in activated sludge swelling prediction at the oil refinery biological treatment unit.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Two-baryon systems from HAL QCD method and the mirage in the temporal correlation of the direct method

NASA Astrophysics Data System (ADS)

Iritani, Takumi

2018-03-01

Both direct and HAL QCD methods are currently used to study the hadron interactions in lattice QCD. In the direct method, the eigen-energy of two-particle is measured from the temporal correlation. Due to the contamination of excited states, however, the direct method suffers from the fake eigen-energy problem, which we call the "mirage problem," while the HAL QCD method can extract information from all elastic states by using the spatial correlation. In this work, we further investigate systematic uncertainties of the HAL QCD method such as the quark source operator dependence, the convergence of the derivative expansion of the non-local interaction kernel, and the single baryon saturation, which are found to be well controlled. We also confirm the consistency between the HAL QCD method and the Lüscher's finite volume formula. Based on the HAL QCD potential, we quantitatively confirm that the mirage plateau in the direct method is indeed caused by the contamination of excited states.

An Adaptive Model of Student Performance Using Inverse Bayes

ERIC Educational Resources Information Center

Lang, Charles

2014-01-01

This article proposes a coherent framework for the use of Inverse Bayesian estimation to summarize and make predictions about student behaviour in adaptive educational settings. The Inverse Bayes Filter utilizes Bayes theorem to estimate the relative impact of contextual factors and internal student factors on student performance using time series…

Nucleon QCD sum rules in the instanton medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryskin, M. G.; Drukarev, E. G., E-mail: drukarev@pnpi.spb.ru; Sadovnikova, V. A.

2015-09-15

We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alarcon Soriano, Jose Manuel; Weiss, Christian

We propose a method for calculating the nucleon form factors (FFs) ofmore » $G$-parity-even operators by combining Chiral Effective Field Theory ($$\\chi$$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $$t > 4 M_\\pi^2$$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $$\\pi\\pi \\rightarrow N\\bar N$$ partial-wave amplitudes and the timelike pion FF. $$\\chi$$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $$\\pi\\pi$$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $$\\chi$$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $$\\pi N$$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$$N_c$$ limit of QCD because the $$\\chi$$EFT includes $N$ and $$\\Delta$$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).« less

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

DOE PAGES

Alarcon Soriano, Jose Manuel; Weiss, Christian

2017-11-20

We propose a method for calculating the nucleon form factors (FFs) ofmore » $G$-parity-even operators by combining Chiral Effective Field Theory ($$\\chi$$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $$t > 4 M_\\pi^2$$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $$\\pi\\pi \\rightarrow N\\bar N$$ partial-wave amplitudes and the timelike pion FF. $$\\chi$$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $$\\pi\\pi$$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $$\\chi$$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $$\\pi N$$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$$N_c$$ limit of QCD because the $$\\chi$$EFT includes $N$ and $$\\Delta$$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).« less

A case-control study of the difficulties in daily functioning experienced by children with depressive disorder.

PubMed

Usami, Masahide; Iwadare, Yoshitaka; Watanabe, Kyota; Ushijima, Hirokage; Kodaira, Masaki; Okada, Takashi; Sasayama, Daimei; Sugiyama, Nobuhiro; Saito, Kazuhiko

2015-07-01

The parent-assessed children-with-difficulties questionnaire (Questionnaire-Children with Difficulties; QCD) is designed to evaluate a child׳s difficulties in functioning during specific periods of the day. This study aimed to use the QCD to evaluate the difficulties in daily functioning experienced by children with depressive disorders. A case-control design was used. The cases comprised 90 junior high school students with depressive disorder, whereas a community sample of 363 junior high school students was enrolled as controls. Behaviors were assessed using the QCD, Depression Self-Rating Scale (DSRS), Tokyo Autistic Behavior Scale (TABS), attention deficit hyperactivity disorder-rating scale (ADHD-RS), and Oppositional Defiant Behavior Inventory (ODBI). We then analyzed the effects of sex and diagnosis on the QCD scores as well as the correlation coefficients between the QCD and the other questionnaires. We included 90 cases (33 boys, 57 girls) with depressive disorders and 363 controls (180 boys, 183 girls). The QCD scores for the children with depressive disorders were significantly lower compared with those from the community sample (P<0.001). The morning, school-time, and night subscores of the QCD were lower for the children with both depressive disorders and truancy problems than for those with depressive disorders alone (P<0.001). Significant correlations were observed between the following: the night QCD subscore and the DSRS scores among boys, the morning QCD subscore and ADHD-RS inattention scores for all groups, and the evening QCD subscore and the TABS score. Parents reported that children with depressive disorders experienced greater difficulties in completing basic daily activities compared with community controls. These difficulties were dependent on sex, symptoms, and the time of day. The use of QCD to assess children with depressive disorders enables clinicians to clarify the time periods at which the children face difficulties. Copyright © 2015 Elsevier B.V. All rights reserved.

Measurement of the $$b \\bar{b}$$ Cross-Section and Correlations using Dimuon Events in $$p \\bar{p}$$ Collisions at $$\\sqrt{s}$$ = 1.8-TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fein, David Kevin

1996-01-01

We have measured the b-quark production cross section formore » $$\\mid y \\mid$$ < 1 using a sample of dimuon events collected with the D0 detector in $$p\\bar{p}$$ collisions at $$\\sqrt{s}$$ = 1:8 TeV at the Fermilab Tevatron. The measured b-quark cross section is consistent with $$O(\\alpha^3_s$$) QCD predictions, but lies at the upper limit of the theoretical uncertainties which is a factor of 1.5 above the mean value. A study of the difference in azimuthal angle of the two muons is in good qualitative agreement with the $$O(\\alpha^3_s$$) QCD predictions« less

Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD

NASA Astrophysics Data System (ADS)

Heitger, Jochen; Joswig, Fabian; Vladikas, Anastassios; Wittemeier, Christian

2018-03-01

We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

Non-perturbative quark mass renormalisation and running in N_{f}=3 QCD

NASA Astrophysics Data System (ADS)

Campos, I.; Fritzsch, P.; Pena, C.; Preti, D.; Ramos, A.; Vladikas, A.

2018-05-01

We determine from first principles the quark mass anomalous dimension in N_{f}=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O (a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O (a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.

The pion form factor from first principles

NASA Astrophysics Data System (ADS)

van der Heide, J.

2004-08-01

We calculate the electromagnetic form factor of the pion in quenched lattice QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is used together with the O(a) improved current. We calculate form factor for pion masses down to mπ = 380 MeV. We compare the mean square radius for the pion extracted from our form factors to the value obtained from the `Bethe Salpeter amplitude'. Using (quenched) chiral perturbation theory, we extrapolate our results towards the physical pion mass.

Radiative Transitions in Charmonium from Lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jozef Dudek; Robert Edwards; David Richards

2006-01-17

Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the {eta}{sub c}, J/{psi} and {chi}{sub c0}. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy {xi} = 3 at a{sub s} {approx} 0.1 fm we findmore » a reasonable gross spectrum and a hyperfine splitting {approx}90 MeV, which compares favorably with other improved actions. In general, after extrapolation of lattice data at non-zero Q{sup 2} to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the J/{psi} quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.« less

Refining new-physics searches in B→Dτν with lattice QCD.

PubMed

Bailey, Jon A; Bazavov, A; Bernard, C; Bouchard, C M; Detar, C; Du, Daping; El-Khadra, A X; Foley, J; Freeland, E D; Gámiz, E; Gottlieb, Steven; Heller, U M; Kim, Jongjeong; Kronfeld, A S; Laiho, J; Levkova, L; Mackenzie, P B; Meurice, Y; Neil, E T; Oktay, M B; Qiu, Si-Wei; Simone, J N; Sugar, R; Toussaint, D; Van de Water, R S; Zhou, Ran

2012-08-17

The semileptonic decay channel B→Dτν is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently, the BABAR experiment reported the first observation of the exclusive semileptonic decay B→Dτ(-)ν, finding an approximately 2σ disagreement with the standard-model prediction for the ratio R(D)=BR(B→Dτν)/BR(B→Dℓν), where ℓ = e,μ. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain R(D)=0.316(12)(7), where the errors are statistical and total systematic, respectively. This result is the first standard-model calculation of R(D) from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor f(0)(q(2)). Our determination of R(D) is approximately 1σ higher than previous estimates and, thus, reduces the tension with experiment. We also compute R(D) in models with electrically charged scalar exchange, such as the type-II two-Higgs-doublet model. Once again, our result is consistent with, but approximately 1σ higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type-II model. As a by-product of our calculation, we also present the standard-model prediction for the longitudinal-polarization ratio P(L)(D)=0.325(4)(3).

Additional strange hadrons from QCD thermodynamics and strangeness freezeout in heavy ion collisions.

PubMed

Bazavov, A; Ding, H-T; Hegde, P; Kaczmarek, O; Karsch, F; Laermann, E; Maezawa, Y; Mukherjee, Swagato; Ohno, H; Petreczky, P; Schmidt, C; Sharma, S; Soeldner, W; Wagner, M

2014-08-15

We compare lattice QCD results for appropriate combinations of net strangeness fluctuations and their correlations with net baryon number fluctuations with predictions from two hadron resonance gas (HRG) models having different strange hadron content. The conventionally used HRG model based on experimentally established strange hadrons fails to describe the lattice QCD results in the hadronic phase close to the QCD crossover. Supplementing the conventional HRG with additional, experimentally uncharted strange hadrons predicted by quark model calculations and observed in lattice QCD spectrum calculations leads to good descriptions of strange hadron thermodynamics below the QCD crossover. We show that the thermodynamic presence of these additional states gets imprinted in the yields of the ground-state strange hadrons leading to a systematic 5-8 MeV decrease of the chemical freeze-out temperatures of ground-state strange baryons.

Critical end point in the presence of a chiral chemical potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Z. -F.; Cloët, I. C.; Lu, Y.

A class of Polyakov-loop-modified Nambu-Jona-Lasinio models has been used to support a conjecture that numerical simulations of lattice-regularized QCD defined with a chiral chemical potential can provide information about the existence and location of a critical end point in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physicallymore » motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the Polyakov-loop-modified Nambu-Jona-Lasinio models and the four-fermion coupling in those models does not react strongly to changes in the mean field that is assumed to mock-up Polyakov-loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with mu(5) > 0 can shed any light on a critical end point in the regular QCD phase diagram.« less

Baryon bags in strong coupling QCD

NASA Astrophysics Data System (ADS)

Gattringer, Christof

2018-04-01

We discuss lattice QCD with one flavor of staggered fermions and show that in the path integral the baryon contributions can be fully separated from quark and diquark contributions. The baryonic degrees of freedom (d.o.f.) are independent of the gauge field, and the corresponding free fermion action describes the baryons through the joint propagation of three quarks. The nonbaryonic dynamics is described by quark and diquark terms that couple to the gauge field. When evaluating the quark and diquark contributions in the strong coupling limit, the partition function completely factorizes into baryon bags and a complementary domain. Baryon bags are regions in space-time where the dynamics is described by a single free fermion made out of three quarks propagating coherently as a baryon. Outside the baryon bags, the relevant d.o.f. are monomers and dimers for quarks and diquarks. The partition sum is a sum over all baryon bag configurations, and for each bag, a free fermion determinant appears as a weight factor.

π π → π γ * amplitude and the resonant ρ → π γ * transition from lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.

2016-06-01

We present a determination of themore » $P$-wave $$\\pi\\pi\\to\\pi\\gamma^\\star$$ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-L\\"uscher formalism. We determine the amplitude for a range of discrete values of the $$\\pi\\pi$$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $$\\rho$$ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the $$\\rho$$ pole extract the $$\\rho\\to\\gamma^\\star\\pi$$ transition form factor. This calculation, at $$m_\\pi\\approx 400$$~MeV, is the first time a form factor of a hadron resonance has been calculated within a first-principles approach to QCD.« less

Performance of the Cray T3D and Emerging Architectures on Canopy QCD Applications

NASA Astrophysics Data System (ADS)

Fischler, Mark; Uchima, Mike

1996-03-01

The Cray T3D, an MIMD system with NUMA shared memory capabilities and in principle very low communications latency, can support the Canopy framework for grid-oriented applications. CANOPY has been ported to the T3D, with the intent of making it available to a spectrum of users. The performance of the T3D running Canopy has been benchmarked on five QCD applications extensively run on ACPMAPS at Fermilab, requiring a variety of data access patterns. The net performance and scaling behavior reveals an efficiency relative to peak Gflops almost identical to that achieved on ACPMAPS. Detailed studies of the major factors impacting performance are presented. Generalizations applying this analysis to the newly emerging crop of commercial systems reveal where their limitations will lie. On these applications, efficiencies of above 25% are not to be expected; eliminating overheads due to Canopy will improve matters, but by less than a factor of two.

Performance of the Cray T3D and emerging architectures on canopy QCD applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fischler, M.; Uchima, M.

1995-11-01

The Cray T3D, an MIMD system with NUMA shared memory capabilities and in principle very low communications latency, can support the Canopy framework for grid-oriented applications. CANOPY has been ported to the T3D, with the intent of making it available to a spectrum of users. The performance of the T3D running Canopy has been benchmarked on five QCD applications extensively run on ACPMAPS at Fermilab, requiring a variety of data access patterns. The net performance and scaling behavior reveals an efficiency relative to peak Gflops almost identical to that achieved on ACPMAPS. Detailed studies of the major factors impacting performancemore » are presented. Generalizations applying this analysis to the newly emerging crop of commercial systems reveal where their limitations will lie. On these applications, efficiencies of above 25% are not to be expected; eliminating overheads due to Canopy will improve matters, but by less than a factor of two.« less

The quark condensate in multi-flavour QCD – planar equivalence confronting lattice simulations

DOE PAGES

Armoni, Adi; Shifman, Mikhail; Shore, Graham; ...

2015-02-01

Planar equivalence between the large N limits of N=1 Super Yang–Mills (SYM) theory and a variant of QCD with fermions in the antisymmetric representation is a powerful tool to obtain analytic non-perturbative results in QCD itself. In particular, it allows the quark condensate for N=3 QCD with quarks in the fundamental representation to be inferred from exact calculations of the gluino condensate in N=1 SYM. In this paper, we review and refine our earlier predictions for the quark condensate in QCD with a general number nf of flavours and confront these with lattice results.

On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

NASA Astrophysics Data System (ADS)

Fathizadeh, Farzad; Gabriel, Olivier

2016-02-01

The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge-de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

QCD tests in $$p\\bar{p}$$ collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huth, John E.; Mangano, Michelangelo L.

1993-02-01

We review the status of QCD tests in high energy p-pbar collisions. Contents: i) Introduction ii) QCD in Hadronic Collisions iii) Jet Production iv) Heavy Flavour Production v) W and Z Production vi) Direct Photons.

Experimental tests of factorization in charmless nonleptonic two-body B decays

NASA Astrophysics Data System (ADS)

Ali, A.; Kramer, G.; Lü, Cai-Dian

1998-11-01

Using a theoretical framework based on the next-to-leading-order QCD-improved effective Hamiltonian and a factorization ansatz for the hadronic matrix elements of the four-quark operators, we reassess branching fractions in two-body nonleptonic decays B-->PP,PV,VV, involving the lowest-lying light pseudoscalar (P) and vector (V) mesons in the standard model. We work out the parametric dependence of the decay rates, making use of the currently available information on the weak mixing matrix elements, form factors, decay constants, and quark masses. Using the sensitivity of the decay rates on the effective number of colors, Nc, as a criterion of theoretical predictivity, we classify all the current-current (tree) and penguin transitions in five different classes. The recently measured charmless two-body B-->PP decays (B+-->K+η', B0-->K0η', B0-->K+π-, B+-->π+K0, and charge conjugates) are dominated by the Nc-stable QCD penguin transitions (class-IV transitions) and their estimates are consistent with the data. The measured charmless B-->PV (B+-->ωK+, B+-->ωh+) and B-->VV transition (B-->φK*), on the other hand, belong to the penguin (class-V) and tree (class-III) transitions. The class-V penguin transitions are Nc sensitive and/or involve large cancellations among competing amplitudes, making their decay rates in general more difficult to predict. Some of these transitions may also receive significant contributions from annihilation and/or final state interactions. We propose a number of tests of the factorization framework in terms of the ratios of branching ratios for some selected B-->h1h2 decays involving light hadrons h1 and h2, which depend only moderately on the form factors. We also propose a set of measurements to determine the effective coefficients of the current-current and QCD penguin operators. The potential impact of B-->h1h2 decays on the CKM phenomenology is emphasized by analyzing a number of decay rates in the factorization framework.

Strangeness S =-1 hyperon-nucleon interactions: Chiral effective field theory versus lattice QCD

NASA Astrophysics Data System (ADS)

Song, Jing; Li, Kai-Wen; Geng, Li-Sheng

2018-06-01

Hyperon-nucleon interactions serve as basic inputs to studies of hypernuclear physics and dense (neutron) stars. Unfortunately, a precise understanding of these important quantities has lagged far behind that of the nucleon-nucleon interaction due to lack of high-precision experimental data. Historically, hyperon-nucleon interactions are either formulated in quark models or meson exchange models. In recent years, lattice QCD simulations and chiral effective field theory approaches start to offer new insights from first principles. In the present work, we contrast the state-of-the-art lattice QCD simulations with the latest chiral hyperon-nucleon forces and show that the leading order relativistic chiral results can already describe the lattice QCD data reasonably well. Given the fact that the lattice QCD simulations are performed with pion masses ranging from the (almost) physical point to 700 MeV, such studies provide a useful check on both the chiral effective field theory approaches as well as lattice QCD simulations. Nevertheless more precise lattice QCD simulations are eagerly needed to refine our understanding of hyperon-nucleon interactions.

Extension of the HAL QCD approach to inelastic and multi-particle scatterings in lattice QCD

NASA Astrophysics Data System (ADS)

Aoki, S.

We extend the HAL QCD approach, with which potentials between two hadrons can be obtained in QCD at energy below inelastic thresholds, to inelastic and multi-particle scatterings. We first derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles, in terms of the one-shell $T$-matrix consrainted by the unitarity of quantum field theories. We show that its asymptotic behavior contains phase shifts and mixing angles of $n$ particle scatterings. This property is one of the essential ingredients of the HAL QCD scheme to define "potential" from the NBS wave function in quantum field theories such as QCD. We next construct energy independent but non-local potentials above inelastic thresholds, in terms of these NBS wave functions. We demonstrate an existence of energy-independent coupled channel potentials with a non-relativistic approximation, where momenta of all particles are small compared with their own masses. Combining these two results, we can employ the HAL QCD approach also to investigate inelastic and multi-particle scatterings.

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

ERIC Educational Resources Information Center

Moen, David H.; Powell, John E.

2005-01-01

Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization

DTIC Science & Technology

2008-07-01

Pietsch and Grothendieck, which are regarded as basic instruments in modern functional analysis [Pis86]. • The methods for computing these... Pietsch factorization and the maxcut semi- definite program [GW95]. 1.2. Overview. We focus on the algorithmic version of the Kashin–Tzafriri theorem...will see that the desired subset is exposed by factoring the random submatrix. This factorization, which was invented by Pietsch , is regarded as a basic

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Bipasha; Davies, C. T. H.; Donald, G. C.

Here, we compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggeredmore » $b$-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarisation. We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the $$\\phi$$ meson. Our final results for these parameters, using single-meson correlators and neglecting quark-line disconnected diagrams are: $$m_{\\phi} =$$ 1.023(5) GeV and $$f_{\\phi} = $$ 0.238(3) GeV in good agreement with experiment. These results come from calculations in the HISQ formalism using gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea with three lattice spacing values and $$m_{u/d}$$ values going down to the physical point.« less

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD.

PubMed

Blum, Thomas; Chowdhury, Saumitra; Hayakawa, Masashi; Izubuchi, Taku

2015-01-09

The most compelling possibility for a new law of nature beyond the four fundamental forces comprising the standard model of high-energy physics is the discrepancy between measurements and calculations of the muon anomalous magnetic moment. Until now a key part of the calculation, the hadronic light-by-light contribution, has only been accessible from models of QCD, the quantum description of the strong force, whose accuracy at the required level may be questioned. A first principles calculation with systematically improvable errors is needed, along with the upcoming experiments, to decisively settle the matter. For the first time, the form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in such a framework, lattice QCD+QED and QED. A nonperturbative treatment of QED is used and checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed for which statistically significant signals are obtained. Initial results are promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.

Heavy quarkonia in a potential model: binding energy, decay width, and survival probability

NASA Astrophysics Data System (ADS)

Srivastava, P. K.; Chaturvedi, O. S. K.; Thakur, Lata

2018-06-01

Recently a lot of progress has been made in deriving the heavy quark potential within a QCD medium. In this article we have considered heavy quarkonium in a hot quark gluon plasma phase. The heavy-quark potential has been modeled properly for short as well as long distances. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. We have numerically solved the 1+1-dimensional Schrodinger equation for this potential and obtained the eigen wavefunction and binding energy for the 1 S and 2 S states of charmonium and bottomonium. Further, we have calculated the decay width and dissociation temperature of quarkonium states in the QCD plasma. Finally, we have used our recently proposed unified model with these new values of decay widths to calculate the survival probability of the various quarkonium states with respect to centrality at relativistic heavy ion collider and large hadron collider energies. This study provides a unified, consistent and comprehensive description of spectroscopic properties of various quarkonium states at finite temperatures along with their nuclear modification factor at different collision energies.

Resonant conversions of QCD axions into hidden axions and suppressed isocurvature perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitajima, Naoya; Takahashi, Fuminobu, E-mail: kitajima@tuhep.phys.tohoku.ac.jp, E-mail: fumi@tuhep.phys.tohoku.ac.jp

2015-01-01

We study in detail MSW-like resonant conversions of QCD axions into hidden axions, including cases where the adiabaticity condition is only marginally satisfied, and where anharmonic effects are non-negligible. When the resonant conversion is efficient, the QCD axion abundance is suppressed by the hidden and QCD axion mass ratio. We find that, when the resonant conversion is incomplete due to a weak violation of the adiabaticity, the CDM isocurvature perturbations can be significantly suppressed, while non-Gaussianity of the isocurvature perturbations generically remain unsuppressed. The isocurvature bounds on the inflation scale can therefore be relaxed by the partial resonant conversion ofmore » the QCD axions into hidden axions.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dine, Michael; Draper, Patrick; Stephenson-Haskins, Laurel

Here, we study the large N θ dependence and the η' potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large N perturbation theory, including the presence of branches and the behavior of theories with matter (both with N f << N and N f ~ N ). But, there are also striking departures from ordinary QCD and the conventional large N description: instanton effects, when under control, are not exponentially suppressed at large N , and branched structure in supersymmetric QCD is always associatedmore » with approximate discrete symmetries. We suggest that these differences motivate further study of large N QCD on the lattice.« less

Update on ɛK with lattice QCD inputs

NASA Astrophysics Data System (ADS)

Jang, Yong-Chull; Lee, Weonjong; Lee, Sunkyu; Leem, Jaehoon

2018-03-01

We report updated results for ɛK, the indirect CP violation parameter in neutral kaons, which is evaluated directly from the standard model with lattice QCD inputs. We use lattice QCD inputs to fix B\\hatk,|Vcb|,ξ0,ξ2,|Vus|, and mc(mc). Since Lattice 2016, the UTfit group has updated the Wolfenstein parameters in the angle-only-fit method, and the HFLAV group has also updated |Vcb|. Our results show that the evaluation of ɛK with exclusive |Vcb| (lattice QCD inputs) has 4.0σ tension with the experimental value, while that with inclusive |Vcb| (heavy quark expansion based on OPE and QCD sum rules) shows no tension.

Scheme Variations of the QCD Coupling and Hadronic τ Decays

NASA Astrophysics Data System (ADS)

Boito, Diogo; Jamin, Matthias; Miravitllas, Ramon

2016-10-01

The quantum chromodynamics (QCD) coupling αs is not a physical observable of the theory, since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by α^s, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling α^s is parametrized by a single parameter C , related to transformations of the QCD scale Λ . It is demonstrated that appropriate choices of C can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study e+e- scattering and decays of the τ lepton into hadrons, both being governed by the QCD Adler function.

High statistics study of in-medium S- and P-wave quarkonium states in lattice Non-relativistic QCD

NASA Astrophysics Data System (ADS)

Kim, S.; Petreczky, P.; Rothkopf, A.

2017-11-01

Many measurements of quarkonium suppression at the LHC, e.g. the nuclear modification factor RAA of J / Ψ, are well described by a multitude of different models. Thus pinpointing the underlying physics aspects is difficult and guidance based on first principles is needed. Here we present the current status of our ongoing high precision study of in-medium spectral properties of both bottomonium and charmonium based on NRQCD on the lattice. This effective field theory allows us to capture the physics of quarkonium without modeling assumptions in a thermal QCD medium. In our study a first principles and realistic description of the QCD medium is provided by state-of-the-art lattices of the HotQCD collaboration at almost physical pion mass. Our updated results corroborate a picture of sequential modification of states with respect to their vacuum binding energy. Using a novel low-gain variant of the Bayesian BR method for reconstructing spectral functions we find that remnant features of the Upsilon may survive up to T ∼ 400MeV, while the χb signal disappears around T ∼ 270MeV. The c c ‾ analysis hints at melting of χc below T ∼ 190MeV while some J / Ψ remnant feature might survive up to T ∼ 245MeV. An improved understanding of the numerical artifacts in the Bayesian approach and the availability of increased statistics have made possible a first quantitative study of the in-medium ground state masses, which tend to lower values as T increases, consistent with lattice potential based studies.

AdS/QCD and Applications of Light-Front Holography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Cao, Fu-Guang

2012-02-16

Light-Front Holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in 3 + 1 physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS5 background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spinmore » and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role. We give an overview of the light-front holographic approach to strongly coupled QCD. In particular, we study the photon-to-meson transition form factors (TFFs) F{sub M{gamma}}(Q{sup 2}) for {gamma}{gamma}* {yields} M using light-front holographic methods. The results for the TFFs for the {eta} and {eta}' mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.« less

The generalized scheme-independent Crewther relation in QCD

NASA Astrophysics Data System (ADS)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.

2017-07-01

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton-nucleon scattering times the Adler function, defined from the cross section for electron-positron annihilation into hadrons, has no pQCD radiative corrections. The ;Generalized Crewther Relation; relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd (Q) =∑i≥1 αˆg1 i (Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.

Dyonic Flux Tube Structure of Nonperturbative QCD Vacuum

NASA Astrophysics Data System (ADS)

Chandola, H. C.; Pandey, H. C.

We study the flux tube structure of the nonperturbative QCD vacuum in terms of its dyonic excitations by using an infrared effective Lagrangian and show that the dyonic condensation of QCD vacuum has a close connection with the process of color confinement. Using the fiber bundle formulation of QCD, the magnetic symmetry condition is presented in a gauge covariant form and the gauge potential has been constructed in terms of the magnetic vectors on global sections. The dynamical breaking of the magnetic symmetry has been shown to lead the dyonic condensation of QCD vacuum in the infrared energy sector. Deriving the asymptotic solutions of the field equations in the dynamically broken phase, the dyonic flux tube structure of QCD vacuum is explored which has been shown to lead the confinement parameters in terms of the vector and scalar mass modes of the condensed vacuum. Evaluating the charge quantum numbers and energy associated with the dyonic flux tube solutions, the effect of electric excitation of monopole is analyzed using the Regge slope parameter (as an input parameter) and an enhancement in the dyonic pair correlations and the confining properties of QCD vacuum in its dyonically condensed mode has been demonstrated.

Symmetric and anti-symmetric LS hyperon potentials from lattice QCD

NASA Astrophysics Data System (ADS)

Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji; Inoue, Takashi; HAL QCD Collaboration

2014-09-01

We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. This work is supported by JSPS KAKENHI Grant Number 25400244.

A Decomposition Theorem for Finite Automata.

ERIC Educational Resources Information Center

Santa Coloma, Teresa L.; Tucci, Ralph P.

1990-01-01

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

Λ b→pl⁻ν¯ l form factors from lattice QCD with static b quarks

DOE PAGES

Detmold, William; Lin, C.-J. David; Meinel, Stefan; ...

2013-07-23

We present a lattice QCD calculation of form factors for the decay Λ b→pμ⁻ν¯ μ, which is a promising channel for determining the Cabibbo-Kobayashi-Maskawa matrix element |V ub| at the Large Hadron Collider. In this initial study we work in the limit of static b quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the Λ b→pμ⁻ν¯ μ differential decaymore » rate in the range 14 GeV²≤q²≤q² max, and obtain the integral ∫ q²max 14 GeV²[dΓ/dq²]dq²/|V ub|²=15.3±4.2 ps⁻¹. Combined with future experimental data, this will give a novel determination of |V ub| with about 15% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the b quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.« less

On the two-loop virtual QCD corrections to Higgs boson pair production in the standard model

DOE PAGES

Degrassi, Giuseppe; Giardino, Pier Paolo; Gröber, Ramona

2016-07-21

Here, we compute the next-to-leading order virtual QCD corrections to Higgs-pair production via gluon fusion. We also present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top-quark mass up to and including terms of O(1/mmore » $$8\\atop{t}$$). We estimate that mass effects can reduce the hadronic cross section by at most 10 %, assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies.« less

Infrared singularities of scattering amplitudes in perturbative QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Becher, Thomas; Neubert, Matthias

2013-11-01

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficientsmore » of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.« less

Nonperturbative renormalization of the axial current in Nf=3 lattice QCD with Wilson fermions and a tree-level improved gauge action

NASA Astrophysics Data System (ADS)

Bulava, John; Della Morte, Michele; Heitger, Jochen; Wittemeier, Christian

2016-06-01

We nonperturbatively determine the renormalization factor of the axial vector current in lattice QCD with Nf=3 flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity, and it is imposed among Schrödinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of ≈0.09 fm and below. An interpolation formula for ZA(g02) , smoothly connecting the nonperturbative values to the 1-loop expression, is provided together with our final results.

Resonant π + γ → π + π 0 amplitude from Quantum Chromodynamics

DOE PAGES

Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; ...

2015-12-08

We present the first ab initio calculation of a radiative transition of a hadronic resonance within Quantum Chromodynamics (QCD). We compute the amplitude formore » $$\\pi\\pi \\to \\pi\\gamma^\\star$$, as a function of the energy of the $$\\pi\\pi$$ pair and the virtuality of the photon, in the kinematic regime where $$\\pi\\pi$$ couples strongly to the unstable $$\\rho$$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $$m_\\pi \\approx 400$$ MeV. As a result, we obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $$\\rho$$ pole and identify from its residue the $$\\rho \\to \\pi\\gamma^\\star$$ form-factor.« less

Modified QCD ghost f(T,TG) gravity

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Rani, Shamaila; Chattopadhyay, Surajit

2015-12-01

In this paper, we explore the reconstruction scenario of modified QCD ghost dark energy model and newly proposed f(T,TG) gravity in flat FRW universe. We consider the well-known assumption of scale factor, i.e., power law form. We construct the f(T,TG) model and discuss its cosmological consequences through various cosmological parameters such as equation of state parameter, squared speed of sound and ω_{DE}-ω '_{DE}. The equation of state parameter provides the quintom-like behavior of the universe. The squared speed of sound exhibits the stability of model in the later time. Also, ω_{DE}- ω '_{DE} corresponds to freezing as well as thawing regions. It is also interesting to remark here that the results of equation of state parameter and w_{DE}-w'_{DE} coincide with the observational data.

QCD on the BlueGene/L Supercomputer

NASA Astrophysics Data System (ADS)

Bhanot, G.; Chen, D.; Gara, A.; Sexton, J.; Vranas, P.

2005-03-01

In June 2004 QCD was simulated for the first time at sustained speed exceeding 1 TeraFlops in the BlueGene/L supercomputer at the IBM T.J. Watson Research Lab. The implementation and performance of QCD in the BlueGene/L is presented.

Vortical susceptibility of finite-density QCD matter

DOE PAGES

Aristova, A.; Frenklakh, D.; Gorsky, A.; ...

2016-10-07

Here, the susceptibility of finite-density QCD matter to vorticity is introduced, as an analog of magnetic susceptibility. It describes the spin polarization of quarks and antiquarks in finite-density QCD matter induced by rotation. We estimate this quantity in the chirally broken phase using the mixed gauge-gravity anomaly at finite baryon density. It is proposed that the vortical susceptibility of QCD matter is responsible for the polarization of Λ and Λ¯ hyperons observed recently in heavy ion collisions at RHIC by the STAR collaboration.

Polyakov loop modeling for hot QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukushima, Kenji; Skokov, Vladimir

Here, we review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.

Polyakov loop modeling for hot QCD

DOE PAGES

Fukushima, Kenji; Skokov, Vladimir

2017-06-19

Here, we review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.

Λc→N form factors from lattice QCD and phenomenology of Λc→n ℓ+νℓ and Λc→p μ+μ- decays

NASA Astrophysics Data System (ADS)

Meinel, Stefan

2018-02-01

A lattice QCD determination of the Λc→N vector, axial vector, and tensor form factors is reported. The calculation was performed with 2 +1 flavors of domain-wall fermions at lattice spacings of a ≈0.11 and 0.085 fm and pion masses in the range 230 MeV ≲mπ≲350 MeV . The form factors are extrapolated to the continuum limit and the physical pion mass using modified z expansions. The rates of the charged-current decays Λc→n e+νe and Λc→n μ+νμ are predicted to be (0.405 ±0.01 6stat±0.02 0syst) |Vc d|2 ps-1 and (0.396 ±0.01 6stat±0.02 0syst) |Vc d|2 ps-1 , respectively. The phenomenology of the rare charm decay Λc→p μ+μ- is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the standard model and in an illustrative new-physics scenario.

Some New/Old Approaches to QCD

DOE R&D Accomplishments Database

Gross, D. J.

1992-11-01

In this lecture I shall discuss some recent attempts to revive some old ideas to address the problem of solving QCD. I believe that it is timely to return to this problem which has been woefully neglected for the last decade. QCD is a permanent part of the theoretical landscape and eventually we will have to develop analytic tools for dealing with the theory in the infra-red. Lattice techniques are useful but they have not yet lived up to their promise. Even if one manages to derive the hadronic spectrum numerically, to an accuracy of 10% or even 1%, we will not be truly satisfied unless we have some analytic understanding of the results. Also, lattice Monte-Carlo methods can only be used to answer a small set of questions. Many issues of great conceptual and practical interest-in particular the calculation of scattering amplitudes, are thus far beyond lattice control. Any progress in controlling QCD in an explicit analytic, fashion would be of great conceptual value. It would also be of great practical aid to experimentalists, who must use rather ad-hoc and primitive models of QCD scattering amplitudes to estimate the backgrounds to interesting new physics. I will discuss an attempt to derive a string representation of QCD and a revival of the large N approach to QCD. Both of these ideas have a long history, many theorist-years have been devoted to their pursuit-so far with little success. I believe that it is time to try again. In part this is because of the progress in the last few years in string theory. Our increased understanding of string theory should make the attempt to discover a stringy representation of QCD easier, and the methods explored in matrix models might be employed to study the large N limit of QCD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anand, Sampurn; Mohanty, Subhendra; Dey, Ujjal Kumar, E-mail: sampurn@prl.res.in, E-mail: ujjal@cts.iitkgp.ernet.in, E-mail: mohanty@prl.res.in

Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ω{sub gw} of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ∼ 50% and the peak frequency of the QCD era SGW are shifted higher by ∼ 25%more » as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.« less

Scheme variations of the QCD coupling

NASA Astrophysics Data System (ADS)

Boito, Diogo; Jamin, Matthias; Miravitllas, Ramon

2017-03-01

The Quantum Chromodynamics (QCD) coupling αs is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In order to capture this dependence in a transparent way, a novel definition of the QCD coupling, denoted by â, is introduced, whose running is explicitly renormalisation scheme invariant. The remaining renormalisation scheme dependence is related to transformations of the QCD scale Λ, and can be parametrised by a single parameter C. Hence, we call â the C-scheme coupling. The dependence on C can be exploited to study and improve perturbative predictions of physical observables. This is demonstrated for the QCD Adler function and hadronic decays of the τ lepton.

Light meson gas in the QCD vacuum and oscillating universe

NASA Astrophysics Data System (ADS)

Prokhorov, George; Pasechnik, Roman

2018-01-01

We have developed a phenomenological effective quantum-field theoretical model describing the "hadron gas" of the lightest pseudoscalar mesons, scalar σ-meson and σ-vacuum, i.e. the expectation value of the σ-field, at finite temperatures. The corresponding thermodynamic approach was formulated in terms of the generating functional derived from the effective Lagrangian providing the basic thermodynamic information about the "meson plasma + QCD condensate" system. This formalism enables us to study the QCD transition from the hadron phase with direct implications for cosmological evolution. Using the hypothesis about a positively-definite QCD vacuum contribution stochastically produced in early universe, we show that the universe could undergo a series of oscillations during the QCD epoch before resuming unbounded expansion.

Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

NASA Astrophysics Data System (ADS)

Kanazawa, Takuya; Kieburg, Mario

2018-06-01

We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3D QCD as well as in 4D QCD at high temperature or in 3D QCD at a finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the ɛ regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.

QCD dipole model and k T factorization

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-01-01

It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k T factorization at the leading logarithm approximation (in - logx Bj). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

The QCD running coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

Here, we review present knowledge onmore » $$\\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\\alpha_s(Q^2)$$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $$\\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $$\\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\\alpha_s$$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less

The QCD running coupling

DOE PAGES

Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

2016-05-09

Here, we review present knowledge onmore » $$\\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\\alpha_s(Q^2)$$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $$\\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $$\\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\\alpha_s$$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less

Relating Factor Models for Longitudinal Data to Quasi-Simplex and NARMA Models

ERIC Educational Resources Information Center

Rovine, Michael J.; Molenaar, Peter C. M.

2005-01-01

In this article we show the one-factor model can be rewritten as a quasi-simplex model. Using this result along with addition theorems from time series analysis, we describe a common general model, the nonstationary autoregressive moving average (NARMA) model, that includes as a special case, any latent variable model with continuous indicators…

Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method

NASA Astrophysics Data System (ADS)

Iritani, T.; HAL QCD Collaboration

We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\\Xi\\Xi$ system at $m_\\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources. The energy shift $\\Delta E_\\mathrm{eff}(t)$ in the direct method shows the strong dependence on the choice of quark source operators, which means that the results with either (or both) source are false. The time-dependent HAL QCD method, on the other hand, gives the quark source independent $\\Xi\\Xi$ potential, thanks to the derivative expansion of the potential, which absorbs the source dependence to the next leading order correction. The HAL QCD potential predicts the absence of the bound state in the $\\Xi\\Xi$($^1$S$_0$) channel at $m_\\pi= 0.51$ GeV, which is also confirmed by the volume dependence of finite volume energy from the potential. We also demonstrate that the origin of the fake plateau in the effective energy shift $\\Delta E_\\mathrm{eff}(t)$ at $t \\sim 1$ fm can be clarified by a few low-lying eigenfunctions and eigenvalues on the finite volume derived from the HAL QCD potential, which implies that the ground state saturation of $\\Xi\\Xi$($^1$S$_0$) requires $t \\sim 10$ fm in the direct method for the smeared source on $(4.3 \\ \\mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such a problem.

The Non-Signalling theorem in generalizations of Bell's theorem

NASA Astrophysics Data System (ADS)

Walleczek, J.; Grössing, G.

2014-04-01

Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents to signal information. In other words, as a proper principle, the non-signalling theorem may only be employed as an epistemic, phenomenological, or operational principle. Critically, our argument emphasizes that the non-signalling principle must not be used as an ontic principle about physical reality as such, i.e. as a theorem about the nature of physical reality independently of epistemic agents e.g. human observers. One major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report. Otherwise, the non-signalling theorem would equal a general "no-influence" theorem. In conclusion, under the assumption that the non-signalling theorem is epistemic (i.e. "epistemic non-signalling"), the search for deterministic approaches to quantum mechanics, including NHVTs and an emergent quantum mechanics, continues to be a viable research program towards disclosing the foundations of physical reality at its smallest dimensions.

Consistency of the adiabatic theorem.

PubMed

Amin, M H S

2009-06-05

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation are discussed.

The QCD running coupling

NASA Astrophysics Data System (ADS)

Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

2016-09-01

We review the present theoretical and empirical knowledge for αs, the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of αs(Q2) on momentum transfer Q encodes the underlying dynamics of hadron physics-from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on αs(Q2) at high Q2, as predicted by perturbative QCD, and its analytic behavior at small Q2, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of αs(Q2) in the high momentum transfer domain of QCD. We review how αs is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as "Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization-scale ambiguity. We also report recent significant measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the "Principle of Maximum Conformality", which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior αs(Q2) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of αs(Q2) in order to bring better unity to the subject.

Optimal no-go theorem on hidden-variable predictions of effect expectations

NASA Astrophysics Data System (ADS)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

High-Accuracy Analysis of Compton Scattering in Chiral EFT: Proton and Neutron Polarisabilities

NASA Astrophysics Data System (ADS)

Griesshammer, Harald W.; Phillips, Daniel R.; McGovern, Judith A.

2013-10-01

Compton scattering from protons and neutrons provides important insight into the structure of the nucleon. A new extraction of the static electric and magnetic dipole polarisabilities αE 1 and βM 1 of the proton and neutron from all published elastic data below 300 MeV in Chiral Effective Field Theory shows that within the statistics-dominated errors, the proton and neutron polarisabilities are identical, i.e. no iso-spin breaking effects of the pion cloud are seen. Particular attention is paid to the precision and accuracy of each data set, and to an estimate of residual theoretical uncertainties. ChiEFT is ideal for that purpose since it provides a model-independent estimate of higher-order corrections and encodes the correct low-energy dynamics of QCD, including, for few-nucleon systems used to extract neutron polarisabilities, consistent nuclear currents, rescattering effects and wave functions. It therefore automatically respects the low-energy theorems for photon-nucleus scattering. The Δ (1232) as active degree of freedom is essential to realise the full power of the world's Compton data.Its parameters are constrained in the resonance region. A brief outlook is provided on what kind of future experiments can improve the database. Supported in part by UK STFC, DOE, NSF, and the Sino-German CRC 110.

First Renormalized Parton Distribution Functions from Lattice QCD

NASA Astrophysics Data System (ADS)

Lin, Huey-Wen; LP3 Collaboration

2017-09-01

We present the first lattice-QCD results on the nonperturbatively renormalized parton distribution functions (PDFs). Using X.D. Ji's large-momentum effective theory (LaMET) framework, lattice-QCD hadron structure calculations are able to overcome the longstanding problem of determining the Bjorken- x dependence of PDFs. This has led to numerous additional theoretical works and exciting progress. In this talk, we will address a recent development that implements a step missing from prior lattice-QCD calculations: renormalization, its effects on the nucleon matrix elements, and the resultant changes to the calculated distributions.

The CP-PACS Project and Lattice QCD Results

NASA Astrophysics Data System (ADS)

Iwasaki, Y.

The aim of the CP-PACS project was to develop a massively parallel computer for performing numerical research in computational physics with primary emphasis on lattice QCD. The CP-PACS computer with a peak speed of 614 GFLOPS with 2048 processors was completed in September 1996, and has been in full operation since October 1996. We present an overview of the CP-PACS project and describe characteristics of the CP-PACS computer. The CP-PACS has been mainly used for hadron spectroscopy studies in lattice QCD. Main results in lattice QCD simulations are given.

Using Pictures to Enhance Students' Understanding of Bayes' Theorem

ERIC Educational Resources Information Center

Trafimow, David

2011-01-01

Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.

Remarks on the Phase Transition in QCD

NASA Astrophysics Data System (ADS)

Wilczek, Frank

The significance of the question of the order of the phase transition in QCD, and recent evidence that real-world QCD is probably close to having a single second order transition as a function of temperature, is reviewed. Although this circumstance seems to remove the possibility that the QCD transition during the big bang might have had spectacular cosmological consequences, there is some good news: it allows highly non-trivial yet reliable quantitative predictions to be made for the behavior near the transition. These predictions can be tested in numerical simulations and perhaps even eventually in heavy ion collisions. The present paper is a very elementary discussion of the relevant concepts, meant to be an accessible introduction for those innocent of the renormalization group approach to critical phenomena and/or the details of QCD.

Towards understanding Regge trajectories in holographic QCD

NASA Astrophysics Data System (ADS)

Catà, Oscar

2007-05-01

We reassess a work done by Migdal on the spectrum of low-energy vector mesons in QCD in the light of the anti-de Sitter (AdS)-QCD correspondence. Recently, a tantalizing parallelism was suggested between Migdal’s work and a family of holographic duals of QCD. Despite the intriguing similarities, both approaches face a major drawback: the spectrum is in conflict with well-tested Regge scaling. However, it has recently been shown that holographic duals can be modified to accommodate Regge behavior. Therefore, it is interesting to understand whether Regge behavior can also be achieved in Migdal’s approach. In this paper we investigate this issue. We find that Migdal’s approach, which is based on a modified Padé approximant, is closely related to the issue of quark-hadron duality breakdown in QCD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dudek, Jozef

Highlights of the research include: the determination of the form of the lowest energy gluonic excitation within QCD and the spectrum of hybrid hadrons which follows; the first calculation of the spectrum of hybrid baryons within a first-principles approach to QCD; a detailed mapping out of the phase-shift of elastic ππ scattering featuring the ρ resonance at two values of the light quark mass within lattice QCD; the first (and to date, only) determinations of coupled-channel meson-meson scattering within first-principles QCD; the first (and to date, only) determinations of the radiative coupling of a resonant state, the ρ appearing inmore » πγ→ππ; the first (and to date, only) determination of the properties of the broad σ resonance in elastic ππ scattering within QCD without unjustified approximations.« less

Highlights in light-baryon spectroscopy and searches for gluonic excitations

NASA Astrophysics Data System (ADS)

Crede, Volker

2016-01-01

The spectrum of excited hadrons - mesons and baryons - serves as an excellent probe of quantum chromodynamics (QCD), the fundamental theory of the strong interaction. The strong coupling however makes QCD challenging. It confines quarks and breaks chiral symmetry, thus providing us with the world of light hadrons. Highly-excited hadronic states are sensitive to the details of quark confinement, which is only poorly understood within QCD. This is the regime of non-perturbative QCD and it is one of the key issues in hadronic physics to identify the corresponding internal degrees of freedom and how they relate to strong coupling QCD. The quark model suggests mesons are made of a constituent quark and an antiquark and baryons consist of three such quarks. QCD predicts other forms of matter. What is the role of glue? Resonances with large gluonic components are predicted as bound states by QCD. The lightest hybrid mesons with exotic quantum numbers are estimated to have masses in the range from 1 to 2 GeV/c2 and are well in reach of current experimental programs. At Jefferson Laboratory (JLab) and other facilities worldwide, the high-energy electron and photon beams present a remarkably clean probe of hadronic matter, providing an excellent microscope for examining atomic nuclei and the strong nuclear force.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

PubMed

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

calculation of B → D*lv form factor at zero recoil using the Oktay-Kronfeld action

NASA Astrophysics Data System (ADS)

Bailey, Jon A.; Bhattacharya, Tanmoy; Gupta, Rajan; Jang, Yong-Chull; Lee, Weonjong; Leem, Jaehoon; Park, Sungwoo; Yoon, Boram

2018-03-01

We present the first preliminary results for the semileptonic form factor hA1 (w = 1)/ρAj at zero recoil for the B → D*lv decay using lattice QCD with four flavors of sea quarks. We use the HISQ staggered action for the light valence and sea quarks (the MILC HISQ configurations), and the Oktay-Kronfeld (OK) action for the heavy valence quarks.

Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Hong -Hao; Wu, Xing -Gang; Ma, Yang

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach tomore » all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R e+e– at four-loop order in pQCD.« less

The generalized scheme-independent Crewther relation in QCD

DOE PAGES

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; ...

2017-05-10

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

The generalized scheme-independent Crewther relation in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

Hadronic and nuclear interactions in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

Despite the evidence that QCD - or something close to it - gives a correct description of the structure of hadrons and their interactions, it seems paradoxical that the theory has thus far had very little impact in nuclear physics. One reason for this is that the application of QCD to distances larger than 1 fm involves coherent, non-perturbative dynamics which is beyond present calculational techniques. For example, in QCD the nuclear force can evidently be ascribed to quark interchange and gluon exchange processes. These, however, are as complicated to analyze from a fundamental point of view as is themore » analogous covalent bond in molecular physics. Since a detailed description of quark-quark interactions and the structure of hadronic wavefunctions is not yet well-understood in QCD, it is evident that a quantitative first-principle description of the nuclear force will require a great deal of theoretical effort. Another reason for the limited impact of QCD in nuclear physics has been the conventional assumption that nuclear interactions can for the most part be analyzed in terms of an effective meson-nucleon field theory or potential model in isolation from the details of short distance quark and gluon structure of hadrons. These lectures, argue that this view is untenable: in fact, there is no correspondence principle which yields traditional nuclear physics as a rigorous large-distance or non-relativistic limit of QCD dynamics. On the other hand, the distinctions between standard nuclear physics dynamics and QCD at nuclear dimensions are extremely interesting and illuminating for both particle and nuclear physics.« less

On the symmetry foundation of double soft theorems

NASA Astrophysics Data System (ADS)

Li, Zhi-Zhong; Lin, Hung-Hwa; Zhang, Shun-Qing

2017-12-01

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

Lattice QCD and the unitarity triangle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andreas S Kronfeld

2001-12-03

Theoretical and computational advances in lattice calculations are reviewed, with focus on examples relevant to the unitarity triangle of the CKM matrix. Recent progress in semi-leptonic form factors for B {yields} {pi}/v and B {yields} D*lv, as well as the parameter {zeta} in B{sup 0}-{bar B}{sup 0} mixing, are highlighted.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Determination of |V(us)|| from a lattice QCD calculation of the K → πℓν semileptonic form factor with physical quark masses.

PubMed

Bazavov, A; Bernard, C; Bouchard, C M; Detar, C; Du, Daping; El-Khadra, A X; Foley, J; Freeland, E D; Gámiz, E; Gottlieb, Steven; Heller, U M; Kim, Jongjeong; Kronfeld, A S; Laiho, J; Levkova, L; Mackenzie, P B; Neil, E T; Oktay, M B; Qiu, Si-Wei; Simone, J N; Sugar, R; Toussaint, D; Van de Water, R S; Zhou, Ran

2014-03-21

We calculate the kaon semileptonic form factor f+(0) from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC Collaboration with Nf = 2 + 1 + 1 flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, f+(0) = 0.9704(32), where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of K semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element |V(us)| = 0.22290(74)(52), where the first error is from f+(0) and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from |V(us)| is now comparable to that from |V(ud)|.

Precise MS light-quark masses from lattice QCD in the regularization invariant symmetric momentum-subtraction scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbahn, Martin; Jaeger, Sebastian; Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH

2010-12-01

We compute the conversion factors needed to obtain the MS and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM{sub {gamma}{sub {mu}} }renormalization schemes. This is important for obtaining the MS masses with the best possible precision from numerical lattice QCD simulations, because the customary RI{sup (')}/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scalemore » dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM{sub {gamma}{sub {mu}} }scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.« less

Gravitation waves from QCD and electroweak phase transitions

NASA Astrophysics Data System (ADS)

Chen, Yidian; Huang, Mei; Yan, Qi-Shu

2018-05-01

We investigate the gravitation waves produced from QCD and electroweak phase transitions in the early universe by using a 5-dimension holographic QCD model and a holographic technicolor model. The dynamical holographic QCD model is to describe the pure gluon system, where a first order confinement-deconfinement phase transition can happen at the critical temperature around 250 MeV. The minimal holographic technicolor model is introduced to model the strong dynamics of electroweak, it can give a first order electroweak phase transition at the critical temperature around 100-360 GeV. We find that for both GW signals produced from QCD and EW phase transitions, in the peak frequency region, the dominant contribution comes from the sound waves, while away from the peak frequency region the contribution from the bubble collision is dominant. The peak frequency of gravitation wave determined by the QCD phase transition is located around 10-7 Hz which is within the detectability of FAST and SKA, and the peak frequency of gravitational wave predicted by EW phase transition is located at 0.002 - 0.007 Hz, which might be detectable by BBO, DECIGO, LISA and ELISA.

XYZ-like spectra from Laplace sum rule at N2LO in the chiral limit

NASA Astrophysics Data System (ADS)

Albuquerque, R.; Narison, S.; Fanomezana, F.; Rabemananjara, A.; Rabetiarivony, D.; Randriamanatrika, G.

2016-12-01

We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark XY Z-like states at lowest order (LO) of perturbative (PT) QCD and up to d = 8 condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the XY Z-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11-14 and compared, in Sec. 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the XZ observed states are compatible with (almost) pure JPC = 1+±, 0++ molecule or/and four-quark states. The ones of the 1-±, 0-± molecule/four-quark states are about 1.5 GeV above the Yc,b mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary D,B mesons (fDD ≈ 10-3f D) and may behave numerically as 1/m¯b3/2 (respectively 1/m¯b) for the 1+, 0+ (respectively 1-, 0-) states which can stimulate further theoretical studies of these decay constants.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Neutron Electric Dipole Moment from Gauge-String Duality.

PubMed

Bartolini, Lorenzo; Bigazzi, Francesco; Bolognesi, Stefano; Cotrone, Aldo L; Manenti, Andrea

2017-03-03

We compute the electric dipole moment of nucleons in the large N_{c} QCD model by Witten, Sakai, and Sugimoto with N_{f}=2 degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological θ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result-a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be d_{n}=1.8×10^{-16}θ e cm. The electric dipole moment of the proton is exactly the opposite.

The Evolution of Soft Collinear Effective Theory

DOE PAGES

Lee, Christopher

2015-02-25

Soft Collinear Effective Theory (SCET) is an effective field theory of Quantum Chromodynamics (QCD) for processes where there are energetic, nearly lightlike degrees of freedom interacting with one another via soft radiation. SCET has found many applications in high-energy and nuclear physics, especially in recent years the physics of hadronic jets in e +e -, lepton-hadron, hadron-hadron, and heavy-ion collisions. SCET can be used to factorize multi-scale cross sections in these processes into single-scale hard, collinear, and soft functions, and to evolve these through the renormalization group to resum large logarithms of ratios of the scales that appear in themore » QCD perturbative expansion, as well as to study properties of nonperturbative effects. We overview the elementary concepts of SCET and describe how they can be applied in high-energy and nuclear physics.« less

Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mert Aybat, Ted Rogers, Alexey Prokudin

In this letter, we show that it is necessary to include the full treatment of QCD evolution of Transverse Momentum Dependent parton densities to explain discrepancies between HERMES data and recent COMPASS data on a proton target for the Sivers transverse single spin asymmetry in Semi-Inclusive Deep Inelastic Scattering (SIDIS). Calculations based on existing fits to TMDs in SIDIS, and including evolution within the Collins-Soper-Sterman with properly defined TMD PDFs are shown to provide a good explanation for the discrepancy. The non-perturbative input needed for the implementation of evolution is taken from earlier analyses of unpolarized Drell-Yan (DY) scattering atmore » high energy. Its success in describing the Sivers function in SIDIS data at much lower energies is strong evidence in support of the unifying aspect of the QCD TMD-factorization formalism.« less

Chemical Equilibrium and Polynomial Equations: Beware of Roots.

ERIC Educational Resources Information Center

Smith, William R.; Missen, Ronald W.

1989-01-01

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…

Approaching Cauchy's Theorem

ERIC Educational Resources Information Center

Garcia, Stephan Ramon; Ross, William T.

2017-01-01

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

Flavor-singlet baryons in the graded symmetry approach to partially quenched QCD

NASA Astrophysics Data System (ADS)

Hall, Jonathan M. M.; Leinweber, Derek B.

2016-11-01

Progress in the calculation of the electromagnetic properties of baryon excitations in lattice QCD presents new challenges in the determination of sea-quark loop contributions to matrix elements. A reliable estimation of the sea-quark loop contributions represents a pressing issue in the accurate comparison of lattice QCD results with experiment. In this article, an extension of the graded symmetry approach to partially quenched QCD is presented, which builds on previous theory by explicitly including flavor-singlet baryons in its construction. The formalism takes into account the interactions among both octet and singlet baryons, octet mesons, and their ghost counterparts; the latter enables the isolation of the quark-flow disconnected sea-quark loop contributions. The introduction of flavor-singlet states enables systematic studies of the internal structure of Λ -baryon excitations in lattice QCD, including the topical Λ (1405 ).

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

Recombination algorithms and jet substructure: Pruning as a tool for heavy particle searches

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ellis, Stephen D.; Vermilion, Christopher K.; Walsh, Jonathan R.

2010-05-01

We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide-angle radiation, improves the mass resolution of jets reconstructing heavy particle decays, and decreases the QCD background to these decays. We show that pruning provides significant improvements overmore » unpruned jets in identifying top quarks and W bosons and separating them from a QCD background, and may be useful in a search for heavy particles.« less

Lattice QCD calculation of the B(s )→D(s) *ℓν form factors at zero recoil and implications for |Vc b|

NASA Astrophysics Data System (ADS)

Harrison, Judd; Davies, Christine T. H.; Wingate, Matthew; Hpqcd Collaboration

2018-03-01

We present results of a lattice QCD calculation of B →D* and Bs→Ds* axial vector matrix elements with both states at rest. These zero recoil matrix elements provide the normalization necessary to infer a value for the CKM matrix element |Vc b| from experimental measurements of B¯ 0→D*+ℓ-ν ¯ and B¯s0→Ds*+ℓ-ν¯ decay. Results are derived from correlation functions computed with highly improved staggered quarks (HISQ) for light, strange, and charm quark propagators, and nonrelativistic QCD for the bottom quark propagator. The calculation of correlation functions employs MILC Collaboration ensembles over a range of three lattice spacings. These gauge field configurations include sea quark effects of charm, strange, and equal-mass up and down quarks. We use ensembles with physically light up and down quarks, as well as heavier values. Our main results are FB→D *(1 )=0.895 ±0.01 0stat±0.024sys and FBs→Ds*(1 )=0.883 ±0.01 2stat±0.02 8sys . We discuss the consequences for |Vc b| in light of recent investigations into the extrapolation of experimental data to zero recoil.

The Conformal Template and New Perspectives for Quantum Chromodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; /SLAC

2007-03-06

Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. For example, there is an exact correspondence between the fifth-dimensional coordinate of AdS space and a specific impact variable which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, themore » fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. One can also use conformal symmetry as a template for perturbative QCD predictions where the effects of the nonzero beta function can be systematically included in the scale of the QCD coupling. This leads to fixing of the renormalization scale and commensurate scale relations which relate observables without scale or scheme ambiguity. The results are consistent with the renormalization group and the analytic connection of QCD to Abelian theory at N{sub C} {yields} 0. I also discuss a number of novel phenomenological features of QCD. Initial- and .nal-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, di.ractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, nonperturbative antisymmetric sea quark distributions, anomalous heavy quark e.ects, and the unexpected effects of direct higher-twist processes.« less

Accurate determinations of alpha(s) from realistic lattice QCD.

PubMed

Mason, Q; Trottier, H D; Davies, C T H; Foley, K; Gray, A; Lepage, G P; Nobes, M; Shigemitsu, J

2005-07-29

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to (1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations), (2) include third-order terms in perturbation theory, (3) systematically estimate fourth and higher-order terms, (4) use an unambiguous lattice spacing, and (5) use an [symbol: see text](a2)-accurate QCD action. We use 28 different (but related) short-distance quantities to obtain alpha((5)/(MS))(M(Z)) = 0.1170(12).

Dimensional Transmutation by Monopole Condensation in QCD

NASA Astrophysics Data System (ADS)

Cho, Y. M.

2015-01-01

The dimensional transmutation by the monopole condensation in QCD is reviewed. Using Abelian projection of the gauge potential which projects out the monopole potential gauge independently, we we show that there are two types of gluons: the color neutral binding gluons which plays the role of the confining agent and the colored valence gluons which become confined prisoners. With this we calculate the one-loop QCD effective potential and show the monopole condensation becomes the true vacuum of QCD. We propose to test the existence of two types of gluons experimentally by re-analyzing the existing gluon jets data.

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Pick's Theorem: What a Lemon!

ERIC Educational Resources Information Center

Russell, Alan R.

2004-01-01

Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.

Light-front holographic QCD and emerging confinement

DOE PAGES

Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; ...

2015-05-21

In this study we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. Themore » light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical spacetime. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q 2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q 2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.« less

Generalized Optical Theorem Detection in Random and Complex Media

NASA Astrophysics Data System (ADS)

Tu, Jing

The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar optical theorem theory applies to arbitrary lossless backgrounds and quite general probing fields including near fields which play a key role in super-resolution imaging. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. Furthermore, the generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks, invisible scatterers, and wireless communications. The latter developments have important military applications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a reactive optical theorem related to the reactive power changes. Meanwhile, the developed approach naturally leads to three optical theorem indicators or statistics, which can be used to detect changes or targets in unknown complex media. In addition, the optical theorem theory is generalized in the time domain so that it applies to arbitrary full vector fields, and arbitrary media including anisotropic media, nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The second component of this Ph.D. research program focuses on the application of the optical theorem to change detection. Three different forms of indicators or statistics are developed for change detection in unknown background media: a real power optical theorem detector, a reactive power optical theorem detector, and a total apparent power optical theorem detector. No prior knowledge is required of the background or the change or target. The performance of the three proposed optical theorem detectors is compared with the classical energy detector approach for change detection. The latter uses a mathematical or functional energy while the optical theorem detectors are based on real physical energy. For reference, the optical theorem detectors are also compared with the matched filter approach which (unlike the optical theorem detectors) assumes perfect target and medium information. The practical implementation of the optical theorem detectors is based for certain random and complex media on the exploitation of time reversal focusing ideas developed in the past 20 years in electromagnetics and acoustics. In the final part of the dissertation, we also discuss the implementation of the optical theorem sensors for one-dimensional propagation systems such as transmission lines. We also present a new generalized likelihood ratio test for detection that exploits a prior data constraint based on the optical theorem. Finally, we also address the practical implementation of the optical theorem sensors for optical imaging systems, by means of holography. The later is the first holographic implementation the optical theorem for arbitrary scenes and targets.

Constraints on the ωπ Form Factor from Analyticity and Unitarity

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Caprini, Irinel; Kubis, Bastian

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review our recent work on the electromagnetic ωπ form factor in a model-independent framework known as the method of unitarity bounds, partly motivated by the discre-pancies noted recently between the theoretical calculations of the form factor based on dispersion relations and certain experimental data measured from the decay ω → π0γ*. We have applied a modified dispersive formalism, which uses as input the discontinuity of the ωπ form factor calculated by unitarity below the ωπ threshold and an integral constraint on the square of its modulus above this threshold. The latter constraint was obtained by exploiting unitarity and the positivity of the spectral function of a QCD correlator, computed on the spacelike axis by operator product expansion and perturbative QCD. An alternative constraint is obtained by using data available at higher energies for evaluating an integral of the modulus squared with a suitable weight function. From these conditions we derived upper and lower bounds on the modulus of the ωπ form factor in the region below the ωπ threshold. The results confirm the existence of a disagreement between dispersion theory and experimental data on the ωπ form factor around 0:6 GeV, including those from NA60 published in 2016.

Constraints on the ωπ form factor from analyticity and unitarity

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Caprini, Irinel; Kubis, Bastian

2016-05-01

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review our recent work on the electromagnetic ωπ form factor in a model-independent framework known as the method of unitarity bounds, partly motivated by the discrepancies noted recently between the theoretical calculations of the form factor based on dispersion relations and certain experimental data measured from the decay ω → π0γ∗. We have applied a modified dispersive formalism, which uses as input the discontinuity of the ωπ form factor calculated by unitarity below the ωπ threshold and an integral constraint on the square of its modulus above this threshold. The latter constraint was obtained by exploiting unitarity and the positivity of the spectral function of a QCD correlator, computed on the spacelike axis by operator product expansion and perturbative QCD. An alternative constraint is obtained by using data available at higher energies for evaluating an integral of the modulus squared with a suitable weight function. From these conditions we derived upper and lower bounds on the modulus of the ωπ form factor in the region below the ωπ threshold. The results confirm the existence of a disagreement between dispersion theory and experimental data on the ωπ form factor around 0.6 GeV, including those from NA60 published in 2016.

Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data

DOE PAGES

Carmignotto, M.; Ali, S.; Aniol, K.; ...

2018-02-28

The 1H(e,e 'K +)Λ reaction was studied as a function of the Mandelstam variable -t using data from the E01-004 (FPI-2) and E93-018 experiments that were carried out in Hall C at the 6 GeV Jefferson Laboratory. The cross section was fully separated into longitudinal and transverse components, and two interference terms at four-momentum transfers Q 2 of 1.00, 1.36, and 2.07 GeV 2. The kaon form factor was extracted from the longitudinal cross section using the Regge model by Vanderhaeghen et al. [Phys. Rev. C 57, 1454 (1998)]. Here, the results establish the method, previously used successfully for pionmore » analyses, for extracting the kaon form factor. Data from 12 GeV Jefferson Laboratory experiments are expected to have sufficient precision to distinguish between theoretical predictions, for example, recent perturbative QCD calculations with modern parton distribution amplitudes. The leading-twist behavior for light mesons is predicted to set in for values of Q 2 between 5 and 10 GeV 2, which makes data in the few-GeV regime particularly interesting. Finally, the Q 2 dependence at fixed x and -t of the longitudinal cross section that we extracted seems consistent with the QCD factorization prediction within the experimental uncertainty.« less

Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carmignotto, M.; Ali, S.; Aniol, K.

The 1H(e,e 'K +)Λ reaction was studied as a function of the Mandelstam variable -t using data from the E01-004 (FPI-2) and E93-018 experiments that were carried out in Hall C at the 6 GeV Jefferson Laboratory. The cross section was fully separated into longitudinal and transverse components, and two interference terms at four-momentum transfers Q 2 of 1.00, 1.36, and 2.07 GeV 2. The kaon form factor was extracted from the longitudinal cross section using the Regge model by Vanderhaeghen et al. [Phys. Rev. C 57, 1454 (1998)]. Here, the results establish the method, previously used successfully for pionmore » analyses, for extracting the kaon form factor. Data from 12 GeV Jefferson Laboratory experiments are expected to have sufficient precision to distinguish between theoretical predictions, for example, recent perturbative QCD calculations with modern parton distribution amplitudes. The leading-twist behavior for light mesons is predicted to set in for values of Q 2 between 5 and 10 GeV 2, which makes data in the few-GeV regime particularly interesting. Finally, the Q 2 dependence at fixed x and -t of the longitudinal cross section that we extracted seems consistent with the QCD factorization prediction within the experimental uncertainty.« less

Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data

NASA Astrophysics Data System (ADS)

Carmignotto, M.; Ali, S.; Aniol, K.; Arrington, J.; Barrett, B.; Beise, E. J.; Blok, H. P.; Boeglin, W.; Brash, E. J.; Breuer, H.; Chang, C. C.; Christy, M. E.; Dittmann, A.; Ent, R.; Fenker, H.; Gaskell, D.; Gibson, E.; Holt, R. J.; Horn, T.; Huber, G. M.; Jin, S.; Jones, M. K.; Keppel, C. E.; Kim, W.; King, P. M.; Kovaltchouk, V.; Liu, J.; Lolos, G. J.; Mack, D. J.; Margaziotis, D. J.; Markowitz, P.; Matsumura, A.; Meekins, D.; Miyoshi, T.; Mkrtchyan, H.; Niculescu, G.; Niculescu, I.; Okayasu, Y.; Pegg, I. L.; Pentchev, L.; Perdrisat, C.; Potterveld, D.; Punjabi, V.; Reimer, P. E.; Reinhold, J.; Roche, J.; Sarty, A.; Smith, G. R.; Tadevosyan, V.; Tang, L. G.; Trotta, R.; Tvaskis, V.; Vargas, A.; Vidakovic, S.; Volmer, J.; Vulcan, W.; Warren, G.; Wood, S. A.; Xu, C.; Zheng, X.; JLAB FPI-2; E93-018 Collaboration

2018-02-01

The 1H(e ,e'K+ )Λ reaction was studied as a function of the Mandelstam variable -t using data from the E01-004 (FPI-2) and E93-018 experiments that were carried out in Hall C at the 6 GeV Jefferson Laboratory. The cross section was fully separated into longitudinal and transverse components, and two interference terms at four-momentum transfers Q2 of 1.00, 1.36, and 2.07 GeV2. The kaon form factor was extracted from the longitudinal cross section using the Regge model by Vanderhaeghen et al. [Phys. Rev. C 57, 1454 (1998), 10.1103/PhysRevC.57.1454]. The results establish the method, previously used successfully for pion analyses, for extracting the kaon form factor. Data from 12 GeV Jefferson Laboratory experiments are expected to have sufficient precision to distinguish between theoretical predictions, for example, recent perturbative QCD calculations with modern parton distribution amplitudes. The leading-twist behavior for light mesons is predicted to set in for values of Q2 between 5 and 10 GeV2, which makes data in the few-GeV regime particularly interesting. The Q2 dependence at fixed x and -t of the longitudinal cross section that we extracted seems consistent with the QCD factorization prediction within the experimental uncertainty.

Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

2018-02-01

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

The geometric Mean Value Theorem

NASA Astrophysics Data System (ADS)

de Camargo, André Pierro

2018-05-01

In a previous article published in the American Mathematical Monthly, Tucker (Amer Math Monthly. 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying Rolle's theorem to a function like Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as a technical existence theorem used to prove intuitively obvious statements. Moreover, he argued that there is nothing obvious about the Mean Value Theorem without the continuity of the derivative. Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.

Timelike pion form factor in lattice QCD

NASA Astrophysics Data System (ADS)

Feng, Xu; Aoki, Sinya; Hashimoto, Shoji; Kaneko, Takashi

2015-03-01

We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2 +1 -flavor overlap fermions at pion masses mπ=380 and 290 MeV. By calculating the I =1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.

Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra

NASA Astrophysics Data System (ADS)

Brodsky, Stanley J.

2017-05-01

A remarkable feature of QCD is that the mass scale κ which controls color confinement and light-quark hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ ^4 ζ ^2 for mesons, where ζ ^2 is the LF radial variable conjugate to the q \\bar{q} invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS_5, the space of isometries of the conformal group—if one modifies the action of AdS_5 by the dilaton e^{κ ^2 z^2} in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κ underlying confinement and hadron masses can be connected to the parameter Λ _{\\overline{MS}} in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α _s(Q^2) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q_0 which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q_0 to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front-form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.

Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.

A remarkable feature of QCD is that the mass scalemore » $k$ which controls color confinement and light-quark hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ 4ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the $$q\\bar{q}$$ invariant mass. The same result, including spin terms, is obtained using light-front holography$-$the duality between the front form and AdS 5, the space of isometries of the conformal group$-$if one modifies the action of AdS 5 by the dilaton e $κ^2z^2$ in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κκ underlying confinement and hadron masses can be connected to the parameter Λ $$\\overline{MS}$$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s (Q 2) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q 0 which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q 0 to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front-form vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.« less

Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra

DOE PAGES

Brodsky, Stanley J.

2017-04-19

A remarkable feature of QCD is that the mass scalemore » $k$ which controls color confinement and light-quark hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ 4ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the $$q\\bar{q}$$ invariant mass. The same result, including spin terms, is obtained using light-front holography$-$the duality between the front form and AdS 5, the space of isometries of the conformal group$-$if one modifies the action of AdS 5 by the dilaton e $κ^2z^2$ in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κκ underlying confinement and hadron masses can be connected to the parameter Λ $$\\overline{MS}$$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s (Q 2) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q 0 which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q 0 to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front-form vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.« less

A note on generalized Weyl's theorem

NASA Astrophysics Data System (ADS)

Zguitti, H.

2006-04-01

We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

The effect of transverse flow on the nuclear modification factor at RHIC and LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Betz, Barbara; Gyulassy, Miklos

2016-01-22

We determine the nuclear modification factor at RHIC and LHC energies using a generic jet-energy loss model that is expanded by an additional flow factor accounting for the impact of transverse flow. We consider a pQCD-based ansatz with and without jet-energy loss fluctuations that is coupled to a state-of-the-art hydrodynamic prescription and includes a running coupling effect. We show that the nuclear modification factor is a rather insensitive quantity that is barely affected by the flow dynamics of the medium created in a heavy-ion collision.

QCD inequalities for the nucleon mass and the free energy of baryonic matter.

PubMed

Cohen, Thomas D

2003-07-18

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.

QCD Evolution 2016

NASA Astrophysics Data System (ADS)

The QCD Evolution 2016 workshop was held at the National Institute for Subatomic Physics (Nikhef) in Amsterdam, May 30 - June 3, 2016. The workshop is a continuation of a series of workshops held during five consecutive years, in 2011, 2012, 2013, 2015 at Jefferson Lab, and in 2014 in Santa Fe, NM. With the rapid developments in our understanding of the evolution of parton distributions including low-x, TMDs, GPDs, higher-twist correlation functions, and the associated progress in perturbative QCD, lattice QCD and effective field theory techniques, we look forward to yet another exciting meeting in 2016. The program of QCD Evolution 2016 will pay special attention to the topics of importance for ongoing experiments, in the full range from Jefferson Lab energies to LHC energies or future experiments such as a future Electron Ion Collider, recently recommended as a highest priority in U.S. Department of Energy's 2015 Long Range Plan for Nuclear Science.

2017 QCD Evolution 2017

NASA Astrophysics Data System (ADS)

2017-05-01

The QCD Evolution 2017 workshop was held at Jefferson Lab, May 22-26, 2017. The workshop is a continuation of a series of workshops held during six consecutive years, in 2011, 2012, 2013, 2015 at Jefferson Lab, and in 2014 in Santa Fe, NM, and in 2016 at the National Institute for Subatomic Physics (Nikhef) in Amsterdam. With the rapid developments in our understanding of the evolution of parton distributions including TMDs, GPDs, low-x, higher-twist correlation functions, and the associated progress in perturbative QCD, lattice QCD and effective field theory techniques, we look forward to yet another exciting meeting in 2017. The program of QCD Evolution 2017 will pay special attention to the topics of importance for ongoing experiments, in the full range from Jefferson Lab energies to RHIC and LHC energies or future experiments such as a future Electron Ion Collider, recently recommended as a highest priority in U.S. Department of Energy's 2015 Long Range Plan for Nuclear Science.

Effective holographic models for QCD: Glueball spectrum and trace anomaly

NASA Astrophysics Data System (ADS)

Ballon-Bayona, Alfonso; Boschi-Filho, Henrique; Mamani, Luis A. H.; Miranda, Alex S.; Zanchin, Vilson T.

2018-02-01

We investigate effective holographic models for QCD arising from five-dimensional dilaton gravity. The models are characterized by a dilaton with a mass term in the UV, dual to a CFT deformation by a relevant operator, and quadratic in the IR. The UV constraint leads to the explicit breaking of conformal symmetry, whereas the IR constraint guarantees linear confinement. We propose semianalytic interpolations between the UV and the IR and obtain a spectrum for scalar and tensor glueballs consistent with lattice QCD data. We use the glueball spectrum as a physical constraint to find the evolution of the model parameters as the mass term goes to 0. Finally, we reproduce the universal result for the trace anomaly of deformed CFTs and propose a dictionary between this result and the QCD trace anomaly. A nontrivial consequence of this dictionary is the emergence of a β function similar to the two-loop perturbative QCD result.

Testing QCD factorization with phase determinations in B →K π , K ρ , and K*π decays

NASA Astrophysics Data System (ADS)

Pham, T. N.

2016-06-01

The success of QCD factorization (QCDF) in predicting branching ratios for charmless B decays to light pseudoscalar and vector mesons and the small C P asymmetries measured at BABAR, Belle, and LHCb show that the phase in these decays, as predicted by QCDF, are not large. For a precise test of QCDF, one needs to extract from the measured decay rates the phase of the decay amplitude which appears in the interference terms between the tree and penguin contribution. Since the tree amplitude is known at the leading order in ΛQCD/mb and is consistent with the measured tree-dominated decay rates, the QCDF value for the tree amplitude can be used with the measured decay rates to obtain the phases in B →K π , K ρ , and K*π decay rates. This is similar to the extraction of the final-state interaction phases in the interference term between p p ¯→J /Ψ →e+e- and p p ¯→e+e- and in J /Ψ →0-0- done previously. In this paper, we present a determination of the phase between the I =3 /2 tree and I =1 /2 penguin amplitudes in B →K π , K ρ , and K*π decays using the measured decay rates and the QCDF I =3 /2 tree amplitude obtained from the I =2 B+→π+π0,ρ0π+,ρ+π0 tree-dominated decays and compare the result with the phase given by QCDF. It is remarkable that the phase extracted from experiments differs only slightly from the QCDF values. This shows that there is no large final-state interaction strong phase in B →K π , K ρ , and K*π decays.

Recent QCD Studies at the Tevatron

DOE Office of Scientific and Technical Information (OSTI.GOV)

Group, Robert Craig

2008-04-01

Since the beginning of Run II at the Fermilab Tevatron the QCD physics groups of the CDF and D0 experiments have worked to reach unprecedented levels of precision for many QCD observables. Thanks to the large dataset--over 3 fb{sup -1} of integrated luminosity recorded by each experiment--important new measurements have recently been made public and will be summarized in this paper.

Lattice quantum chromodynamical approach to nuclear physics

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji; HAL QCD Collaboration

2012-09-01

We review recent progress in the HAL QCD method, which was recently proposed to investigate hadron interactions in lattice quantum chromodynamics (QCD). The strategy to extract the energy-independent non-local potential in lattice QCD is explained in detail. The method is applied to study nucleon-nucleon, nucleon-hyperon, hyperon-hyperon, and meson-baryon interactions. Several extensions of the method are also discussed.

On microscopic structure of the QCD vacuum

NASA Astrophysics Data System (ADS)

Pak, D. G.; Lee, Bum-Hoon; Kim, Youngman; Tsukioka, Takuya; Zhang, P. M.

2018-05-01

We propose a new class of regular stationary axially symmetric solutions in a pure QCD which correspond to monopole-antimonopole pairs at macroscopic scale. The solutions represent vacuum field configurations which are locally stable against quantum gluon fluctuations in any small space-time vicinity. This implies that the monopole-antimonopole pair can serve as a structural element in microscopic description of QCD vacuum formation.

Equivalence of the AdS-metric and the QCD running coupling

NASA Astrophysics Data System (ADS)

Pirner, H. J.; Galow, B.

2009-08-01

We use the functional form of the QCD running coupling to modify the conformal metric in AdS/CFT mapping the fifth-dimensional z-coordinate to the energy scale in the four-dimensional QCD. The resulting type-0 string theory in five dimensions is solved with the Nambu-Goto action giving good agreement with the Coulombic and confinement QQbar potential.

Renormalizability of quasiparton distribution functions

DOE PAGES

Ishikawa, Tomomi; Ma, Yan-Qing; Qiu, Jian-Wei; ...

2017-11-21

Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations. However, unlike the parton distribution functions, the quasi-parton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. Here in this article, we identify all sources of ultraviolet divergences for the quasi-parton distribution functions in coordinate-space, and demonstrated that power divergences, as well as all logarithmic divergences can be renormalized multiplicatively to all ordersmore » in QCD perturbation theory.« less

Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields.

PubMed

D'Elia, Massimo; Mariti, Marco; Negro, Francesco

2013-02-22

We investigate two flavor quantum chromodynamics (QCD) in the presence of CP-odd electromagnetic background fields and determine, by means of lattice QCD simulations, the induced effective θ term to first order in E[over →] · B[over →]. We employ a rooted staggered discretization and study lattice spacings down to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a positive measure, we consider purely imaginary electric fields and real magnetic fields, and then exploit the analytic continuation. Our results are relevant to a description of the effective pseudoscalar quantum electrodynamics-QCD interactions.

Renormalizability of quasiparton distribution functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ishikawa, Tomomi; Ma, Yan-Qing; Qiu, Jian-Wei

Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations. However, unlike the parton distribution functions, the quasi-parton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. Here in this article, we identify all sources of ultraviolet divergences for the quasi-parton distribution functions in coordinate-space, and demonstrated that power divergences, as well as all logarithmic divergences can be renormalized multiplicatively to all ordersmore » in QCD perturbation theory.« less

Quark–hadron phase structure, thermodynamics, and magnetization of QCD matter

NASA Astrophysics Data System (ADS)

Nasser Tawfik, Abdel; Magied Diab, Abdel; Hussein, M. T.

2018-05-01

The SU(3) Polyakov linear-sigma model (PLSM) is systematically implemented to characterize the quark-hadron phase structure and to determine various thermodynamic quantities and the magnetization of quantum chromodynamic (QCD) matter. Using mean-field approximation, the dependence of the chiral order parameter on a finite magnetic field is also calculated. Under a wide range of temperatures and magnetic field strengths, various thermodynamic quantities including trace anomaly, speed of sound squared, entropy density, and specific heat are presented, and some magnetic properties are described as well. Where available these results are compared to recent lattice QCD calculations. The temperature dependence of these quantities confirms our previous finding that the transition temperature is reduced with the increase in the magnetic field strength, i.e. QCD matter is characterized by an inverse magnetic catalysis. Furthermore, the temperature dependence of the magnetization showing that QCD matter has paramagnetic properties slightly below and far above the pseudo-critical temperature is confirmed as well. The excellent agreement with recent lattice calculations proves that our QCD-like approach (PLSM) seems to possess the correct degrees of freedom in both the hadronic and partonic phases and describes well the dynamics deriving confined hadrons to deconfined quark-gluon plasma.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richards, David G.

I present a survey of calculations of the excited $N^*$ spectrum in lattice QCD. I then describe recent advances aimed at extracting the momentum-dependent phase shifts from lattice calculations, notably in the meson sector, and the potential for their application to baryons. I conclude with a discussion of calculations of the electromagnetic transition form factors to excited nucleons, including calculations at high $Q^2$.

Discovering the Theorem of Pythagoras

NASA Technical Reports Server (NTRS)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Guided Discovery of the Nine-Point Circle Theorem and Its Proof

ERIC Educational Resources Information Center

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Superconformal Algebraic Approach to Hadron Structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Teramond, Guy F.; Brodsky, Stanley J.; Deur, Alexandre

2017-03-01

Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physics is also suitable to describe nonperturbative QCD observables based on structure functions,more » such as GPDs, which are not amenable to a first-principle computation. The formalism is also successful in the description of form factors, the nonperturbative behavior of the strong coupling and diffractive processes. We also discuss in this article how the framework can be extended rather successfully to the heavy-light hadron sector.« less

A measurement and QCD analysis of the proton structure function F2 ( x, Q2) at HERA

NASA Astrophysics Data System (ADS)

Aid, S.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Arpagaus, M.; Babaev, A.; Bähr, J.; Bán, J.; Ban, Y.; Baranov, P.; Barrelet, E.; Barschke, R.; Bartel, W.; Barth, M.; Bassler, U.; Beck, H. P.; Behrend, H.-J.; Belousov, A.; Berger, Ch.; Bernardi, G.; Bernet, R.; Bertrand-Coremans, G.; Besançoni, M.; Beyer, R.; Biddulph, P.; Bispham, P.; Bizot, J. C.; Blobel, V.; Borras, K.; Botterweck, F.; Boudry, V.; Braemer, A.; Braunschweig, W.; Brisson, V.; Bruncko, D.; Brune, C.; Buchholz, R.; Büngener, L.; BurgerF. W. Büsser, J.; Buniatian, A.; Burke, S.; Burton, M. J.; Buschhorn, G.; Campbell, A. J.; Carli, T.; Charles, F.; Charlet, M.; Clarke, D.; Clegg, A. B.; Clerbaux, B.; Cocks, S.; Contreras, J. G.; Cormack, C.; Coughlan, J. A.; Courau, A.; Cousinou, M.-C.; Cozzika, G.; Criegee, L.; Cussans, D. G.; Cvach, J.; Dagoret, S.; Dainton, J. B.; Dau, W. D.; Daum, K.; David, M.; Davis, C. L.; Delcourt, B.; De Roeck, A.; De Wolf, E. A.; Dirkmann, M.; Dixon, P.; Di Nezza, P.; Dlugosz, W.; Dollfus, C.; Dowell, J. D.; Dreis, H. B.; Droutskoi, A.; Düllmann, D.; Dünger, O.; Duhm, H.; Ebert, J.; Ebert, T. R.; Eckerlin, G.; Efremenko, V.; Egli, S.; Eichler, R.; Eisele, F.; Eisenhandler, E.; Ellison, R. J.; Elsen, E.; Erdmann, M.; Erdmann, W.; Evrard, E.; Fahr, A. B.; Favart, L.; Fedotov, A.; Feeken, D.; Felst, R.; Feltesse, J.; Ferencei, J.; Ferrarotto, F.; Flamm, K.; Fleischer, M.; Flieser, M.; Flügge, G.; Fomenko, A.; Fominykh, B.; Formánek, J.; Foster, J. M.; Franke, G.; Fretwurst, E.; Gabathuler, E.; Gabathuler, K.; Gaede, F.; Garvey, J.; Gayler, J.; Gebauer, M.; Gellrich, A.; Genzel, H.; Gerhards, R.; Glazov, A.; Goerlach, U.; Goerlich, L.; Gogitidze, N.; Goldberg, M.; Goldner, D.; Golec-Biernat, K.; Gonzalez-Pineiro, B.; Gorelov, I.; Grab, C.; Grässler, H.; Grässler, R.; Greenshaw, T.; Griffiths, R.; Grindhammer, G.; Gruber, A.; Gruber, C.; Haack, J.; Haidt, D.; Hajduk, L.; Hampel, M.; Haynes, W. J.; Heinzelmann, G.; Henderson, R. C. W.; Henschel, H.; Herynek, I.; Hess, M. F.; Hildesheim, W.; Hiller, K. H.; Hilton, C. D.; Hladký, J.; Hoeger, K. C.; Höppner, M.; Hoffmann, D.; Holtom, T.; Horisberger, R.; Hudgson, V. L.; Hütte, M.; Hufnagel, H.; Ibbotson, M.; Itterbeck, H.; Jacholkowska, A.; Jacobsson, C.; Jaffre, M.; Janoth, J.; Jansen, T.; Jönsson, L.; Johannsen, K.; Johnson, D. P.; Johnson, L.; Jung, H.; Kalmus, P. I. P.; Kander, M.; Kant, D.; Kaschowitz, R.; Kathage, U.; Katzy, J.; Kaufmann, H. H.; Kazarian, S.; Kenyon, I. R.; Kermiche, S.; Keuker, C.; Kiesling, C.; Klein, M.; Kleinwort, C.; Knies, G.; Köhler, T.; Köhne, J. H.; Kolanoski, H.; Kole, F.; Kolya, S. D.; Korbel, V.; Korn, M.; Kostka, P.; Kotelnikov, S. K.; Krämerkämper, T.; Krasny, M. W.; Krehbie, H.; Krücker, D.; Krüger, U.; Krüner-Marquis, U.; Küster, H.; Kuhlen, M.; Kurča, T.; Kurzhöfer, J.; Lacour, D.; Laforge, B.; Lander, R.; Landon, M. P. J.; Lange, W.; Langenegger, U.; Laporte, J.-F.; Lebedev, A.; Lehner, F.; Leverenz, C.; Levonian, S.; Ley, Ch.; Lindström, G.; Lindstroem, M.; Link, J.; Linsel, F.; Lipinski, J.; List, B.; Lobo, G.; Lohmander, H.; Lomas, J. W.; Lopez, G. C.; Lubimov, V.; Lüke, D.; Magnussen, N.; Malinovski, E.; Mani, S.; Maraček, R.; Marage, P.; Marks, J.; Marshall, R.; Martens, J.; Martin, G.; Martin, R.; Martyn, H.-U.; Martyniak, J.; Mavroidis, T.; Maxfield, S. J.; McMahon, S. J.; Mehta, A.; Meier, K.; Merz, T.; Meyer, A.; MeyerH. Meyer, A.; Meyer, J.; Meyer, P.-O.; Migliori, A.; Mikocki, S.; Milstead, D.; Moeck, J.; Moreau, F.; Morris, J. V.; Mroczko, E.; Müller, D.; Müller, G.; Müller, K.; Murín, P.; Nagovizin, V.; Nahnhauer, R.; Naroska, B.; Naumann, Th.; Newman, P. R.; Newton, D.; Neyret, D.; Nguyen, H. K.; Nicholls, T. C.; Niebergall, F.; Niebuhr, C.; Niedzballa, Ch.; Niggli, H.; Nisius, R.; Nowak, G.; Noyes, G. W.; Nyberg-Werther, M.; Oakden, M.; Oberlack, H.; Obrock, U.; Olsson, J. E.; Ozerov, D.; Palmen, P.; Panaro, E.; Panitch, A.; Pascaud, C.; Patel, G. D.; Pawletta, H.; Peppel, E.; Perez, E.; Phillips, J. P.; Pieuchot, A.; Pitzl, D.; Pope, G.; Prell, S.; Prosi, R.; Rabbertz, K.; Rädel, G.; Raupach, F.; Reimer, P.; Reinshagen, S.; Rick, H.; Riech, V.; Riedlberger, J.; Riepenhausen, F.; Riess, S.; Rizvi, E.; Robertson, S. M.; Robmann, P.; Roloff, H. E.; Roosen, R.; Rosenbauer, K.; Rostovtsev, A.; Rouse, F.; Royon, C.; Rüter, K.; Rusakov, S.; Rybicki, K.; Sahlmann, N.; Sankey, D. P. C.; Schacht, P.; Schiek, S.; Schleif, S.; Schleper, P.; von Schlippe, W.; Schmidt, D.; Schmidt, G.; Schöning, A.; Schröder, V.; Schuhmann, E.; Schwab, B.; Sefkow, F.; Seidel, M.; Sell, R.; Semenov, A.; Shekelyan, V.; Sheviakov, I.; Shtarkov, L. N.; Siegmon, G.; Siewert, U.; Sirois, Y.; Skillicorn, I. O.; Smirnov, P.; Smith, J. R.; Solochenko, V.; Soloviev, H.; Specka, A.; Spiekermann, J.; Spielman, S.; Spitzer, H.; Squinabl, F.; Starosta, R.; Steenbock, M.; Steffen, P.; Steinberg, R.; Steiner, H.; Stella, B.; Stellberger, A.; Stier, J.; Stiewe, J.; Stößlein, U.; Stolze, K.; Straumann, U.; Struczinski, W.; Sutton, J. P.; Tapprogge, S.; Taševský, M.; Tchernyshov, V.; Tchetchelnitski, S.; Theissen, J.; Thiebaux, C.; Thompson, G.; Truöl, P.; Turnau, J.; Tutas, J.; Uelkes, P.; Usik, A.; Valkár, S.; Valkárová, A.; Vallée, C.; Vandenplas, D.; Van Esch, P.; Van Mechelen, P.; Vazdik, Y.; Verrecchi, P.; Villet, G.; Wacker, K.; Wagener, A.; Wagener, M.; Walther, A.; Waugh, B.; Weber, G.; Weber, M.; Wegener, D.; Wegner, A.; Wengler, T.; Werner, M.; West, L. R.; Wilksen, T.; Willard, S.; Winde, M.; Winter, G.-G.; Wittek, C.; Wünsch, E.; Žáček, J.; Zarbock, D.; Zhang, Z.; Zhokin, A.; Zimmer, M.; Zomer, F.; Zsembery, J.; Zuber, K.; zurNedden, M.; Kaufmannxa, O.; H1 Collaboration

1996-02-01

A new measurement of the proton structure function F2 ( x, Q2) is reported for momentum transfers squared Q2 between ].5 GeV 2 and 5000 GeV 2 and for Bjorken x between 3 · 10 -5 and 0.32 using data collected by the HERA experiment H1 in 1994. The data represent an increase in statistics by a factor of ten with respect to the analysis of the 1993 data. Substantial extension of the kinematic range towards low Q2 and x has been achieved using dedicated data samples and events with initial state photon radiation. The structure function is found to increase significantly with decreasing x, even in the lowest accessible Q2 region. The data are well described by a Next to Leading Order QCD fit and the gluon density is extracted.

Three-body decays B →ϕ (ρ )K γ in perturbative QCD approach

NASA Astrophysics Data System (ADS)

Wang, Chao; Liu, Jing-Bin; Li, Hsiang-nan; Lü, Cai-Dian

2018-02-01

We study the three-body radiative decays B →ϕ (ρ )K γ induced by a flavor-changing neutral current in the perturbative QCD approach. Pseudoscalar-vector (P V ) distribution amplitudes (DAs) are introduced for the final-state ϕ K (ρ K ) pair to capture important infrared dynamics in the region with a small P V -pair invariant mass. The dependence of these P V DAs on the parton momentum fraction is parametrized in terms of the Gegenbauer polynomials, and the dependence on the meson momentum fraction is derived through their normalizations to timelike P V form factors. In addition to the dominant electromagnetic penguin, the subleading chromomagnetic penguin, quark-loop and annihilation diagrams are also calculated. After determining the P V DAs from relevant branching-ratio data, the direct C P asymmetries and decay spectra in the P V -pair invariant mass are predicted for each B →ϕ (ρ )K γ mode.

Pion distribution amplitude from lattice QCD.

PubMed

Cloët, I C; Chang, L; Roberts, C D; Schmidt, S M; Tandy, P C

2013-08-30

A method is explained through which a pointwise accurate approximation to the pion's valence-quark distribution amplitude (PDA) may be obtained from a limited number of moments. In connection with the single nontrivial moment accessible in contemporary simulations of lattice-regularized QCD, the method yields a PDA that is a broad concave function whose pointwise form agrees with that predicted by Dyson-Schwinger equation analyses of the pion. Under leading-order evolution, the PDA remains broad to energy scales in excess of 100 GeV, a feature which signals persistence of the influence of dynamical chiral symmetry breaking. Consequently, the asymptotic distribution φπ(asy)(x) is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on φ φπ(asy)(x) should be revised.

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

Next-to-leading order QCD predictions for top-quark pair production with up to three jets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Höche, S.; Maierhöfer, P.; Moretti, N.

2017-03-07

Here, we present theoretical predictions for the production of top-quark pairs with up to three jets at the next-to leading order in perturbative QCD. The relevant calculations are performed with Sherpa and OpenLoops. In order to address the issue of scale choices and related uncertainties in the presence of multiple scales, we compare results obtained with the standard scale HT/2HT/2 at fixed order and the MiNLO procedure. By analyzing various cross sections and distributions for tmore » $$\\bar{t}$$+0,1,2,3 jets at the 13 TeV LHC we found a remarkable overall agreement between fixed-order and MiNLO results. The differences are typically below the respective factor-two scale variations, suggesting that for all considered jet multiplicities missing higher-order effects should not exceed the ten percent level.« less

Higgs boson decay into b-quarks at NNLO accuracy

NASA Astrophysics Data System (ADS)

Del Duca, Vittorio; Duhr, Claude; Somogyi, Gábor; Tramontano, Francesco; Trócsányi, Zoltán

2015-04-01

We compute the fully differential decay rate of the Standard Model Higgs boson into b-quarks at next-to-next-to-leading order (NNLO) accuracy in αs. We employ a general subtraction scheme developed for the calculation of higher order perturbative corrections to QCD jet cross sections, which is based on the universal infrared factorization properties of QCD squared matrix elements. We show that the subtractions render the various contributions to the NNLO correction finite. In particular, we demonstrate analytically that the sum of integrated subtraction terms correctly reproduces the infrared poles of the two-loop double virtual contribution to this process. We present illustrative differential distributions obtained by implementing the method in a parton level Monte Carlo program. The basic ingredients of our subtraction scheme, used here for the first time to compute a physical observable, are universal and can be employed for the computation of more involved processes.

The analytical {\\mathscr{O}}({a}_{s}^{4}) expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation

NASA Astrophysics Data System (ADS)

Kataev, A. L.; Molokoedov, V. S.

2017-12-01

The analytical {\\mathscr{O}}({a}s4) perturbative QCD expression for the flavour non-singlet contribution to the Bjorken polarized sum rule in the rather applicable at present gauge-dependent miniMOM scheme is obtained. For the considered three values of the gauge parameter, namely ξ = 0 (Landau gauge), ξ = -1 (anti-Feynman gauge) and ξ = -3 (Stefanis-Mikhailov gauge), the scheme-dependent coefficients are considerably smaller than the gauge-independent {\\overline{{MS}}} results. It is found that the fundamental property of the factorization of the QCD renormalization group β-function in the generalized Crewther relation, which is valid in the gauge-invariant {\\overline{{MS}}} scheme up to {\\mathscr{O}}({a}s4)-level at least, is unexpectedly valid at the same level in the miniMOM-scheme for ξ = 0, and for ξ = -1 and ξ = -3 in part.

Fragmentation contributions to J / ψ photoproduction at HERA

DOE PAGES

Bodwin, Geoffrey T.; Chung, Hee Sok; Kim, U-Rae; ...

2015-10-28

Here, we compute leading-power fragmentation corrections to J/ψ photoproduction at DESY HERA, making use of the nonrelativistic QCD factorization approach. Our calculations include parton production cross sections through order α 3 s, fragmentation functions though order α 2 s, and leading logarithms of the transverse momentum divided by the charm-quark mass to all orders in α s. We find that the leading-power fragmentation corrections, beyond those that are included through next-to-leading order in α s, are small relative to the fixed-order contributions through next-to-leading order in α s. Consequently, an important discrepancy remains between the experimental measurements of the J/ψmore » photoproduction cross section and predictions that make use of nonrelativistic-QCD long-distance matrix elements that are extracted from the J/ψ hadroproduction cross-section and polarization data.« less

DØ Results on Diphoton Direct Production and Photon + b and c Jet Production

NASA Astrophysics Data System (ADS)

Sawyer, Lee

2013-11-01

In this note we present measurements of the direct photon pair production cross sections using 8.5 fb-1 of data collected with the DØ detector at the Fermilab Tevatron pmathop plimits^ collider at √s = 1.96 TeV. The results are shown as differential distributions with respect to the photon pair mass, pair transverse momentum, azimuthal angle, and polar scattering angle in the Collins-Soper frame. We also present measurements of the differential cross section dσ/dpTγ for the inclusive production of a photon in association with a b- or c-quark jet. The results are based on 8.7 fb-1 of data, and the measured cross sections are compared with next-to-leading order perturbative QCD calculations using different sets of parton distribution functions as well as to predictions based on the kT-factorization QCD approach, and those from various Monte Carlo event generators.

DOE Office of Scientific and Technical Information (OSTI.GOV)

MAEZAWA,Y.; AOKI, S.; EJIRI, S.

The authors report the current status of the systematic studies of the QCD thermodynamics by lattice QCD simulations with two flavors of improved Wilson quarks. They evaluate the critical temperature of two flavor QCD in the chiral limit at zero chemical potential and show the preliminary result. Also they discuss fluctuations at none-zero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to chemical potential.

Λb→p ℓ-ν¯ ℓ and Λb→Λcℓ-ν¯ ℓ form factors from lattice QCD with relativistic heavy quarks

NASA Astrophysics Data System (ADS)

Detmold, William; Lehner, Christoph; Meinel, Stefan

2015-08-01

Measurements of the Λb→p ℓ-ν¯ ℓ and Λb→Λcℓ-ν¯ ℓ decay rates can be used to determine the magnitudes of the Cabibbo-Kobayashi-Maskawa matrix elements Vu b and Vc b, provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2 +1 flavors of dynamical domain-wall fermions. The b and c quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, using gauge-field configurations generated by the RBC and UKQCD Collaborations. The b →u and b →c currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the q2 dependence using z expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the Λb→p ℓ-ν¯ℓ and Λb→Λc ℓ-ν¯ℓ differential and integrated decay rates. Combined with experimental data, our results enable determinations of |Vu b|, |Vc b|, and |Vu b/Vc b| with theory uncertainties of 4.4%, 2.2%, and 4.9%, respectively.

Experimental access to Transition Distribution Amplitudes with the P¯ANDA experiment at FAIR

NASA Astrophysics Data System (ADS)

Singh, B. P.; Erni, W.; Keshelashvili, I.; Krusche, B.; Steinacher, M.; Liu, B.; Liu, H.; Liu, Z.; Shen, X.; Wang, C.; Zhao, J.; Albrecht, M.; Fink, M.; Heinsius, F. H.; Held, T.; Holtmann, T.; Koch, H.; Kopf, B.; Kümmel, M.; Kuhl, G.; Kuhlmann, M.; Leyhe, M.; Mikirtychyants, M.; Musiol, P.; Mustafa, A.; Pelizäus, M.; Pychy, J.; Richter, M.; Schnier, C.; Schröder, T.; Sowa, C.; Steinke, M.; Triffterer, T.; Wiedner, U.; Beck, R.; Hammann, C.; Kaiser, D.; Ketzer, B.; Kube, M.; Mahlberg, P.; Rossbach, M.; Schmidt, C.; Schmitz, R.; Thoma, U.; Walther, D.; Wendel, C.; Wilson, A.; Bianconi, A.; Bragadireanu, M.; Caprini, M.; Pantea, D.; Pietreanu, D.; Vasile, M. E.; Patel, B.; Kaplan, D.; Brandys, P.; Czyzewski, T.; Czyzycki, W.; Domagala, M.; Hawryluk, M.; Filo, G.; Krawczyk, M.; Kwiatkowski, D.; Lisowski, E.; Lisowski, F.; Fiutowski, T.; Idzik, M.; Mindur, B.; Przyborowski, D.; Swientek, K.; Czech, B.; Kliczewski, S.; Korcyl, K.; Kozela, A.; Kulessa, P.; Lebiedowicz, P.; Malgorzata, K.; Pysz, K.; Schäfer, W.; Siudak, R.; Szczurek, A.; Biernat, J.; Jowzaee, S.; Kamys, B.; Kistryn, S.; Korcyl, G.; Krzemien, W.; Magiera, A.; Moskal, P.; Palka, M.; Psyzniak, A.; Rudy, Z.; Salabura, P.; Smyrski, J.; Strzempek, P.; Wrońska, A.; Augustin, I.; Lehmann, I.; Nicmorus, D.; Schepers, G.; Schmitt, L.; Al-Turany, M.; Cahit, U.; Capozza, L.; Dbeyssi, A.; Deppe, H.; Dzhygadlo, R.; Ehret, A.; Flemming, H.; Gerhardt, A.; Götzen, K.; Karabowicz, R.; Kliemt, R.; Kunkel, J.; Kurilla, U.; Lehmann, D.; Lühning, J.; Maas, F.; Morales Morales, C.; Mora Espí, M. C.; Nerling, F.; Orth, H.; Peters, K.; Rodríguez Piñeiro, D.; Saito, N.; Saito, T.; Sánchez Lorente, A.; Schmidt, C. J.; Schwarz, C.; Schwiening, J.; Traxler, M.; Valente, R.; Voss, B.; Wieczorek, P.; Wilms, A.; Zühlsdorf, M.; Abazov, V. M.; Alexeev, G.; Arefiev, A.; Astakhov, V. I.; Barabanov, M. Yu.; Batyunya, B. V.; Davydov, Yu. I.; Dodokhov, V. Kh.; Efremov, A. A.; Fedunov, A. G.; Festchenko, A. A.; Galoyan, A. S.; Grigoryan, S.; Karmokov, A.; Koshurnikov, E. K.; Lobanov, V. I.; Lobanov, Yu. Yu.; Makarov, A. F.; Malinina, L. V.; Malyshev, V. L.; Mustafaev, G. A.; Olshevskiy, A.; Pasyuk, M. A.; Perevalova, E. A.; Piskun, A. A.; Pocheptsov, T. A.; Pontecorvo, G.; Rodionov, V. K.; Rogov, Yu. N.; Salmin, R. A.; Samartsev, A. G.; Sapozhnikov, M. G.; Shabratova, G. S.; Skachkov, N. B.; Skachkova, A. N.; Strokovsky, E. A.; Suleimanov, M. K.; Teshev, R. Sh.; Tokmenin, V. V.; Uzhinsky, V. V.; Vodopyanov, A. S.; Zaporozhets, S. A.; Zhuravlev, N. I.; Zorin, A. G.; Branford, D.; Glazier, D.; Watts, D.; Woods, P.; Britting, A.; Eyrich, W.; Lehmann, A.; Uhlig, F.; Dobbs, S.; Seth, K.; Tomaradze, A.; Xiao, T.; Bettoni, D.; Carassiti, V.; Cotta Ramusino, A.; Dalpiaz, P.; Drago, A.; Fioravanti, E.; Garzia, I.; Savriè, M.; Stancari, G.; Akishina, V.; Kisel, I.; Kulakov, I.; Zyzak, M.; Arora, R.; Bel, T.; Gromliuk, A.; Kalicy, G.; Krebs, M.; Patsyuk, M.; Zuehlsdorf, M.; Bianchi, N.; Gianotti, P.; Guaraldo, C.; Lucherini, V.; Pace, E.; Bersani, A.; Bracco, G.; Macri, M.; Parodi, R. F.; Bianco, S.; Bremer, D.; Brinkmann, K. T.; Diehl, S.; Dormenev, V.; Drexler, P.; Düren, M.; Eissner, T.; Etzelmüller, E.; Föhl, K.; Galuska, M.; Gessler, T.; Gutz, E.; Hayrapetyan, A.; Hu, J.; Kröck, B.; Kühn, W.; Kuske, T.; Lange, S.; Liang, Y.; Merle, O.; Metag, V.; Mülhheim, D.; Münchow, D.; Nanova, M.; Novotny, R.; Pitka, A.; Quagli, T.; Rieke, J.; Rosenbaum, C.; Schnell, R.; Spruck, B.; Stenzel, H.; Thöring, U.; Ullrich, M.; Wasem, T.; Werner, M.; Zaunick, H. G.; Ireland, D.; Rosner, G.; Seitz, B.; Deepak, P. N.; Kulkarni, A. V.; Apostolou, A.; Babai, M.; Kavatsyuk, M.; Lemmens, P.; Lindemulder, M.; Löhner, H.; Messchendorp, J.; Schakel, P.; Smit, H.; van der Weele, J. C.; Tiemens, M.; Veenstra, R.; Vejdani, S.; Kalita, K.; Mohanta, D. P.; Kumar, A.; Roy, A.; Sahoo, R.; Sohlbach, H.; Büscher, M.; Cao, L.; Cebulla, A.; Deermann, D.; Dosdall, R.; Esch, S.; Georgadze, I.; Gillitzer, A.; Goerres, A.; Goldenbaum, F.; Grunwald, D.; Herten, A.; Hu, Q.; Kemmerling, G.; Kleines, H.; Kozlov, V.; Lehrach, A.; Leiber, S.; Maier, R.; Nellen, R.; Ohm, H.; Orfanitski, S.; Prasuhn, D.; Prencipe, E.; Ritman, J.; Schadmand, S.; Schumann, J.; Sefzick, T.; Serdyuk, V.; Sterzenbach, G.; Stockmanns, T.; Wintz, P.; Wüstner, P.; Xu, H.; Li, S.; Li, Z.; Sun, Z.; Xu, H.; Rigato, V.; Fissum, S.; Hansen, K.; Isaksson, L.; Lundin, M.; Schröder, B.; Achenbach, P.; Bleser, S.; Cardinali, M.; Corell, O.; Deiseroth, M.; Denig, A.; Distler, M.; Feldbauer, F.; Fritsch, M.; Jasinski, P.; Hoek, M.; Kangh, D.; Karavdina, A.; Lauth, W.; Leithoff, H.; Merkel, H.; Michel, M.; Motzko, C.; Müller, U.; Noll, O.; Plueger, S.; Pochodzalla, J.; Sanchez, S.; Schlimme, S.; Sfienti, C.; Steinen, M.; Thiel, M.; Weber, T.; Zambrana, M.; Dormenev, V. I.; Fedorov, A. A.; Korzihik, M. V.; Missevitch, O. V.; Balanutsa, P.; Balanutsa, V.; Chernetsky, V.; Demekhin, A.; Dolgolenko, A.; Fedorets, P.; Gerasimov, A.; Goryachev, V.; Varentsov, V.; Boukharov, A.; Malyshev, O.; Marishev, I.; Semenov, A.; Konorov, I.; Paul, S.; Grieser, S.; Hergemöller, A. K.; Khoukaz, A.; Köhler, E.; Täschner, A.; Wessels, J.; Dash, S.; Jadhav, M.; Kumar, S.; Sarin, P.; Varma, R.; Chandratre, V. B.; Datar, V.; Dutta, D.; Jha, V.; Kumawat, H.; Mohanty, A. K.; Roy, B.; Yan, Y.; Chinorat, K.; Khanchai, K.; Ayut, L.; Pornrad, S.; Barnyakov, A. Y.; Blinov, A. E.; Blinov, V. E.; Bobrovnikov, V. S.; Kononov, S. A.; Kravchenko, E. A.; Kuyanov, I. A.; Onuchin, A. P.; Sokolov, A. A.; Tikhonov, Y. A.; Atomssa, E.; Hennino, T.; Imre, M.; Kunne, R.; Le Galliard, C.; Ma, B.; Marchand, D.; Ong, S.; Ramstein, B.; Rosier, P.; Tomasi-Gustafsson, E.; Van de Wiele, J.; Boca, G.; Costanza, S.; Genova, P.; Lavezzi, L.; Montagna, P.; Rotondi, A.; Abramov, V.; Belikov, N.; Bukreeva, S.; Davidenko, A.; Derevschikov, A.; Goncharenko, Y.; Grishin, V.; Kachanov, V.; Kormilitsin, V.; Melnik, Y.; Levin, A.; Minaev, N.; Mochalov, V.; Morozov, D.; Nogach, L.; Poslavskiy, S.; Ryazantsev, A.; Ryzhikov, S.; Semenov, P.; Shein, I.; Uzunian, A.; Vasiliev, A.; Yakutin, A.; Yabsley, B.; Bäck, T.; Cederwall, B.; Makónyi, K.; Tegnér, P. E.; von Würtemberg, K. M.; Belostotski, S.; Gavrilov, G.; Izotov, A.; Kashchuk, A.; Levitskaya, O.; Manaenkov, S.; Miklukho, O.; Naryshkin, Y.; Suvorov, K.; Veretennikov, D.; Zhadanov, A.; Rai, A. K.; Godre, S. S.; Duchat, R.; Amoroso, A.; Bussa, M. P.; Busso, L.; De Mori, F.; Destefanis, M.; Fava, L.; Ferrero, L.; Greco, M.; Maggiora, M.; Maniscalco, G.; Marcello, S.; Sosio, S.; Spataro, S.; Zotti, L.; Calvo, D.; Coli, S.; De Remigis, P.; Filippi, A.; Giraudo, G.; Lusso, S.; Mazza, G.; Mingnore, M.; Rivetti, A.; Wheadon, R.; Balestra, F.; Iazzi, F.; Introzzi, R.; Lavagno, A.; Younis, H.; Birsa, R.; Bradamante, F.; Bressan, A.; Martin, A.; Clement, H.; Gålnander, B.; Caldeira Balkeståhl, L.; Calén, H.; Fransson, K.; Johansson, T.; Kupsc, A.; Marciniewski, P.; Pettersson, J.; Schönning, K.; Wolke, M.; Zlomanczuk, J.; Díaz, J.; Ortiz, A.; Vinodkumar, P. C.; Parmar, A.; Chlopik, A.; Melnychuk, D.; Slowinski, B.; Trzcinski, A.; Wojciechowski, M.; Wronka, S.; Zwieglinski, B.; Bühler, P.; Marton, J.; Suzuki, K.; Widmann, E.; Zmeskal, J.; Fröhlich, B.; Khaneft, D.; Lin, D.; Zimmermann, I.; Semenov-Tian-Shansky, K.

2015-08-01

Baryon-to-meson Transition Distribution Amplitudes (TDAs) encoding valuable new information on hadron structure appear as building blocks in the collinear factorized description for several types of hard exclusive reactions. In this paper, we address the possibility of accessing nucleon-to-pion ( πN) TDAs from reaction with the future P¯ANDA detector at the FAIR facility. At high center-of-mass energy and high invariant mass squared of the lepton pair q 2, the amplitude of the signal channel admits a QCD factorized description in terms of πN TDAs and nucleon Distribution Amplitudes (DAs) in the forward and backward kinematic regimes. Assuming the validity of this factorized description, we perform feasibility studies for measuring with the P¯ANDA detector. Detailed simulations on signal reconstruction efficiency as well as on rejection of the most severe background channel, i.e. were performed for the center-of-mass energy squared s = 5 GeV2 and s = 10 GeV2, in the kinematic regions 3.0 < q 2 < 4.3 GeV2 and 5 < q 2 GeV2, respectively, with a neutral pion scattered in the forward or backward cone in the proton-antiproton center-of-mass frame. Results of the simulation show that the particle identification capabilities of the P¯ANDA detector will allow to achieve a background rejection factor of 5 · 107 (1 · 107) at low (high) q 2 for s = 5 GeV2, and of 1 · 108 (6 · 106) at low (high) q 2 for s = 10 GeV2, while keeping the signal reconstruction efficiency at around 40%. At both energies, a clean lepton signal can be reconstructed with the expected statistics corresponding to 2 fb-1 of integrated luminosity. The cross sections obtained from the simulations are used to show that a test of QCD collinear factorization can be done at the lowest order by measuring scaling laws and angular distributions. The future measurement of the signal channel cross section with P¯ANDA will provide a new test of the perturbative QCD description of a novel class of hard exclusive reactions and will open the possibility of experimentally accessing π TDAs.

Characterization of Generalized Young Measures Generated by Symmetric Gradients

NASA Astrophysics Data System (ADS)

De Philippis, Guido; Rindler, Filip

2017-06-01

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The "local" proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti's rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.

The Poincaré-Hopf Theorem for line fields revisited

NASA Astrophysics Data System (ADS)

Crowley, Diarmuid; Grant, Mark

2017-07-01

A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.

Common fixed point theorems for maps under a contractive condition of integral type

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

Heavy-quark production in gluon fusion at two loops in QCD

NASA Astrophysics Data System (ADS)

Czakon, M.; Mitov, A.; Moch, S.

2008-07-01

We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark-quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron-hadron collisions.

Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD corrections.

PubMed

Noth, David; Spira, Michael

2008-10-31

We present two-loop supersymmetry (SUSY) QCD corrections to the effective bottom Yukawa couplings within the minimal supersymmetric extension of the standard model (MSSM). The effective Yukawa couplings include the resummation of the nondecoupling corrections Deltam_{b} for large values of tanbeta. We have derived the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-quark-induced SUSY-electroweak contributions to Deltam_{b}. The scale dependence of the resummed Yukawa couplings is reduced from O(10%) to the percent level. These results reduce the theoretical uncertainties of the MSSM Higgs branching ratios to the accuracy which can be achieved at a future linear e;{+}e;{-} collider.

A Converse of the Mean Value Theorem Made Easy

ERIC Educational Resources Information Center

Mortici, Cristinel

2011-01-01

The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…

Recurrence theorems: A unified account

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

A variational theorem for creep with applications to plates and columns

NASA Technical Reports Server (NTRS)

Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R

1958-01-01

A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.

Correcting Duporcq's theorem☆

PubMed Central

Nawratil, Georg

2014-01-01

In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem. PMID:25540467

Dissociation of heavy quarkonium in hot QCD medium in a quasiparticle model

NASA Astrophysics Data System (ADS)

Agotiya, Vineet Kumar; Chandra, Vinod; Jamal, M. Yousuf; Nilima, Indrani

2016-11-01

Following a recent work on the effective description of the equations of state for hot QCD obtained from a hard thermal loop expression for the gluon self-energy, in terms of the quasigluons and quasiquarks and antiquarks with respective effective fugacities, the dissociation process of heavy quarkonium in hot QCD medium has been investigated. This has been done by investigating the medium modification to a heavy quark potential. The medium-modified potential has a quite different form (a long-range Coulomb tail in addition to the usual Yukawa term) in contrast to the usual picture of Debye screening. The flavor dependence binding energies of the heavy quarkonia states and the dissociation temperature have been obtained by employing the Debye mass for pure gluonic and full QCD case computed employing the quasiparticle picture. Thus, estimated dissociation patterns of the charmonium and bottomonium states, considering Debye mass from different approaches in the pure gluonic case and full QCD, have shown good agreement with the other potential model studies.

Going Beyond QCD in Lattice Gauge Theory

NASA Astrophysics Data System (ADS)

Fleming, G. T.

2011-01-01

Strongly coupled gauge theories (SCGT's) have been studied theoretically for many decades using numerous techniques. The obvious motivation for these efforts stemmed from a desire to understand the source of the strong nuclear force: Quantum Chromo-dynamics (QCD). Guided by experimental results, theorists generally consider QCD to be a well-understood SCGT. Unfortunately, it is not clear how to extend the lessons learned from QCD to other SCGT's. Particularly urgent motivators for new studies of other SCGT's are the ongoing searches for physics beyond the standard model (BSM) at the Large Hadron Collider (LHC) and the Tevatron. Lattice gauge theory (LGT) is a technique for systematically-improvable calculations in many SCGT's. It has become the standard for non-perturbative calculations in QCD and it is widely believed that it may be useful for study of other SCGT's in the realm of BSM physics. We will discuss the prospects and potential pitfalls for these LGT studies, focusing primarily on the flavor dependence of SU(3) gauge theory.

A study of jet production rates and a test of QCD on the Z 0 resonance

NASA Astrophysics Data System (ADS)

Akrawy, M. Z.; Alexander, G.; Allison, J.; Allport, P. P.; Anderson, K. J.; Armitage, J. C.; Arnison, G. T. J.; Ashton, P.; Azuelos, G.; Baines, J. T. M.; Ball, A. H.; Banks, J.; Barker, G. J.; Barlow, R. J.; Batley, J. R.; Bavaria, G.; Beard, C.; Beck, F.; Bell, K. W.; Bella, G.; Bethke, S.; Biebel, O.; Bloodworth, I. J.; Bock, P.; Boerner, H.; Breuker, H.; Brown, R. M.; Brun, R.; Buijs, A.; Burckhart, H. J.; Capiluppi, P.; Carnegie, R. K.; Carter, A. A.; Carter, J. R.; Chang, C. Y.; Charlton, D. G.; Chrin, J. T. M.; Cohen, I.; Conboy, J. E.; Couch, M.; Coupland, M.; Cuffiani, M.; Dado, S.; Dallavalle, G. M.; Davies, O. W.; Deninno, M. M.; Dieckmann, A.; Dittmar, M.; Dixit, M. S.; Duchesneau, D.; Duchovni, E.; Duerdoth, I. P.; Dumas, D.; El Mamouni, H.; Elcombe, P. A.; Estabrooks, P. G.; Fabbri, F.; Farthouat, P.; Fischer, H. M.; Fong, D. G.; French, M. T.; Fukunaga, C.; Gandois, B.; Ganel, O.; Gary, J. W.; Geddes, N. I.; Gee, C. N. P.; Geich-Gimbel, C.; Gensler, S. W.; Gentit, F. X.; Giacomelli, G.; Gibson, W. R.; Gillies, J. D.; Goldberg, J.; Goodrick, M. J.; Gorn, W.; Granite, D.; Gross, E.; Grosse-Wiesmann, P.; Grunhaus, J.; Hagedorn, H.; Hagemann, J.; Hansroul, M.; Hargrove, C. K.; Hart, J.; Hattersley, P. M.; Hatzifotiadou, D.; Hauschild, M.; Hawkes, C. M.; Heflin, E.; Heintze, J.; Hemingway, R. J.; Heuer, R. D.; Hill, J. C.; Hillier, S. J.; Hinde, P. S.; Ho, C.; Hobbs, J. D.; Hobson, P. R.; Hochman, D.; Holl, B.; Homer, R. J.; Hou, S. R.; Howarth, C. P.; Hughes-Jones, R. E.; Igo-Kemenes, P.; Imori, M.; Imrie, D. C.; Jawahery, A.; Jeffreys, P. W.; Jeremie, H.; Jimack, M.; Jin, E.; Jobes, M.; Jones, R. W. L.; Jovanovic, P.; Karlen, D.; Kawagoe, K.; Kawamoto, T.; Kellogg, R. G.; Kennedy, B. W.; Kleinwort, C.; Klem, D. E.; Knop, G.; Kobayashi, T.; Köpke, L.; Kokott, T. P.; Koshiba, M.; Kowalewski, R.; Kreutzmann, H.; Von Krogh, J.; Kroll, J.; Kyberd, P.; Lafferty, G. D.; Lamarche, F.; Larson, W. J.; Lasota, M. M. B.; Layter, J. G.; Le Du, P.; Leblanc, P.; Lellouch, D.; Lennert, P.; Lessard, L.; Levinson, L.; Lloyd, S. L.; Loebinger, F. K.; Lorah, J. M.; Lorazo, B.; Losty, M. J.; Ludwig, J.; Lupu, N.; Ma, J.; Macbeth, A. A.; Mannelli, M.; Marcellini, S.; Maringer, G.; Martin, J. P.; Mashimo, T.; Mättig, P.; Maur, U.; McMahon, T. J.; McPherson, A. C.; Meijers, F.; Menszner, D.; Merritt, F. S.; Mes, H.; Michelini, A.; Middleton, R. P.; Mikenberg, G.; Miller, D. J.; Milstene, C.; Minowa, M.; Mohr, W.; Montanari, A.; Mori, T.; Moss, M. W.; Muller, A.; Murphy, P. G.; Murray, W. J.; Nellen, B.; Nguyen, H. H.; Nozaki, M.; O'Dowd, A. J. P.; O'Neale, S. W.; O'Neill, B.; Oakham, F. G.; Odorici, F.; Ogg, M.; Oh, H.; Oreglia, M. J.; Orito, S.; Patrick, G. N.; Pawley, S. J.; Perez, A.; Pilcher, J. E.; Pinfold, J. L.; Plane, D. E.; Poli, B.; Possoz, A.; Pouladdej, A.; Pritchard, T. W.; Quast, G.; Raab, J.; Redmond, M. W.; Rees, D. L.; Regimbald, M.; Riles, K.; Roach, C. M.; Roehner, F.; Rollnik, A.; Roney, J. M.; Rossi, A. M.; Routenburg, P.; Runge, K.; Runolfsson, O.; Sanghera, S.; Sansum, R. A.; Sasaki, M.; Saunders, B. J.; Schaile, A. D.; Schaile, O.; Schappert, W.; Scharff-Hansen, P.; von der Schmitt, H.; Schreiber, S.; Schwarz, J.; Shapira, A.; Shen, B. C.; Sherwood, P.; Simon, A.; Siroli, G. P.; Skuja, A.; Smith, A. M.; Smith, T. J.; Snow, G. A.; Spreadbury, E. J.; Springer, R. W.; Sproston, M.; Stephens, K.; Stier, H. E.; Ströhmer, R.; Strom, D.; Takeda, H.; Takeshita, T.; Tsukamoto, T.; Turner, M. F.; Tysarczyk, G.; van den Plas, D.; Vandalen, G. J.; Virtue, C. J.; Wagner, A.; Wahl, C.; Wang, H.; Ward, C. P.; Ward, D. R.; Waterhouse, J.; Watkins, P. M.; Watson, A. T.; Watson, N. K.; Weber, M.; Weisz, S.; Wermes, N.; Weymann, M.; Wilson, G. W.; Wilson, J. A.; Wingerter, I.; Winterer, V.-H.; Wood, N. C.; Wotton, S.; Wuensch, B.; Wyatt, T. R.; Yaari, R.; Yamashita, H.; Yang, Y.; Yekutieli, G.; Zeuner, W.; Zorn, G. T.; Zylberajch, S.; OPAL Collaboration

1990-02-01

Relative production rates of multijet hadronic final states of Z 0 boson decays, observed in e +e - annihilation around 91 GeV centre of mass energy, are presented. The data can be well described by analytic O( αs2) QCD calculations and by QCD shower model calaculations with parameters as determined at lower energies. A first judgement of Λ overlineMS and of the renormalization scale μ2 in O( αs2) QCD results in values similar to those obtained in the continuum of e +e - annihilations. Significant scaling violations are observed when the 3-jet fractions are compared to the corresponding results from smaller centre of mass energies. They can be interpreted as being entirely due tot the energy dependence of αs, as proposed by the nonabelian nature of QCD, The possibility of an energy independent coupling constant can be excluded with a significance of 5.7 standard deviations.

Nuclear reactions from lattice QCD

DOE PAGES

Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.

2015-01-13

In this study, one of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculationsmore » of some of the low-energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.« less

The Top Quark, QCD, And New Physics.

DOE R&D Accomplishments Database

Dawson, S.

2002-06-01

The role of the top quark in completing the Standard Model quark sector is reviewed, along with a discussion of production, decay, and theoretical restrictions on the top quark properties. Particular attention is paid to the top quark as a laboratory for perturbative QCD. As examples of the relevance of QCD corrections in the top quark sector, the calculation of e{sup+}e{sup -}+ t{bar t} at next-to-leading-order QCD using the phase space slicing algorithm and the implications of a precision measurement of the top quark mass are discussed in detail. The associated production of a t{bar t} pair and a Higgs boson in either e{sup+}e{sup -} or hadronic collisions is presented at next-to-leading-order QCD and its importance for a measurement of the top quark Yulrawa coupling emphasized. Implications of the heavy top quark mass for model builders are briefly examined, with the minimal supersymmetric Standard Model and topcolor discussed as specific examples.

Phenomenological consequences of enhanced bulk viscosity near the QCD critical point

DOE PAGES

Monnai, Akihiko; Mukherjee, Swagato; Yin, Yi

2017-03-06

In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. Here, this work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding 1 + 1 dimensional causal relativistic hydrodynamical evolution at nonzero baryon density. We demonstrate that the critically enhanced bulk viscosity induces a substantial nonequilibrium pressure, effectively softening themore » equation of state, and leads to sizable effects in the flow velocity and single-particle distributions at the freeze-out. In conclusion, the observable effects that may arise due to the enhanced bulk viscosity in the vicinity of the QCD critical point can be used as complementary information to facilitate searches for the QCD critical point.« less

Progress towards quantum simulating the classical O(2) Model

DTIC Science & Technology

2014-12-01

approach by building up on simple models sharing some of the basic features of lattice QCD . In the context of condensed matter, a proof of principle that...independently. Explicit Hilbert space repre- sentations of the physical states and of their matrix elements are mostly absent from today’s lattice QCD ...to lattice QCD , seems possible and interesting. ACKNOWLEDGMENTS We thank Masanori Hanada, Peter Orland, Lode Pollet, Boris Svistunov, the participants

The International Conference on Vector and Parallel Computing (2nd)

DTIC Science & Technology

1989-01-17

Computation of the SVD of Bidiagonal Matrices" ...................................... 11 " Lattice QCD -As a Large Scale Scientific Computation...vectorizcd for the IBM 3090 Vector Facility. In addition, elapsed times " Lattice QCD -As a Large Scale Scientific have been reduced by using 3090...benchmarked Lattice QCD on a large number ofcompu- come from the wavefront solver routine. This was exten- ters: CrayX-MP and Cray 2 (vector

Computational Science: Ensuring America’s Competitiveness

DTIC Science & Technology

2005-06-01

Supercharging U. S. Innovation & Competitiveness, Washington, D.C. , July 2004. Davies, C. T. H. , et al. , “High-Precision Lattice QCD Confronts Experiment...together to form a class of particles call hadrons (that include protons and neutrons) . For 30 years, researchers in lattice QCD have been trying to use...the basic QCD equations to calculate the properties of hadrons, especially their masses, using numerical lattice gauge theory calculations in order to

QCDOC: A 10-teraflops scale computer for lattice QCD

NASA Astrophysics Data System (ADS)

Chen, D.; Christ, N. H.; Cristian, C.; Dong, Z.; Gara, A.; Garg, K.; Joo, B.; Kim, C.; Levkova, L.; Liao, X.; Mawhinney, R. D.; Ohta, S.; Wettig, T.

2001-03-01

The architecture of a new class of computers, optimized for lattice QCD calculations, is described. An individual node is based on a single integrated circuit containing a PowerPC 32-bit integer processor with a 1 Gflops 64-bit IEEE floating point unit, 4 Mbyte of memory, 8 Gbit/sec nearest-neighbor communications and additional control and diagnostic circuitry. The machine's name, QCDOC, derives from "QCD On a Chip".

Three-point Green functions in the odd sector of QCD

NASA Astrophysics Data System (ADS)

Kadavý, T.; Kampf, K.; Novotný, J.

2016-11-01

A review of familiar results of the three-point Green functions of currents in the odd-intrinsic parity sector of QCD is presented. Such Green functions include very well-known examples of VVP, VAS or AAP correlators. We also shortly present some of the new results for VVA and AAA Green functions with a discussion of their high-energy behaviour and its relation to the QCD condensates.

Renormalization scheme dependence of high-order perturbative QCD predictions

NASA Astrophysics Data System (ADS)

Ma, Yang; Wu, Xing-Gang

2018-02-01

Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Rossi, Giancarlo; Veneziano, Gabriele; Yankielowicz, Shimon

2017-12-01

Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong- CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.

Kenneth Wilson and Lattice QCD

NASA Astrophysics Data System (ADS)

Ukawa, Akira

2015-09-01

We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.

Flavour symmetry breaking in the kaon parton distribution amplitude

DOE PAGES

none,

2014-11-01

We compute the kaon's valence-quark (twist-two parton) distribution amplitude (PDA) by projecting its Poincaré-covariant Bethe–Salpeter wave-function onto the light-front. At a scale ζ = 2 GeV, the PDA is a broad, concave and asymmetric function, whose peak is shifted 12–16% away from its position in QCD's conformal limit. These features are a clear expression of SU(3)-flavour-symmetry breaking. They show that the heavier quark in the kaon carries more of the bound-state's momentum than the lighter quark and also that emergent phenomena in QCD modulate the magnitude of flavour-symmetry breaking: it is markedly smaller than one might expect based on themore » difference between light-quark current masses. Our results add to a body of evidence which indicates that at any energy scale accessible with existing or foreseeable facilities, a reliable guide to the interpretation of experiment requires the use of such nonperturbatively broadened PDAs in leading-order, leading-twist formulae for hard exclusive processes instead of the asymptotic PDA associated with QCD's conformal limit. We illustrate this via the ratio of kaon and pion electromagnetic form factors: using our nonperturbative PDAs in the appropriate formulae, F K/F π=1.23 at spacelike-Q 2=17 GeV 2, which compares satisfactorily with the value of 0.92(5) inferred in e +e - annihilation at s=17 GeV 2.« less

Production of heavy Higgs bosons and decay into top quarks at the LHC

NASA Astrophysics Data System (ADS)

Bernreuther, W.; Galler, P.; Mellein, C.; Si, Z.-G.; Uwer, P.

2016-02-01

We investigate the production of heavy, neutral Higgs boson resonances and their decays to top-quark top-antiquark (t t ¯) pairs at the Large Hadron Collider (LHC) at next-to-leading order (NLO) in the strong coupling of quantum chromodynamics (QCD). The NLO corrections to heavy Higgs boson production and the Higgs-QCD interference are calculated in the large mt limit with an effective K-factor rescaling. The nonresonant t t ¯ background is taken into account at NLO QCD including weak-interaction corrections. In order to consistently determine the total decay widths of the heavy Higgs bosons, we consider for definiteness the type-II two-Higgs-doublet extension of the standard model and choose three parameter scenarios that entail two heavy neutral Higgs bosons with masses above the t t ¯ threshold and unsuppressed Yukawa couplings to top quarks. For these three scenarios we compute, for the LHC operating at 13 TeV, the t t ¯ cross section and the distributions of the t t ¯ invariant mass, of the transverse top-quark momentum and rapidity, and of the cosine of the Collins-Soper angle with and without the two heavy Higgs resonances. For selected Mt t ¯ bins we estimate the significances for detecting a heavy Higgs signal in the t t ¯ dileptonic and lepton plus jets decay channels.

New Methods in Non-Perturbative QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Unsal, Mithat

2017-01-31

In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), andmore » there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.« less

Voronovskaja's theorem revisited

NASA Astrophysics Data System (ADS)

Tachev, Gancho T.

2008-07-01

We represent a new quantitative variant of Voronovskaja's theorem for Bernstein operator. This estimate improves the recent quantitative versions of Voronovskaja's theorem for certain Bernstein-type operators, obtained by H. Gonska, P. Pitul and I. Rasa in 2006.

The infrared behaviour of QCD Green's functions. Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

NASA Astrophysics Data System (ADS)

Alkofer, Reinhard; von Smekal, Lorenz

2001-11-01

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarised. Properties of ground state mesons are discussed on the basis of the ladder Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark-diquark correlations in the quantum field theory of confined quarks and gluons.

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Diagrammatic exponentiation for products of Wilson lines

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Sterman, George; Sung, Ilmo

2010-11-01

We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form factors and cross sections with two eikonal lines, to general soft functions in QCD and related gauge theories. Our coordinate space arguments apply to arbitrary paths for the lines.

A factorization approach to next-to-leading-power threshold logarithms

NASA Astrophysics Data System (ADS)

Bonocore, D.; Laenen, E.; Magnea, L.; Melville, S.; Vernazza, L.; White, C. D.

2015-06-01

Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading-power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the radiative jet function, responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey

NASA Astrophysics Data System (ADS)

Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan; Wang, Yifan

2018-03-01

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F-theorem and possibly a C-theorem in five-dimensional superconformal theories.

Closeout Report for CTEQ Summer School 2015

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Tao

The CTEQ Collaboration is an informal group of 37 experimental and theoretical high energy physicists from 20 universities and 5 national labs, engaged in a program to advance research in and understanding of QCD. This program includes the well-known collaborative project on global QCD analysis of parton distributions, the organization of a variety of workshops, periodic collaboration meetings, and the subject of this proposal: the CTEQ Summer Schools on QCD Analysis and Phenomenology.

Complex Langevin dynamics and zeroes of the fermion determinant

NASA Astrophysics Data System (ADS)

Aarts, Gert; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu

2017-05-01

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.

Quark-hadron phase structure of QCD matter from SU(4) Polyakov linear sigma model

NASA Astrophysics Data System (ADS)

Diab, Abdel Magied Abdel Aal; Tawfik, Abdel Nasser

2018-04-01

The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral condensates, σl, σs and σc of light, strange and charm quarks, respectively and the deconfinement order-parameters φ and φ at finite temperatures and densities (chemical potentials). The PLSM is considered to study the QCD equation of state in the presence of the chiral condensate of charm for different finite chemical potentials. The PLSM results are in a good agreement with the recent lattice QCD simulations. We conclude that, the charm condensate is likely not affected by the QCD phase-transition, where the corresponding critical temperature is greater than that of the light and strange quark condensates.

Moving Forward to Constrain the Shear Viscosity of QCD Matter

DOE PAGES

Denicol, Gabriel; Monnai, Akihiko; Schenke, Björn

2016-05-26

In this work, we demonstrate that measurements of rapidity differential anisotropic flow in heavy-ion collisions can constrain the temperature dependence of the shear viscosity to entropy density ratio η/s of QCD matter. Comparing results from hydrodynamic calculations with experimental data from the RHIC, we find evidence for a small η/s ≈ 0.04 in the QCD crossover region and a strong temperature dependence in the hadronic phase. A temperature independent η/s is disfavored by the data. We further show that measurements of the event-by-event flow as a function of rapidity can be used to independently constrain the initial state fluctuations inmore » three dimensions and the temperature dependent transport properties of QCD matter.« less

Lepton-rich cold QCD matter in protoneutron stars

NASA Astrophysics Data System (ADS)

Jiménez, J. C.; Fraga, E. S.

2018-05-01

We investigate protoneutron star matter using the state-of-the-art perturbative equation of state for cold and dense QCD in the presence of a fixed lepton fraction in which both electrons and neutrinos are included. Besides computing the modifications in the equation of state due to the presence of trapped neutrinos, we show that stable strange quark matter has a more restricted parameter space. We also study the possibility of nucleation of unpaired quark matter in the core of protoneutron stars by matching the lepton-rich QCD pressure onto a hadronic equation of state, namely TM1 with trapped neutrinos. Using the inherent dependence of perturbative QCD on the renormalization scale parameter, we provide a measure of the uncertainty in the observables we compute.

Curvature of the freeze-out line in heavy ion collisions

DOE PAGES

Bazavov, A.; Ding, H. -T.; Hegde, P.; ...

2016-01-28

Here, we calculate the mean and variance of net-baryon number and net-electric charge distributions from quantum chromodynamics (QCD) using a next-to-leading order Taylor expansion in terms of temperature and chemical potentials. Moreover, these expansions with experimental data from STAR and PHENIX are compared, we determine the freeze-out temperature in the limit of vanishing baryon chemical potential, and, for the first time, constrain the curvature of the freeze-out line through a direct comparison between experimental data on net-charge fluctuations and a QCD calculation. We obtain a bound on the curvature coefficient, κmore » $^f$$_2$$<0.011, that is compatible with lattice QCD results on the curvature of the QCD transition line.« less

Visual Theorems.

ERIC Educational Resources Information Center

Davis, Philip J.

1993-01-01

Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

Note on the theorems of Bjerknes and Crocco

NASA Technical Reports Server (NTRS)

Theodorsen, Theodore

1946-01-01

The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.

Analysis of non locality proofs in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2012-02-01

Two kinds of non-locality theorems in Quantum Mechanics are taken into account: the theorems based on the criterion of reality and the quite different theorem proposed by Stapp. In the present work the analyses of the theorem due to Greenberger, Horne, Shimony and Zeilinger, based on the criterion of reality, and of Stapp's argument are shown. The results of these analyses show that the alleged violations of locality cannot be considered definitive.

PYGMALION: A Creative Programming Environment

DTIC Science & Technology

1975-06-01

iiiiiimimmmimm wm^m^mmm’ wi-i ,»■»’■’.■- v* 26 Examples of Purely Iconic Reasoning 1-H Pythagoras ’ original proof of the Pythagorean Theorem ... Theorem Proving Machine񓟋. His program employed properties of the representation to guide the proof of theorems . His simple heruristic "Reject...one theorem the square of the hypotenuse. "Every proposition is presented as a self-contained fact relying on its own intrinsic evidence. Instead

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

Studies of L-T Separated Kaon Electroproduction

NASA Astrophysics Data System (ADS)

Trotta, Richard; Horn, Tanja; Vargas, Andres

2017-09-01

QCD is characterized by two emergent phenomena: confinement and dynamical chiral symmetry breaking (DCSB). Pion and kaon form factors are of particular interest as they are connected to the Goldstone modes of DCSB. The flavor degrees of freedom of the produced meson selectively probe aspects of the reaction mechanism and the transition from hadronic to partonic degrees of freedom. There has been significant progress in the theoretical description of the nucleon structure in terms of QCD degrees of freedom, in particular through Generalized Parton Distributions (GPDs).The last decade saw a dramatic improvement in precision of charged pion form factor data and new results have become available on the pion transition form factor. The kaon provides an interesting way to expand these studies, opening the possibility to access the production mechanism involving strangeness. Kaon data at larger virtual photon mass allow one to search for the onset of the partonic picture. In this regime, hard and soft physics have been shown to factorize and GPDs provide the most complete description of the non-perturbative physics. The lack of necessary experimental facilities has left a gap in L-T separated data for exclusive K + production from the proton above the resonance region.The newly upgraded 12 GeV beam energy at Jlab, in addition to the recently built SHMS spectrometer for Hall C, has provided an opportunity to expand the kaon data. Recent kaon form factor and cross section results will be discussed showing the impact of E12-09-011, the running Jlab 12 GeV kaon experiment. NSF Grants PHY1306227, PHY1306418 and PHY1530874.

Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

NASA Astrophysics Data System (ADS)

Collins, J.; Gamberg, L.; Prokudin, A.; Rogers, T. C.; Sato, N.; Wang, B.

2016-08-01

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W +Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and Q dependence of the cross sections at lower Q are largely governed by the matching to the Y term.

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

DOE PAGES

Brodsky, Stanley J.

2018-01-01

Tmore » he QCD light-front Hamiltonian equation H L F Ψ = M 2 Ψ derived from quantization at fixed LF time τ = t     +     z / c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. he QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the q q ¯ invariant mass squared. he same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and A d S 5 , if one modifies the A d S 5 action by the dilaton e κ 2 z 2 in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. he pion q q ¯ eigenstate has zero mass at m q = 0 . he superconformal relations also can be extended to heavy-light quark mesons and baryons. his approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 . he mass scale κ underlying hadron masses can be connected to the parameter Λ M S ¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. he result is an effective coupling α s ( Q 2 ) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.« less

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.

Tmore » he QCD light-front Hamiltonian equation H L F Ψ = M 2 Ψ derived from quantization at fixed LF time τ = t     +     z / c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. he QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the q q ¯ invariant mass squared. he same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and A d S 5 , if one modifies the A d S 5 action by the dilaton e κ 2 z 2 in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. he pion q q ¯ eigenstate has zero mass at m q = 0 . he superconformal relations also can be extended to heavy-light quark mesons and baryons. his approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 . he mass scale κ underlying hadron masses can be connected to the parameter Λ M S ¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. he result is an effective coupling α s ( Q 2 ) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.« less

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

General Theorems about Homogeneous Ellipsoidal Inclusions

ERIC Educational Resources Information Center

Korringa, J.; And Others

1978-01-01

Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

Concerns Expressed by Parents of Children with Pervasive Developmental Disorders for Different Time Periods of the Day: A Case–Control Study

PubMed Central

Sasaki, Yoshinori; Usami, Masahide; Sasayama, Daimei; Okada, Takashi; Iwadare, Yoshitaka; Watanabe, Kyota; Ushijima, Hirokage; Tanaka, Tetsuya; Harada, Maiko; Tanaka, Hiromi; Kodaira, Masaki; Sugiyama, Nobuhiro; Sawa, Tetsuji; Saito, Kazuhiko

2015-01-01

Background/Aim The Questionnaire: Children with Difficulties (QCD) is a parent-assessed questionnaire designed to evaluate child’s difficulties in functioning during specific periods of the day. This study aimed to evaluate difficulties in daily functioning of children and adolescents with pervasive developmental disorder (PDD) using the QCD. Results were compared with those for a community sample. Methods A case–control design was used. The cases comprised elementary school students (182 males, 51 females) and junior high school students (100 males, 39 females) with PDD, whereas a community sample of elementary school students (568 males, 579 females) and junior high school students (180 males, 183 females) was enrolled as controls. Their behavior was assessed using the QCD, the Tokyo Autistic Behavior Scale (TABS), the ADHD-rating scale (ADHD-RS), and the Oppositional Defiant Behavior Inventory (ODBI) for elementary and junior high school students, respectively. Effects of gender and diagnosis on the QCD scores were analyzed. Correlation coefficients between QCD and TABS, ADHD-RS, and ODBI scores were analyzed. Results The QCD scores for the children with PDD were significantly lower compared with those from the community sample (P < 0.001). Significantly strong correlations were observed in more areas of the ADHD-RS and ODBI scores compared with the TABS scores. Conclusions Children with PDD experienced greater difficulties in completing basic daily activities; moreover, their QCD scores revealed stronger associations with their ADHD-RS and ODBI scores in comparison with their TABS scores. The difficulties of PDD, ADHD and OBDI symptoms combined in children makes it necessary to assess all diagnoses before any therapy for PDD is initiated in order to be able to evaluate its results properly. PMID:25898260

QCD and Light-Front Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; de Teramond, Guy F.; /SLAC /Southern Denmark U., CP3-Origins /Costa Rica U.

2011-01-10

AdS/QCD, the correspondence between theories in a dilaton-modified five-dimensional anti-de Sitter space and confining field theories in physical space-time, provides a remarkable semiclassical model for hadron physics. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The result is a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equalmore » light-front time and determines the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. The hadron eigenstates generally have components with different orbital angular momentum; e.g., the proton eigenstate in AdS/QCD with massless quarks has L = 0 and L = 1 light-front Fock components with equal probability. Higher Fock states with extra quark-anti quark pairs also arise. The soft-wall model also predicts the form of the nonperturbative effective coupling and its {beta}-function. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method to systematically include QCD interaction terms. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.« less

A no-hair theorem for black holes in f(R) gravity

NASA Astrophysics Data System (ADS)

Cañate, Pedro

2018-01-01

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

Generalized Browder's and Weyl's theorems for Banach space operators

NASA Astrophysics Data System (ADS)

Curto, Raúl E.; Han, Young Min

2007-12-01

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).

Post-Lie algebras and factorization theorems

NASA Astrophysics Data System (ADS)

Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

2017-09-01

In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

Three-particle N π π state contribution to the nucleon two-point function in lattice QCD

NASA Astrophysics Data System (ADS)

Bär, Oliver

2018-05-01

The three-particle N π π state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients, the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice.

Better than $l/Mflops sustained: a scalable PC-based parallel computer for lattice QCD

NASA Astrophysics Data System (ADS)

Fodor, Zoltán; Katz, Sándor D.; Papp, Gábor

2003-05-01

We study the feasibility of a PC-based parallel computer for medium to large scale lattice QCD simulations. The Eötvös Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single precision sustained performance for dynamical QCD without communication is 1510 Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD, respectively (for 64-bit applications the performance is approximately halved). The novel feature of our system is its communication architecture. In order to have a scalable, cost-effective machine we use Gigabit Ethernet cards for nearest-neighbor communications in a two-dimensional mesh. This type of communication is cost effective (only 30% of the hardware costs is spent on the communication). According to our benchmark measurements this type of communication results in around 40% communication time fraction for lattices upto 48 3·96 in full QCD simulations. The price/sustained-performance ratio for full QCD is better than l/Mflops for Wilson (and around 1.5/Mflops for staggered) quarks for practically any lattice size, which can fit in our parallel computer. The communication software is freely available upon request for non-profit organizations.

Lanchester-Type Models of Warfare. Volume II

DTIC Science & Technology

1980-10-01

the so-called PERRON - FROBENIUS theorem50 for nonnegative matrices that one can guarantee that (without any further assumptions about A and B) there...always exists a vector of nonnegative values such that, for example, (7.18.6) holds. Before we state the PERRON - FROBENIUS theorem for nonnegative...a proof of this important theorem). THEOREM .5.-1.1 ( PERRON [121] and FROBENIUS [60]): Let C z 0 be an n x n matrix. Then, 1. C has a nonnegative real

A remark on the energy conditions for Hawking's area theorem

NASA Astrophysics Data System (ADS)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bose-Fermi degeneracies in large N adjoint QCD

DOE PAGES

Basar, Gokce; Cherman, Aleksey; McGady, David

2015-07-06

Here, we analyze the large N limit of adjoint QCD, an SU( N) gauge theory with N f flavors of massless adjoint Majorana fermions, compactified on S 3 × S 1. We focus on the weakly-coupled confining small- S 3 regime. If the fermions are given periodic boundary conditions on S 1, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any S 1 size L, even though the bosonicmore » and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any L ~ N 0, explaining how it is able to enjoy large N volume independence for any L. The large N boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite N, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large N limit.« less

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Haque, Najmul; Mustafa, Munshi G.; Strickland, Michael

2016-03-01

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials μq using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and finite baryon, strangeness, and isospin chemical potentials μB, μS, and μI. We calculate the pressure at nonzero μB and μI with μS=0 , and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero μI with μB=μS=0 . The second- and fourth-order isospin susceptibilities are calculated at μB=μS=μI=0 . Our results can be directly compared to lattice QCD without Taylor expansions around μq=0 since QCD has no sign problem at μB=μS=0 and finite isospin chemical potential μI.

Lattice QCD results on soft and hard probes of strongly interacting matter

NASA Astrophysics Data System (ADS)

Kaczmarek, Olaf

2017-11-01

We present recent results from lattice QCD relevant for the study of strongly interacting matter as it is produced in heavy ion collision experiments. The equation of state at non-vanishing density from a Taylor expansion up to 6th order will be discussed for a strangeness neutral system and using the expansion coefficients of the series limits on the critical point are estimated. Chemical freeze-out temperatures from the STAR and ALICE Collaborations will be compared to lines of constant physics calculated from the Taylor expansion of QCD bulk thermodynamic quantities. We show that qualitative features of the √{sNN} dependence of skewness and kurtosis ratios of net proton-number fluctuations measured by the STAR Collaboration can be understood from QCD results for cumulants of conserved baryon-number fluctuations. As an example for recent progress towards the determination of spectral and transport properties of the QGP from lattice QCD, we will present constraints on the thermal photon rate determined from a spectral reconstruction of continuum extrapolated lattice correlation functions in combination with input from most recent perturbative calculations.

Inclusive jet cross section and strong coupling constant measurements at CMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cerci, Salim, E-mail: Salim.Cerci@cern.ch

2016-03-25

The probes which are abundantly produced in high energetic proton-proton (pp) collisions at the LHC are called jets. Events with jets can be described by Quantum Chromodynamics (QCD) in terms of parton-parton scattering. The inclusive jet cross section in pp collision is the fundamental quantity which can be measured and predicted within the framework of perturbative QCD (pQCD). The strong coupling constant α{sub S} which can be determined empirically in the limit of massless quarks, is the single parameter in QCD. The jet measurements can also be used to determine strong coupling constant α{sub S} and parton density functions (PDFs).more » The recent jet measurements which are performed with the data collected by the CMS detector at different center-of-mass energies and down to very low transverse momentum p{sub T} are presented. The measurements are compared to Monte Carlo predictions and perturbative calculations up to next-to-next-to leading order. Finally, the precision jet measurements give further insight into the QCD dynamics.« less

Conjecture about the 2-Flavour QCD Phase Diagram

NASA Astrophysics Data System (ADS)

Nava Blanco, M. A.; Bietenholz, W.; Fernández Téllez, A.

2017-10-01

The QCD phase diagram, in particular its sector of high baryon density, is one of the most prominent outstanding mysteries within the Standard Model of particle physics. We sketch a project how to arrive at a conjecture for the case of two massless quark flavours. The pattern of spontaneous chiral symmetry breaking is isomorphic to the spontaneous magnetisation in an O(4) non-linear σ-model, which can be employed as a low-energy effective theory to study the critical behaviour. We focus on the 3d O(4) model, where the configurations are divided into topological sectors, as in QCD. A topological winding with minimal Euclidean action is denoted as a skyrmion, and the topological charge corresponds to the QCD baryon number. This effective model can be simulated on a lattice with a powerful cluster algorithm, which should allow us to identify the features of the critical temperature, as we proceed from low to high baryon density. In this sense, this projected numerical study has the potential to provide us with a conjecture about the phase diagram of QCD with two massless quark flavours.

Precision Light Flavor Physics from Lattice QCD

NASA Astrophysics Data System (ADS)

Murphy, David

In this thesis we present three distinct contributions to the study of light flavor physics using the techniques of lattice QCD. These results are arranged into four self-contained papers. The first two papers concern global fits of the quark mass, lattice spacing, and finite volume dependence of the pseudoscalar meson masses and decay constants, computed in a series of lattice QCD simulations, to partially quenched SU(2) and SU(3) chiral perturbation theory (chiPT). These fits determine a subset of the low energy constants of chiral perturbation theory -- in some cases with increased precision, and in other cases for the first time -- which, once determined, can be used to compute other observables and amplitudes in chiPT. We also use our formalism to self-consistently probe the behavior of the (asymptotic) chiral expansion as a function of the quark masses by repeating the fits with different subsets of the data. The third paper concerns the first lattice QCD calculation of the semileptonic K0 → pi-l +nul ( Kl3) form factor at vanishing momentum transfer, f+Kpi(0), with physical mass domain wall quarks. The value of this form factor can be combined with a Standard Model analysis of the experimentally measured K0 → pi -l+nu l decay rate to extract a precise value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus, and to test unitarity of the CKM matrix. We also discuss lattice calculations of the pion and kaon decay constants, which can be used to extract Vud through an analogous Standard Model analysis of experimental constraints on leptonic pion and kaon decays. The final paper explores the recently proposed exact one flavor algorithm (EOFA). This algorithm has been shown to drastically reduce the memory footprint required to simulate single quark flavors on the lattice relative to the widely used rational hybrid Monte Carlo (RHMC) algorithm, while also offering modest O(20%) speed-ups. We independently derive the exact one flavor action, explore its equivalence to the RHMC action, and demonstrate that additional preconditioning techniques can be used to significantly accelerate EOFA simulations. We apply EOFA to the ongoing RBC/UKQCD calculation of the Delta I = 1/2 K → pipi decay amplitude, and demonstrate that, in this context, gauge field configurations can be generated a factor of 4.2 times faster using an EOFA-based simulation rather than the previous RHMC-based simulations. We expect that EOFA will help to significantly reduce the statistical error in the first-principles determination of the Standard Model CP-violation parameters epsilon and epsilon' offered by the K → pipi calculation.

Features and flaws of a contact interaction treatment of the kaon

NASA Astrophysics Data System (ADS)

Chen, Chen; Chang, Lei; Roberts, Craig D.; Schmidt, Sebastian M.; Wan, Shaolong; Wilson, David J.

2013-04-01

Elastic and semileptonic transition form factors for the kaon and pion are calculated using the leading order in a global-symmetry-preserving truncation of the Dyson-Schwinger equations and a momentum-independent form for the associated kernels in the gap and Bethe-Salpeter equations. The computed form factors are compared both with those obtained using the same truncation but an interaction that preserves the one-loop renormalization-group behavior of QCD and with data. The comparisons show that in connection with observables revealed by probes with |Q2|≲M2, where M≈0.4GeV is an infrared value of the dressed-quark mass, results obtained using a symmetry-preserving regularization of the contact interaction are not realistically distinguishable from those produced by more sophisticated kernels, and available data on kaon form factors do not extend into the domain whereupon one could distinguish among the interactions. The situation differs if one includes the domain Q2>M2. Thereupon, a fully consistent treatment of the contact interaction produces form factors that are typically harder than those obtained with QCD renormalization-group-improved kernels. Among other things also described are a Ward identity for the inhomogeneous scalar vertex, similarity between the charge distribution of a dressed u quark in the K+ and that of the dressed u quark in the π+, and reflections upon the point whereat one might begin to see perturbative behavior in the pion form factor. Interpolations of the form factors are provided, which should assist in working to chart the interaction between light quarks by explicating the impact on hadron properties of differing assumptions about the behavior of the Bethe-Salpeter kernel.

Axial-vector form factors of the nucleon from lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Rajan; Jang, Yong-Chull; Lin, Huey-Wen

In this paper, we present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2 + 1 + 1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06 , 0.09, and 0.12 fm and light-quark masses corresponding to the pion masses M π ≈ 135, 225, and 310 MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of G A (Q 2)more » and the induced pseudoscalar form factor G P(Q 2) . We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius r A data to obtain physical estimates. Using the dipole ansatz to fit the Q 2 behavior we obtain r A | dipole = 0.49(3) fm , which corresponds to M A = 1.39(9) GeV , and is consistent with M A = 1.35(17) GeV obtained by the miniBooNE collaboration. The estimate obtained using the z -expansion is r A | z - expansion = 0.46(6) fm, and the combined result is r A | combined = 0.48(4) fm. Analysis of the induced pseudoscalar form factor G P (Q 2) yields low estimates for g* P and g πNN compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. Lastly, we find that these low values are due to large deviations in the PCAC relation between the three form factors, and in the pion-pole dominance hypothesis.« less

Λ b → pℓ¯ν¯ ℓ and Λ b → Λ cℓ¯ν¯ ℓ form factors from lattice QCD with relativistic heavy quarks

DOE PAGES

Detmold, William; Lehner, Christoph; Meinel, Stefan

2015-08-04

Measurements of the Λ b → pℓ¯ν¯ ℓ and Λ b → Λ cℓ¯ν¯ ℓ decay rates can be used to determine the magnitudes of the Cabibbo-Kobayashi-Maskawa matrix elements V ub and V cb, provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2+1 flavors of dynamical domain-wall fermions. The b and c quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, usingmore » gauge-field configurations generated by the RBC and UKQCD Collaborations. The b → u and b → c currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the q² dependence using z expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the Λ b → pℓ¯ν¯ ℓ and Λ b → Λ cℓ¯ν¯ ℓdifferential and integrated decay rates. Combined with experimental data, our results enable determinations of |V ub|, |V cb|, and |V ub/V cb| with theory uncertainties of 4.4%, 2.2%, and 4.9%, respectively.« less

Axial-vector form factors of the nucleon from lattice QCD

DOE PAGES

Gupta, Rajan; Jang, Yong-Chull; Lin, Huey-Wen; ...

2017-12-04

In this paper, we present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2 + 1 + 1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06 , 0.09, and 0.12 fm and light-quark masses corresponding to the pion masses M π ≈ 135, 225, and 310 MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of G A (Q 2)more » and the induced pseudoscalar form factor G P(Q 2) . We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius r A data to obtain physical estimates. Using the dipole ansatz to fit the Q 2 behavior we obtain r A | dipole = 0.49(3) fm , which corresponds to M A = 1.39(9) GeV , and is consistent with M A = 1.35(17) GeV obtained by the miniBooNE collaboration. The estimate obtained using the z -expansion is r A | z - expansion = 0.46(6) fm, and the combined result is r A | combined = 0.48(4) fm. Analysis of the induced pseudoscalar form factor G P (Q 2) yields low estimates for g* P and g πNN compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. Lastly, we find that these low values are due to large deviations in the PCAC relation between the three form factors, and in the pion-pole dominance hypothesis.« less

Search for the pentaquark resonance signature in lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

B. G. Lasscock; J. Hedditch; Derek Leinweber

2005-02-01

Claims concerning the possible discovery of the {Theta}{sup +} pentaquark, with minimal quark content uudd{bar s}, have motivated our comprehensive study into possible pentaquark states using lattice QCD. We review various pentaquark interpolating fields in the literature and create a new candidate ideal for lattice QCD simulations. Using these interpolating fields we attempt to isolate a signal for a five-quark resonance. Calculations are performed using improved actions on a large 20{sup 3} x 40 lattice in the quenched approximation. The standard lattice resonance signal of increasing attraction between baryon constituents for increasing quark mass is not observed for spin-1/2 pentaquarkmore » states. We conclude that evidence supporting the existence of a spin-1/2 pentaquark resonance does not exist in quenched QCD.« less

RPA treatment of a motivated QCD Hamiltonian in the SO(4) (2 + 1)-flavor limit: Light and strange mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle-hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like η,η‧,K,ρ,ω,ϕ, as well as the pion (π).

Hadron interactions and exotic hadrons from lattice QCD

NASA Astrophysics Data System (ADS)

Ikeda, Yoichi

2014-09-01

One of the interesting subjects in hadron physics is to look for the multiquark configurations. One of candidates is the H-dibaryon (udsuds), and the possibility of the bound H-dibaryon has been recently studied from lattice QCD. We also extend the HAL QCD method to define potentials on the lattice between baryons to meson-meson systems including charm quarks to search for the bound tetraquark Tcc (ud c c) and Tcs (ud c s). In the presentation, after reviewing the HAL QCD method, we report the results on the H-dibaryon, the tetraquark Tcc (ud c c) and Tcs (ud c s), where we have employed the relativistic heavy quark action to treat the charm quark dynamics with pion masses, mπ = 410, 570, 700 MeV.

Kaon-Nucleon potential from lattice QCD

NASA Astrophysics Data System (ADS)

Ikeda, Y.; Aoki, S.; Doi, T.; Hatsuda, T.; Inoue, T.; Ishii, N.; Murano, K.; Nemura, H.; Sasaki, K.

2010-04-01

We study the K N interactions in the I(Jπ) = 0(1/2-) and 1(1/2-) channels and associated exotic state Θ+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to mπ = 871 MeV. The s-wave K N potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I = 1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I = 0 potential is found to have attractive well at mid range. From these potentials, the K N scattering phase shifts are calculated and compared with the experimental data.

Inclusive parton cross sections in photoproduction and photon structure

NASA Astrophysics Data System (ADS)

Ahmed, T.; Aid, S.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Arpagaus, M.; Babaev, A.; Baehr, J.; Bán, J.; Ban, Y.; Baranov, P.; Barrelet, E.; Bartel, W.; Barth, M.; Bassler, U.; Beck, H. P.; Behrend, H.-J.; Belousov, A.; Berger, Ch.; Bernardi, G.; Bernet, R.; Bertrand-Coremans, G.; Besançon, M.; Beyer, R.; Biddulph, P.; Bispham, P.; Bizot, J. C.; Blobel, V.; Borras, K.; Botterweck, F.; Boudry, V.; Braemer, A.; Brasse, F.; Braunschweig, W.; Brisson, V.; Bruncko, D.; Brune, C.; Buchholz, R.; Büngener, L.; Bürger, J.; Büsser, F. W.; Buniatian, A.; Burke, S.; Burton, M.; Buschhorn, G.; Campbell, A. J.; Carli, T.; Charles, F.; Charlet, M.; Clarke, D.; Clegg, A. B.; Clerbaux, B.; Colombo, M.; Contreras, J. G.; Cormack, C.; Coughlan, J. A.; Courau, A.; Coutures, Ch.; Cozzika, G.; Criegee, L.; Cussans, D. G.; Cvach, J.; Dagoret, S.; Dainton, J. B.; Dau, W. D.; Daum, K.; David, M.; Delcourt, B.; Del Buono, L.; De Roeck, A.; De Wolf, E. A.; Di Nezza, P.; Dollfus, C.; Dowell, J. D.; Dreis, H. B.; Droutskoi, A.; Duboc, J.; Düllmann, D.; Dünger, O.; Duhm, H.; Ebert, J.; Ebert, T. R.; Eckerlin, G.; Efremenko, V.; Egli, S.; Ehrlichmann, H.; Eichenberger, S.; Eichler, R.; Eisele, F.; Eisenhandler, E.; Ellison, R. J.; Elsen, E.; Erdmann, M.; Erdmann, W.; Evrard, E.; Favart, L.; Fedotov, A.; Feeken, D.; Felst, R.; Feltesse, J.; Ferencei, J.; Ferrarotto, F.; Flamm, K.; Fleischer, M.; Flieser, M.; Flügge, G.; Fomenko, A.; Fominykh, B.; Forbush, M.; Formánek, J.; Foster, J. M.; Franke, G.; Fretwurst, E.; Gabathuler, E.; Gabathuler, K.; Gamerdinger, K.; Garvey, J.; Gayler, J.; Gebauer, M.; Gellrich, A.; Genzel, H.; Gerhards, R.; Goerlach, U.; Goerlich, L.; Gogitidze, N.; Goldberg, M.; Goldner, D.; Gonzalez-Pineiro, B.; Gorelov, I.; Goritchev, P.; Grab, C.; Grässler, H.; Grässler, R.; Greenshaw, T.; Grindhammer, G.; Gruber, A.; Gruber, C.; Haack, J.; Haidt, D.; Hajduk, L.; Hamon, O.; Hampel, M.; Hanlon, E. M.; Hapke, M.; Haynes, W. J.; Heatherington, J.; Heinzelmann, G.; Henderson, R. C. W.; Henschel, H.; Herynek, I.; Hess, M. F.; Hildesheim, W.; Hill, P.; Hiller, K. H.; Hilton, C. D.; Hladký, J.; Hoeger, K. C.; Höppner, M.; Horisberger, R.; Hudgson, V. L.; Huet, Ph.; Hütte, M.; Hufnagel, H.; Ibbotson, M.; Itterbeck, H.; Jabiol, M.-A.; Jacholkowska, A.; Jacobsson, C.; Jaffre, M.; Janoth, J.; Jansen, T.; Jönsson, L.; Johnson, D. P.; Johnson, L.; Jung, H.; Kalmus, P. I. P.; Kant, D.; Kaschowitz, R.; Kasselmann, P.; Kathage, U.; Katzy, J.; Kaufmann, H. H.; Kazarian, S.; Kenyon, I. R.; Kermiche, S.; Keuker, C.; Kiesling, C.; Klein, M.; Kleinwort, C.; Knies, G.; Ko, W.; Köhler, T.; Köhne, J. H.; Kolanoski, H.; Kole, F.; Kolya, S. D.; Korbel, V.; Korn, M.; Kostka, P.; Kotelnikov, S. K.; Krämerkämper, T.; Krasny, M. W.; Krehbiel, H.; Krücker, D.; Krüger, U.; Krüner-Marquis, U.; Kubenka, J. P.; Küster, H.; Kuhlen, M.; Kurča, T.; Kurzhöfer, J.; Kuznik, B.; Lacour, D.; Lamarche, F.; Lander, R.; Landon, M. P. J.; Lange, W.; Lanius, P.; Laporte, J.-F.; Lebedev, A.; Leverenz, C.; Levonian, S.; Ley, Ch.; Lindner, A.; Lindström, G.; Link, J.; Linsel, F.; Lipinski, J.; List, B.; Lobo, G.; Loch, P.; Lohmander, H.; Lomas, J.; Lopez, G. C.; Lubimov, V.; Lüke, D.; Magnussen, N.; Malinovski, E.; Mani, S.; Maraček, R.; Marage, P.; Marks, J.; Marshall, R.; Martens, J.; Martin, R.; Martyn, H.-U.; Martyniak, J.; Masson, S.; Mavroidis, T.; Maxfield, S. J.; McMahon, S. J.; Mehta, A.; Meier, K.; Mercer, D.; Merz, T.; Meyer, C. A.; Meyer, H.; Meyer, J.; Migliori, A.; Mikocki, S.; Milstead, D.; Moreau, F.; Morris, J. V.; Mroczko, E.; Müller, G.; Müller, K.; Murín, P.; Nagovizin, V.; Nahnhauer, R.; Naroska, B.; Naumann, Th.; Newman, P. R.; Newton, D.; Neyret, D.; Nguyen, H. K.; Nicholls, T. C.; Niebergall, F.; Niebuhr, C.; Niedzballa, Ch.; Nisius, R.; Nowak, G.; Noyes, G. W.; Nyberg-Werther, M.; Oakden, M.; Oberlack, H.; Obrock, U.; Olsson, J. E.; Ozerov, D.; Panaro, E.; Panitch, A.; Pascaud, C.; Patel, G. D.; Peppel, E.; Perez, E.; Phillips, J. P.; Pichler, Ch.; Pieuchot, A.; Pitzl, D.; Pope, G.; Prell, S.; Prosi, R.; Rabbertz, K.; Rädel, G.; Raupach, F.; Reimer, P.; Reinshagen, S.; Ribarics, P.; Rick, H.; Riech, V.; Riedlberger, J.; Riess, S.; Rietz, M.; Rizvi, E.; Robertson, S. M.; Robmann, P.; Roloff, H. E.; Roosen, R.; Rosenbauer, K.; Rostovtsev, A.; Rouse, F.; Royon, C.; Rüter, K.; Rusakov, S.; Rybicki, K.; Rylko, R.; Sahlmann, N.; Salesch, S. G.; Sanchez, E.; Sankey, D. P. C.; Schacht, P.; Schiek, S.; Schleper, P.; von Schlippe, W.; Schmidt, C.; Schmidt, D.; Schmidt, G.; Schöning, A.; Schröder, V.; Schuhmann, E.; Schwab, B.; Schwind, A.; Sefkow, F.; Seidel, M.; Sell, R.; Semenov, A.; Shekelyan, V.; Sheviakov, I.; Shooshtari, H.; Shtarkov, L. N.; Siegmon, G.; Siewert, U.; Sirois, Y.; Skillicorn, I. O.; Smirnov, P.; Smith, J. R.; Solochenko, V.; Soloviev, Y.; Spiekermann, J.; Spielman, S.; Spitzer, H.; Starosta, R.; Steenbock, M.; Steffen, P.; Steinberg, R.; Stella, B.; Stephens, K.; Stier, J.; Stiewe, J.; Stösslein, U.; Stolze, K.; Strachota, J.; Straumann, U.; Struczinski, W.; Sutton, J. P.; Tapprogge, S.; Tchernyshov, V.; Thiebaux, C.; Thompson, G.; Truöl, P.; Turnau, J.; Tutas, J.; Uelkes, P.; Usik, A.; Valkár, S.; Valkárová, A.; Vallée, C.; Van Esch, P.; Van Mechelen, P.; Vartapetian, A.; Vazdik, Y.; Verrecchia, P.; Villet, G.; Wacker, K.; Wagener, A.; Wagener, M.; Walker, I. W.; Walther, A.; Weber, G.; Weber, M.; Wegener, D.; Wegner, A.; Wellisch, H. P.; West, L. R.; Willard, S.; Winde, M.; Winter, G.-G.; Wittek, C.; Wright, A. E.; Wünsch, E.; Wulff, N.; Yiou, T. P.; Žáček, J.; Zarbock, D.; Zhang, Z.; Zhokin, A.; Zimmer, M.; Zimmermann, W.; Zomer, F.; Zuber, K.; H1 Collaboration

1995-02-01

Photoproduction of 2-jet events is studied with the H1 detector at HERA. Parton cross sections are extracted from the data by an unfolding method using leading order parton-jet correlations of a QCD generator. The gluon distribution in the photon is derived in the fractional momentum range 0.04 ⩽ xγ ⩽ 1 at the average factorization scale 75 GeV 2.

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

Generalized Dandelin’s Theorem

NASA Astrophysics Data System (ADS)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.

Impossible colorings and Bell's theorem

NASA Astrophysics Data System (ADS)

Aravind, P. K.

1999-11-01

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell-Kochen-Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.

Understanding Rolle's Theorem

ERIC Educational Resources Information Center

Parameswaran, Revathy

2009-01-01

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…

An Application of the Perron-Frobenius Theorem to a Damage Model Problem.

DTIC Science & Technology

1985-04-01

RO-RI6I 20B AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A ill I DAMAGOE MODEL PR BLEM.. (U) PITTSBURGH UNIV PA CENTER FOR I MULTIYARIATE...any copyright notation herein. * . .r * j * :h ~ ** . . .~. ~ % *~’ :. ~ ~ v 4 .% % %~ AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A DAMAGE...University of Sheffield, U.K. S ~ Summry Using the Perron - Frobenius theorem, it is established that if’ (X,Y) is a random vector of non-negative

International Conference on Fixed Point Theory and Applications (Colloque International Theorie Du Point Fixe et Applications)

DTIC Science & Technology

1989-06-09

Theorem and the Perron - Frobenius Theorem in matrix theory. We use the Hahn-Banach theorem and do not use any fixed-point related concepts. 179 A...games defined b’, tions 87 Isac G. Fixed point theorems on convex cones , generalized pseudo-contractive mappings and the omplementarity problem 89...and (II), af(x) ° denotes the negative polar cone ot of(x). This condition are respectively called "inward" and "outward". Indeed, when X is convex

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Markov Property of the Conformal Field Theory Vacuum and the a Theorem.

PubMed

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-06-30

We use strong subadditivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give new proof of the irreversibility of the renormalization group in d=4 space-time dimensions-the a theorem. This extends the proofs of the c and F theorems in dimensions d=2 and d=3 based on vacuum entanglement entropy, and gives a unified picture of all known irreversibility theorems in relativistic quantum field theory.

A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers

NASA Technical Reports Server (NTRS)

Piepmeier, J. R.; Simon, N. K.

2004-01-01

The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.

Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, J.; Gamberg, L.; Prokudin, A.

We construct an improved implementation for combining TMD factorization transverse- momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suit- able for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. As a result, we further argue that questions regarding the shape and Q- dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.

Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

DOE PAGES

Collins, J.; Gamberg, L.; Prokudin, A.; ...

2016-08-08

We construct an improved implementation for combining TMD factorization transverse- momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suit- able for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. As a result, we further argue that questions regarding the shape and Q- dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.

The gluon density of the proton at low x from a QCD analysis of F2

NASA Astrophysics Data System (ADS)

Aid, S.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Arpagaus, M.; Babaev, A.; Baehr, J.; Bán, J.; Ban, Y.; Baranov, P.; Barrelet, E.; Barschke, R.; Bartel, W.; Barth, M.; Bassler, U.; Beck, H. P.; Behrend, H.-J.; Belousov, A.; Berger, Ch.; Bernardi, G.; Bernet, R.; Bertrand-Coremans, G.; Besançon, M.; Beyer, R.; Biddulph, P.; Bispham, P.; Bizot, J. C.; Blobel, V.; Borras, K.; Botterweck, F.; Boudry, V.; Braemer, A.; Brasse, F.; Braunschweig, W.; Brisson, V.; Bruncko, D.; Brune, C.; Buchholz, R.; Büngener, L.; Bürger, J.; Büsser, F. W.; Buniatian, A.; Burke, S.; Burton, M.; Buschhorn, G.; Campbell, A. J.; Carli, T.; Charles, F.; Charlet, M.; Clarke, D.; Clegg, A. B.; Clerbaux, B.; Colombo, M.; Contreras, J. G.; Cormack, C.; Coughlan, J. A.; Courau, A.; Coutures, Ch.; Cozzika, G.; Criegee, L.; Cussans, D. G.; Cvach, J.; Dagoret, S.; Dainton, J. B.; Dau, W. D.; Daum, K.; David, M.; Delcourt, B.; Del Buono, L.; De Roeck, A.; De Wolf, E. A.; Di Nezza, P.; Dollfus, C.; Dowell, J. D.; Dreis, H. B.; Droutskoi, A.; Duboc, J.; Düllmann, D.; Dünger, O.; Duhm, H.; Ebert, J.; Ebert, T. R.; Eckerlin, G.; Efremenko, V.; Egli, S.; Ehrlichmann, H.; Eichenberger, S.; Eichler, R.; Eisele, F.; Eisenhandler, E.; Ellison, R. J.; Elsen, E.; Erdmann, M.; Erdmann, W.; Evrard, E.; Favart, L.; Fedotov, A.; Feeken, D.; Felst, R.; Feltesse, J.; Ferencei, J.; Ferrarotto, F.; Flamm, K.; Fleischer, M.; Flieser, M.; Flügge, G.; Fomenko, A.; Fominykh, B.; Forbush, M.; Formánek, J.; Foster, J. M.; Franke, G.; Fretwurst, E.; Gabathuler, E.; Gabathuler, K.; Gamerdinger, K.; Garvey, J.; Gayler, J.; Gebauer, M.; Gellrich, A.; Genzel, H.; Gerhards, R.; Goerlach, U.; Goerlich, L.; Gogitidze, N.; Goldberg, M.; Goldner, D.; Gonzalez-Pineiro, B.; Gorelov, I.; Goritchev, P.; Grab, C.; Grässler, H.; Grässler, R.; Greenshaw, T.; Grindhammer, G.; Gruber, A.; Gruber, C.; Haack, J.; Haidt, D.; Hajduk, L.; Hamon, O.; Hampel, M.; Hanlon, E. M.; Hapke, M.; Haynes, W. J.; Heatherington, J.; Heinzelmann, G.; Henderson, R. C. W.; Henschel, H.; Herynek, I.; Hess, M. F.; Hildesheim, W.; Hill, P.; Hiller, K. H.; Hilton, C. D.; Hladký, J.; Hoeger, K. C.; Höppner, M.; Horisberger, R.; Hudgson, V. L.; Huet, Ph.; Hütte, M.; Hufnagel, H.; Ibbotson, M.; Itterbeck, H.; Jabiol, M.-A.; Jacholkowska, A.; Jacobsson, C.; Jaffre, M.; Janoth, J.; Jansen, T.; Jönsson, L.; Johnson, D. P.; Johnson, L.; Jung, H.; Kalmus, P. I. P.; Kant, D.; Kaschowitz, R.; Kasselmann, P.; Kathage, U.; Katzy, J.; Kaufmann, H. H.; Kazarian, S.; Kenyon, I. R.; Kermiche, S.; Keuker, C.; Kiesling, C.; Klein, M.; Kleinwort, C.; Knies, G.; Ko, W.; Köhler, T.; Köhne, J. H.; Kolanoski, H.; Kole, F.; Kolya, S. D.; Korbel, V.; Korn, M.; Kostka, P.; Kotelnikov, S. K.; Krämerkämper, T.; Krasny, M. W.; Krehbiel, H.; Krücker, D.; Krüger, U.; Krüner-Marquis, U.; Kubenka, J. P.; Küster, H.; Kuhlen, M.; Kurča, T.; Kurzhöfer, J.; Kuznik, B.; Lacour, D.; Lamarche, F.; Lander, R.; Landon, M. P. J.; Lange, W.; Lanius, P.; Laporte, J.-F.; Lebedev, A.; Leverenz, C.; Levonian, S.; Ley, Ch.; Lindner, A.; Lindström, G.; Link, J.; Linsel, F.; Lipinski, J.; List, B.; Lobo, G.; Loch, P.; Lohmander, H.; Lomas, J.; Lopez, G. C.; Lubimov, V.; Lüke, D.; Magnussen, N.; Malinovski, E.; Mani, S.; Maraček, R.; Marage, P.; Marks, J.; Marshall, R.; Martens, J.; Martin, R.; Martyn, H.-U.; Martyniak, J.; Masson, S.; Mavroidis, T.; Maxfield, S. J.; McMahon, S. J.; Mehta, A.; Meier, K.; Mercer, D.; Merz, T.; Meyer, C. A.; Meyer, H.; Meyer, J.; Migliori, A.; Mikocki, S.; Milstead, D.; Moreau, F.; Morris, J. V.; Mroczko, E.; Müller, G.; Müller, K.; Murín, P.; Nagovizin, V.; Nahnhauer, R.; Naroska, B.; Naumann, Th.; Newman, P. R.; Newton, D.; Neyret, D.; Nguyen, H. K.; Nicholls, T. C.; Niebergall, F.; Niebuhr, C.; Niedzballa, Ch.; Nisius, R.; Nowak, G.; Noyes, G. W.; Nyberg-Werther, M.; Oakden, M.; Oberlack, H.; Obrock, U.; Olsson, J. E.; Ozerov, D.; Panaro, E.; Panitch, A.; Pascaud, C.; Patel, G. D.; Peppel, E.; Perez, E.; Phillips, J. P.; Pichler, Ch.; Pieuchot, A.; Pitzl, D.; Pope, G.; Prell, S.; Prosi, R.; Rabbertz, K.; Rädel, G.; Raupach, F.; Reimer, P.; Reinshagen, S.; Ribarics, P.; Rick, H.; Riech, V.; Riedlberger, J.; Riess, S.; Rietz, M.; Rizvi, E.; Robertson, S. M.; Robmann, P.; Roloff, H. E.; Roosen, R.; Rosenbauer, K.; Rostovtsev, A.; Rouse, F.; Royon, C.; Rüter, K.; Rusakov, S.; Rybicki, K.; Rylko, R.; Sahlmann, N.; Sanchez, E.; Sankey, D. P. C.; Schacht, P.; Schiek, S.; Schleper, P.; von Schlippe, W.; Schmidt, C.; Schmidt, D.; Schmidt, G.; Schöning, A.; Schröder, V.; Schuhmann, E.; Schwab, B.; Schwind, A.; Sefkow, F.; Seidel, M.; Sell, R.; Semenov, A.; Shekelyan, V.; Sheviakov, I.; Shooshtari, H.; Shtarkov, L. N.; Siegmon, G.; Siewert, U.; Sirois, Y.; Skillicorn, I. O.; Smirnov, P.; Smith, J. R.; Solochenko, V.; Soloviev, Y.; Spiekermann, J.; Spielman, S.; Spitzer, H.; Starosta, R.; Steenbock, M.; Steffen, P.; Steinberg, R.; Stella, B.; Stephens, K.; Stier, J.; Stiewe, J.; Stösslein, U.; Stolze, K.; Strachota, J.; Straumann, U.; Struczinski, W.; Sutton, J. P.; Tapprogge, S.; Tchernyshov, V.; Thiebaux, C.; Thompson, G.; Truöl, P.; Turnau, J.; Tutas, J.; Uelkes, P.; Usik, A.; Valkár, S.; Valkárová, A.; Vallée, C.; Van Esch, P.; Van Mechelen, P.; Vartapetian, A.; Vazdik, Y.; Verrecchia, P.; Villet, G.; Wacker, K.; Wagener, A.; Wagener, M.; Walker, I. W.; Walther, A.; Weber, G.; Weber, M.; Wegener, D.; Wegner, A.; Wellisch, H. P.; West, L. R.; Willard, S.; Willard, S.; Winde, M.; Winter, G.-G.; Wittek, C.; Wright, A. E.; Wünsch, E.; Wulff, N.; Yiou, T. P.; Žáček, J.; Zarbock, D.; Zhang, Z.; Zhokin, A.; Zimmer, M.; Zimmermann, W.; Zomer, F.; Zuber, K.; H1 Collaboration

1995-02-01

We present a QCD analysis of the proton structure function F2 measured by the H1 experiment at HERA, combined with data from previous fixed target experiments. The gluon density is extracted from the scaling violations of F2 in the range 2 · 10 -4 < x < 3 · 10 -2 and compared with an approximate solution of the QCD evolution equations. The gluon density is found to rise steeply with decreasing x.

Archeology and evolution of QCD

NASA Astrophysics Data System (ADS)

De Rújula, A.

2017-03-01

These are excerpts from the closing talk at the "XIIth Conference on Quark Confinement and the Hadron Spectrum", which took place last Summer in Thessaloniki -an excellent place to enjoy an interest in archeology. A more complete personal view of the early days of QCD and the rest of the Standard Model is given in [1]. Here I discuss a few of the points which -to my judgement- illustrate well the QCD evolution (in time), both from a scientific and a sociological point of view.

Two loop renormalization of the magnetic coupling in hot QCD

NASA Astrophysics Data System (ADS)

Giovannangeli, P.

2004-04-01

Well above the critical temperature hot QCD is described by 3d electrostatic QCD with gauge coupling gE and Debye mass mE. We integrate out the Debye scales to two loop accuracy and find for the gauge coupling in the resulting magnetostatic action gM2=gE21-{1}/{48}{gE2N}/{πmE}-{17}/{4608}{gE2N}/{πmE}2+O{gE2N}/{πmE}3.

QCD unitarity constraints on Reggeon Field Theory

NASA Astrophysics Data System (ADS)

Kovner, Alex; Levin, Eugene; Lublinsky, Michael

2016-08-01

We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD.

PubMed

Aarts, Gert; Allton, Chris; Foley, Justin; Hands, Simon; Kim, Seyong

2007-07-13

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.

Nuclear physics from lattice QCD at strong coupling.

PubMed

de Forcrand, Ph; Fromm, M

2010-03-19

We study numerically the strong coupling limit of lattice QCD with one flavor of massless staggered quarks. We determine the complete phase diagram as a function of temperature and chemical potential, including a tricritical point. We clarify the nature of the low temperature dense phase, which is strongly bound "nuclear" matter. This strong binding is explained by the nuclear potential, which we measure. Finally, we determine, from this first-principles limiting case of QCD, the masses of "atomic nuclei" up to A=12 "carbon".

OPE of Green functions in the odd sector of QCD

NASA Astrophysics Data System (ADS)

Kadavý, T.; Kampf, K.; Novotný, J.

2017-03-01

A review of familiar results of the three-point Green functions of currents in the odd-intrinsic parity sector of QCD is presented. Such Green functions include very well-known examples of VVP, VAS or AAP correlators. We also present new results for VVA and AAA Green functions that have not yet been studied extensively in the literature before, more importantly with a phenomenological study and a discussion of the highenergy behaviour and its relation to the QCD condensates.

Fragmentation functions at next-to-next-to-leading order accuracy

DOE PAGES

Anderle, Daniele P.; Stratmann, Marco; Ringer, Felix

2015-12-01

We present a first analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order accuracy in QCD based on single-inclusive pion production in electron-positron annihilation. Special emphasis is put on the technical details necessary to perform the QCD scale evolution and cross section calculation in Mellin moment space. Lastly, we demonstrate how the description of the data and the theoretical uncertainties are improved when next-to-next-to-leading order QCD corrections are included.

New QCD sum rules based on canonical commutation relations

NASA Astrophysics Data System (ADS)

Hayata, Tomoya

2012-04-01

New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg’s sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed.

REMARKS ON THE MAXIMUM ENTROPY METHOD APPLIED TO FINITE TEMPERATURE LATTICE QCD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

UMEDA, T.; MATSUFURU, H.

2005-07-25

We make remarks on the Maximum Entropy Method (MEM) for studies of the spectral function of hadronic correlators in finite temperature lattice QCD. We discuss the virtues and subtlety of MEM in the cases that one does not have enough number of data points such as at finite temperature. Taking these points into account, we suggest several tests which one should examine to keep the reliability for the results, and also apply them using mock and lattice QCD data.

Anomaly inflow on QCD axial domain-walls and vortices

NASA Astrophysics Data System (ADS)

Fukushima, Kenji; Imaki, Shota

2018-06-01

We study the chiral effective theory in the presence of quantum chromodynamics (QCD) vortices. Gauge invariance requires novel terms from vortex singularities in the gauged Wess-Zumino-Witten action, which incorporate anomaly-induced currents along the vortices. We examine these terms for systems with QCD axial domain-walls bounded by vortices (vortons) under magnetic fields. We discuss how the baryon and electric charge conservations are satisfied in these systems through interplay between domain-walls and vortices, manifesting Callan-Harvey's mechanism of anomaly inflow.

Nonlocal Quantum Information Transfer Without Superluminal Signalling and Communication

NASA Astrophysics Data System (ADS)

Walleczek, Jan; Grössing, Gerhard

2016-09-01

It is a frequent assumption that—via superluminal information transfers—superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a `no-go' theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell's theorem, we argue that Bell employed both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie-Bohm theory. This position we refer to as "effective non-signalling". By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as "axiomatic non-signalling". In search of a decisive communication-theoretic criterion for differentiating between "axiomatic" and "effective" non-signalling, we employ the operational framework offered by Shannon's mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. We find that an effective non-signalling theorem represents two sub-theorems: (1) Non-transfer-control (NTC) theorem, and (2) Non-signification-control (NSC) theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. Effective non-signalling prevents the instantaneous, i.e., superluminal, transfer of message-encoded information through the controlled use—by a sender-receiver pair —of informationally-correlated detection events, e.g., in EPR-type experiments. An effective non-signalling theorem allows for nonlocal quantum information transfer yet—at the same time—effectively denies superluminal signalling and communication.

On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

Ergodic theorem, ergodic theory, and statistical mechanics

PubMed Central

Moore, Calvin C.

2015-01-01

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

NASA Astrophysics Data System (ADS)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

The structure of the nucleon: Elastic electromagnetic form factors

DOE PAGES

Punjabi, V.; Perdrisat, C. F.; Jones, M. K.; ...

2015-07-10

Precise proton and neutron form factor measurements at Jefferson Lab, using spin observables, have recently made a significant contribution to the unraveling of the internal structure of the nucleon. Accurate experimental measurements of the nucleon form factors are a test-bed for understanding how the nucleon's static properties and dynamical behavior emerge from QCD, the theory of the strong interactions between quarks. There has been enormous theoretical progress, since the publication of the Jefferson Lab proton form factor ratio data, aiming at reevaluating the picture of the nucleon. We will review the experimental and theoretical developments in this field and discussmore » the outlook for the future.« less

F(R) cosmology via Noether symmetry and Λ-Chaplygin Gas like model

NASA Astrophysics Data System (ADS)

Fazlollahi, H. R.

2018-06-01

In this work, we consider f (R) alternative theories of gravity with an eye to Noether symmetry through the gauge theorem. For non-vacuum models, one finds Λ like gravity with energy density of Chaplygin Gas. We also obtain the effective equation of state parameter for corresponding cosmology and scale factor behavior with respect to cosmic time which show that the model provides viable EoS and scale factor with respect to observational data.

Bring the Pythagorean Theorem "Full Circle"

ERIC Educational Resources Information Center

Benson, Christine C.; Malm, Cheryl G.

2011-01-01

Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…

The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project

ERIC Educational Resources Information Center

Robiette, Alan G.

1975-01-01

Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)

Using Discovery in the Calculus Class

ERIC Educational Resources Information Center

Shilgalis, Thomas W.

1975-01-01

This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)

Three Lectures on Theorem-proving and Program Verification

NASA Technical Reports Server (NTRS)

Moore, J. S.

1983-01-01

Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.