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.

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.

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.

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.

Index theorem and universality properties of the low-lying eigenvalues of improved staggered quarks.

PubMed

Follana, E; Hart, A; Davies, C T H

2004-12-10

We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the index theorem, and their chirality expectation value is large ( approximately 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.

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…

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.

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.

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.

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.

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

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-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.

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.

Analytic boosted boson discrimination

DOE PAGES

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

2016-05-20

Observables which discriminate boosted topologies from massive QCD jets are of great importance for the success of the jet substructure program at the Large Hadron Collider. Such observables, while both widely and successfully used, have been studied almost exclusively with Monte Carlo simulations. In this paper we present the first all-orders factorization theorem for a two-prong discriminant based on a jet shape variable, D 2, valid for both signal and background jets. Our factorization theorem simultaneously describes the production of both collinear and soft subjets, and we introduce a novel zero-bin procedure to correctly describe the transition region between thesemore » limits. By proving an all orders factorization theorem, we enable a systematically improvable description, and allow for precision comparisons between data, Monte Carlo, and first principles QCD calculations for jet substructure observables. Using our factorization theorem, we present numerical results for the discrimination of a boosted Z boson from massive QCD background jets. We compare our results with Monte Carlo predictions which allows for a detailed understanding of the extent to which these generators accurately describe the formation of two-prong QCD jets, and informs their usage in substructure analyses. In conclusion, our calculation also provides considerable insight into the discrimination power and calculability of jet substructure observables in general.« less

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

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

Observables which discriminate boosted topologies from massive QCD jets are of great importance for the success of the jet substructure program at the Large Hadron Collider. Such observables, while both widely and successfully used, have been studied almost exclusively with Monte Carlo simulations. In this paper we present the first all-orders factorization theorem for a two-prong discriminant based on a jet shape variable, D 2, valid for both signal and background jets. Our factorization theorem simultaneously describes the production of both collinear and soft subjets, and we introduce a novel zero-bin procedure to correctly describe the transition region between thesemore » limits. By proving an all orders factorization theorem, we enable a systematically improvable description, and allow for precision comparisons between data, Monte Carlo, and first principles QCD calculations for jet substructure observables. Using our factorization theorem, we present numerical results for the discrimination of a boosted Z boson from massive QCD background jets. We compare our results with Monte Carlo predictions which allows for a detailed understanding of the extent to which these generators accurately describe the formation of two-prong QCD jets, and informs their usage in substructure analyses. In conclusion, our calculation also provides considerable insight into the discrimination power and calculability of jet substructure observables in general.« less

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

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

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.

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

{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

QCD as a Theory of Hadrons

NASA Astrophysics Data System (ADS)

Narison, Stephan

2004-05-01

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

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.

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.

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

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.

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.

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.

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.

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)

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

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

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.

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

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

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.

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.

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.

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of "Fundamental Problems in Field Theory and their Implications". Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to nonrelativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

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.

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

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].

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.

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

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.

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

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2016-05-01

On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

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.

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.

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…

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.

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.

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.

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.

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.

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…

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.

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…

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

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

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

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.

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.

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.

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.

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

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)

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.

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.

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.

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.

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

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.

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.

FOREWORD: Extreme QCD 2012 (xQCD)

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bazavov, Alexei; Liu, Keh-Fei

2013-04-01

The Extreme QCD 2012 conference, held at the George Washington University in August 2012, celebrated the 10th event in the series. It has been held annually since 2003 at different locations: San Carlos (2011), Bad Honnef (2010), Seoul (2009), Raleigh (2008), Rome (2007), Brookhaven (2006), Swansea (2005), Argonne (2004), and Nara (2003). As usual, it was a very productive and inspiring meeting that brought together experts in the field of finite-temperature QCD, both theoretical and experimental. On the experimental side, we heard about recent results from major experiments, such as PHENIX and STAR at Brookhaven National Laboratory, ALICE and CMS at CERN, and also about the constraints on the QCD phase diagram coming from astronomical observations of one of the largest laboratories one can imagine, neutron stars. The theoretical contributions covered a wide range of topics, including QCD thermodynamics at zero and finite chemical potential, new ideas to overcome the sign problem in the latter case, fluctuations of conserved charges and how they allow one to connect calculations in lattice QCD with experimentally measured quantities, finite-temperature behavior of theories with many flavors of fermions, properties and the fate of heavy quarkonium states in the quark-gluon plasma, and many others. The participants took the time to write up and revise their contributions and submit them for publication in these proceedings. Thanks to their efforts, we have now a good record of the ideas presented and discussed during the workshop. We hope that this will serve both as a reminder and as a reference for the participants and for other researchers interested in the physics of nuclear matter at high temperatures and density. To preserve the atmosphere of the event the contributions are ordered in the same way as the talks at the conference. We are honored to have helped organize the 10th meeting in this series, a milestone that reflects the lasting interest in this

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.

Cooperation Among Theorem Provers

NASA Technical Reports Server (NTRS)

Waldinger, Richard J.

1998-01-01

In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.

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

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.

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.

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.

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 Nucleon Axial Form Factor and Staggered Lattice QCD

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

Meyer, Aaron Scott

The study of neutrino oscillation physics is a major research goal of the worldwide particle physics program over the upcoming decade. Many new experiments are being built to study the properties of neutrinos and to answer questions about the phenomenon of neutrino oscillation. These experiments need precise theoretical cross sections in order to access fundamental neutrino properties. Neutrino oscillation experiments often use large atomic nuclei as scattering targets, which are challenging for theorists to model. Nuclear models rely on free-nucleon amplitudes as inputs. These amplitudes are constrained by scattering experiments with large nuclear targets that rely on the very samemore » nuclear models. The work in this dissertation is the rst step of a new initiative to isolate and compute elementary amplitudes with theoretical calculations to support the neutrino oscillation experimental program. Here, the eort focuses on computing the axial form factor, which is the largest contributor of systematic error in the primary signal measurement process for neutrino oscillation studies, quasielastic scattering. Two approaches are taken. First, neutrino scattering data on a deuterium target are reanalyzed with a model-independent parametrization of the axial form factor to quantify the present uncertainty in the free-nucleon amplitudes. The uncertainties on the free-nucleon cross section are found to be underestimated by about an order of magnitude compared to the ubiquitous dipole model parametrization. The second approach uses lattice QCD to perform a rst-principles computation of the nucleon axial form factor. The Highly Improved Staggered Quark (HISQ) action is employed for both valence and sea quarks. The results presented in this dissertation are computed at physical pion mass for one lattice spacing. This work presents a computation of the axial form factor at zero momentum transfer, and forms the basis for a computation of the axial form factor momentum

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

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

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

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.

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.

The Parity Theorem Shuffle

ERIC Educational Resources Information Center

Smith, Michael D.

2016-01-01

The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…

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.

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.

The Levy sections theorem revisited

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2007-06-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

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.

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.

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.

$$B\\to\\pi\\ell\\ell$$ 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

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.

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.

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.

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.

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.

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

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

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.

Discrete Jordan curve theorem

NASA Astrophysics Data System (ADS)

Chen, Li

1999-09-01

According to a general definition of discrete curves, surfaces, and manifolds (Li Chen, 'Generalized discrete object tracking algorithms and implementations, ' In Melter, Wu, and Latecki ed, Vision Geometry VI, SPIE Vol. 3168, pp 184 - 195, 1997.). This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected surface into two components. Based on the definition of discrete surfaces, we give three reasonable definitions of simply connected spaces. Theoretically, these three definition shall be equivalent. We have proved the Jordan curve theorem under the third definition of simply connected spaces. The Jordan theorem shows the relationship among an object, its boundary, and its outside area. In continuous space, the boundary of an mD manifold is an (m - 1)D manifold. The similar result does apply to regular discrete manifolds. The concept of a new regular nD-cell is developed based on the regular surface point in 2D, and well-composed objects in 2D and 3D given by Latecki (L. Latecki, '3D well-composed pictures,' In Melter, Wu, and Latecki ed, Vision Geometry IV, SPIE Vol 2573, pp 196 - 203, 1995.).

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

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.

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

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.

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.

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

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.

Cooperation Among Theorem Provers

NASA Technical Reports Server (NTRS)

Waldinger, Richard J.

1998-01-01

This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

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

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able tomore » extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.« 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.

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.

Conformal Aspects of QCD

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

Brodsky, S

2003-11-19

Theoretical and phenomenological evidence is now accumulating that the QCD coupling becomes constant at small virtuality; i.e., {alpha}{sub s}(Q{sup 2}) develops an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. For example, the hadronic decays of the {tau} lepton can be used to determine the effective charge {alpha}{sub {tau}}(m{sub {tau}{prime}}{sup 2}) for a hypothetical {tau}-lepton with mass in the range 0 < m{sub {tau}{prime}} < m{sub {tau}}. The {tau} decay data at low mass scales indicates that the effective charge freezes at a value of s = m{sub {tau}{prime}}{sup 2} of order 1more » GeV{sup 2} with a magnitude {alpha}{sub {tau}} {approx} 0.9 {+-} 0.1. The near-constant behavior of effective couplings suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer and why there are no significant running coupling corrections to quark counting rules for exclusive processes. The AdS/CFT correspondence of large N{sub c} supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time also has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes and light-front wavefunctions. The utility of light-front quantization and light-front Fock wavefunctions for analyzing nonperturbative QCD and representing the dynamics of QCD bound states is also discussed.« less

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.

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

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.

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.

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.

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…

Novel QCD Phenomenology

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

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

2011-08-12

I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard higher-twist QCD subprocess, rather than from jet fragmentation. Such 'direct' processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed x{sub T} = 2p{sub T}/{radical}s, as well as the 'baryon anomaly', the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, the soft-gluon rescattering associated with its Wilson line, lead to Bjorken-scaling single-spinmore » asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish 'static' structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus 'dynamical' structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. Eliminating the renormalization scale ambiguity greatly improves the precision of QCD predictions and increases the sensitivity of searches for new physics at the

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

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)

Exclusive processes and the fundamental structure of hadrons

DOE PAGES

Brodsky, Stanley J.

2015-01-20

I review the historical development of QCD predictions for exclusive hadronic processes, beginning with constituent counting rules and the quark interchange mechanism, phenomena which gave early validation for the quark structure of hadrons. The subsequent development of pQCD factorization theorems for hard exclusive amplitudes and the development of evolution equations for the hadron distribution amplitudes provided a rigorous framework for calculating hadronic form factors and hard scattering exclusive scattering processes at high momentum transfer. I also give a brief introduction to the field of "light-front holography" and the insights it brings to quark confinement, the behavior of the QCD couplingmore » in the nonperturbative domain, as well as hadron spectroscopy and the dynamics of exclusive processes.« less

Exclusive processes and the fundamental structure of hadrons

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

Brodsky, Stanley J.

I review the historical development of QCD predictions for exclusive hadronic processes, beginning with constituent counting rules and the quark interchange mechanism, phenomena which gave early validation for the quark structure of hadrons. The subsequent development of pQCD factorization theorems for hard exclusive amplitudes and the development of evolution equations for the hadron distribution amplitudes provided a rigorous framework for calculating hadronic form factors and hard scattering exclusive scattering processes at high momentum transfer. I also give a brief introduction to the field of "light-front holography" and the insights it brings to quark confinement, the behavior of the QCD couplingmore » in the nonperturbative domain, as well as hadron spectroscopy and the dynamics of exclusive processes.« less

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

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

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.

Applications of square-related theorems

NASA Astrophysics Data System (ADS)

Srinivasan, V. K.

2014-04-01

The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.

Kato type operators and Weyl's theorem

NASA Astrophysics Data System (ADS)

Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos

2005-09-01

A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).

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

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.

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…

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.

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.

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

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

Logical errors on proving theorem

NASA Astrophysics Data System (ADS)

Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.

2018-01-01

In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.

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.

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

Unpacking Rouché's Theorem

ERIC Educational Resources Information Center

Howell, Russell W.; Schrohe, Elmar

2017-01-01

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

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

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.

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

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.

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

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.

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.

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.

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)

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

A Converse of Fermat's Little Theorem

ERIC Educational Resources Information Center

Bruckman, P. S.

2007-01-01

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

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.

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

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

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.

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.

Tree-manipulating systems and Church-Rosser theorems.

NASA Technical Reports Server (NTRS)

Rosen, B. K.

1973-01-01

Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.

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.

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

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.

A Generalization of the Prime Number Theorem

ERIC Educational Resources Information Center

Bruckman, Paul S.

2008-01-01

In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…

The Classical Version of Stokes' Theorem Revisited

ERIC Educational Resources Information Center

Markvorsen, Steen

2008-01-01

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

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.

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.

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 QCD proposes that scattering on the noncondensed component of the monopole ensemble 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.

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 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

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.

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)…

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Visualizing the Central Limit Theorem through Simulation

ERIC Educational Resources Information Center

Ruggieri, Eric

2016-01-01

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

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.

Republication of: A theorem on Petrov types

NASA Astrophysics Data System (ADS)

Goldberg, J. N.; Sachs, R. K.

2009-02-01

This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

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.

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.

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

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.

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.

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)

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)).

Four Theorems on the Psychometric Function

PubMed Central

May, Keith A.; Solomon, Joshua A.

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, . This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull “slope” parameter, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4–0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456

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.

QCD PHASE TRANSITIONS-VOLUME 15.

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

SCHAFER,T.

1998-11-04

The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theoristsmore » working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some. efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.« less

QCD Phase Transitions, Volume 15

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

Schaefer, T.; Shuryak, E.

1999-03-20

The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theoristsmore » working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.« less

A Physical Proof of the Pythagorean Theorem

ERIC Educational Resources Information Center

Treeby, David

2017-01-01

What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one…

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

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

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.

QCD inequalities for hadron interactions.

PubMed

Detmold, William

2015-06-05

We derive generalizations of the Weingarten-Witten QCD mass inequalities for particular multihadron systems. For systems of any number of identical pseudoscalar mesons of maximal isospin, these inequalities prove that near threshold interactions between the constituent mesons must be repulsive and that no bound states can form in these channels. Similar constraints in less symmetric systems are also extracted. These results are compatible with experimental results (where known) and recent lattice QCD calculations, and also lead to a more stringent bound on the nucleon mass than previously derived, m_{N}≥3/2m_{π}.

Hadron scattering, resonances, and QCD

NASA Astrophysics Data System (ADS)

Briceño, R. A.

2016-11-01

The non-perturbative nature of quantum chromodynamics (QCD) has historically left a gap in our understanding of the connection between the fundamental theory of the strong interactions and the rich structure of experimentally observed phenomena. For the simplest properties of stable hadrons, this is now circumvented with the use of lattice QCD (LQCD). In this talk I discuss a path towards a rigorous determination of few-hadron observables from LQCD. I illustrate the power of the methodology by presenting recently determined scattering amplitudes in the light-meson sector and their resonance content.

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.

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.

Disconnected Diagrams in Lattice QCD

NASA Astrophysics Data System (ADS)

Gambhir, Arjun Singh

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

Adiabatic Theorem for Quantum Spin Systems

NASA Astrophysics Data System (ADS)

Bachmann, S.; De Roeck, W.; Fraas, M.

2017-08-01

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

Theorem Proving In Higher Order Logics

NASA Technical Reports Server (NTRS)

Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene

2002-01-01

The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

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.

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.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions

Moriond QCD 2013 Experimental Summary

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

Denisov, Dmitri

2013-06-28

The article presents experimental highlights of Moriond 2013 QCD conference. This was fantastic conference and the first Moriond QCD since the discovery of the Higgs boson. Many new results about its properties have been presented at the conference with Higgs-like particle becoming a Higgs as it properties match expected for the Higgs boson pretty well. There were many new results presented in all experimental areas including QCD, elecroweak, studies of the top, bottom and charm quarks, searches for physics beyond Standard Model as well as studies of the heavy ion collisions. 56 experimental talks have been presented at the conferencemore » and it is impossible to cover each result in the summary, so highlights are limited to what I was able to present in my summary talk presented on March 16 2013. The proceedings of the conference cover in depth all talks presented and I urge you to get familiar with all of them. Theoretical Summary of the conference was given by Michelangelo Mangano, so theory talks are not covered in the article.« less

Optimal Keno Strategies and the Central Limit Theorem

ERIC Educational Resources Information Center

Johnson, Roger W.

2006-01-01

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

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.

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.

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

A Stochastic Version of the Noether Theorem

NASA Astrophysics Data System (ADS)

González Lezcano, Alfredo; Cabo Montes de Oca, Alejandro

2018-06-01

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

Quantum voting and violation of Arrow's impossibility theorem

NASA Astrophysics Data System (ADS)

Bao, Ning; Yunger Halpern, Nicole

2017-06-01

We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

When 95% Accurate Isn't: Exploring Bayes's Theorem

ERIC Educational Resources Information Center

CadwalladerOlsker, Todd D.

2011-01-01

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

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.

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.

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

Most Strange Dibaryon from Lattice QCD

NASA Astrophysics Data System (ADS)

Gongyo, Shinya; Sasaki, Kenji; Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Nemura, Hidekatsu; HAL QCD Collaboration

2018-05-01

The Ω Ω system in the 1S0 channel (the most strange dibaryon) is studied on the basis of the (2 +1 )-flavor lattice QCD simulations with a large volume (8.1 fm )3 and nearly physical pion mass mπ≃146 MeV at a lattice spacing of a ≃0.0846 fm . We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length a0=4.6 (6 )(-0.5+1.2) fm , the effective range reff=1.27 (3 )(-0.03+0.06) fm , and the binding energy BΩ Ω=1.6 (6 )(-0.6+0.7) MeV . These results indicate that the Ω Ω system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.

H-theorem in quantum physics.

PubMed

Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

H-theorem in quantum physics

PubMed Central

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.

2016-01-01

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571

Leaning on Socrates to Derive the Pythagorean Theorem

ERIC Educational Resources Information Center

Percy, Andrew; Carr, Alistair

2010-01-01

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

Four theorems on the psychometric function.

PubMed

May, Keith A; Solomon, Joshua A

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

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.

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.

Kochen-Specker theorem studied with neutron interferometer.

PubMed

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

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.

Most Strange Dibaryon from Lattice QCD.

PubMed

Gongyo, Shinya; Sasaki, Kenji; Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Nemura, Hidekatsu

2018-05-25

The ΩΩ system in the ^{1}S_{0} channel (the most strange dibaryon) is studied on the basis of the (2+1)-flavor lattice QCD simulations with a large volume (8.1  fm)^{3} and nearly physical pion mass m_{π}≃146  MeV at a lattice spacing of a≃0.0846  fm. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length a_{0}=4.6(6)(_{-0.5}^{+1.2})  fm, the effective range r_{eff}=1.27(3)(_{-0.03}^{+0.06})  fm, and the binding energy B_{ΩΩ}=1.6(6)(_{-0.6}^{+0.7})  MeV. These results indicate that the ΩΩ system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.

Disconnected Diagrams in Lattice QCD

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

Gambhir, Arjun

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagramsmore » is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix

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.

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

H-theorem in quantum physics

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

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

H-theorem in quantum physics

DOE PAGES

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; ...

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

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.

Reliable semiclassical computations in QCD

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

Dine, Michael; Department of Physics, Stanford University Stanford, California 94305-4060; Festuccia, Guido

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For N{sub f}>N, a systematic computation is possible; for N{sub f}QCD lattice gauge theory computations in the chiral limit.

Strong converse theorems using Rényi entropies

NASA Astrophysics Data System (ADS)

Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana

2016-08-01

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Strong converse theorems using Rényi entropies

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

Leditzky, Felix; Datta, Nilanjana; Wilde, Mark M.

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for themore » boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.« less

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…

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)

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.

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.

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.

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.

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).

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.

Critical opalescence in baryonic QCD matter.

PubMed

Antoniou, N G; Diakonos, F K; Kapoyannis, A S; Kousouris, K S

2006-07-21

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behavior is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.

Identifying QCD Transition Using Deep Learning

NASA Astrophysics Data System (ADS)

Zhou, Kai; Pang, Long-gang; Su, Nan; Petersen, Hannah; Stoecker, Horst; Wang, Xin-Nian

2018-02-01

In this proceeding we review our recent work using supervised learning with a deep convolutional neural network (CNN) to identify the QCD equation of state (EoS) employed in hydrodynamic modeling of heavy-ion collisions given only final-state particle spectra ρ(pT, V). We showed that there is a traceable encoder of the dynamical information from phase structure (EoS) that survives the evolution and exists in the final snapshot, which enables the trained CNN to act as an effective "EoS-meter" in detecting the nature of the QCD transition.

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

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.

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.

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.

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.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.

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

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.

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

QCD and Asymptotic Freedom:. Perspectives and Prospects

NASA Astrophysics Data System (ADS)

Wilczek, Frank

QCD is now a mature theory, and it is possible to begin to view its place in the conceptual universe of physics with an appropriate perspective. There is a certain irony in the achievements of QCD. For the problems which initially drove its development — specifically, the desire to understand in detail the force that holds atomic nuclei together, and later the desire to calculate the spectrum of hadrons and their interactions — only limited insight has been achieved. However, I shall argue that QCD is actually more special and important a theory than one had any right to anticipate. In many ways, the importance of the solution transcends that of the original motivating problems. After elaborating on these quasiphilosophical remarks, I discuss two current frontiers of physics that illustrate the continuing vitality of the ideas. The recent wealth of beautiful precision experiments measuring the parameters of the standard model have made it possible to consider the unification of couplings in unprecedented quantitative detail. One central result emerging from these developments is a tantalizing hint of virtual supersymmetry. The possibility of phase transitions in matter at temperatures of order ~102 MeV, governed by QCD dynamics, is of interest from several points of view. Besides having a certain intrinsic grandeur, the question “Does the nature of matter change qualitatively, as it is radically heated?” is important for cosmology, relevant to planned high-energy heavy-ion collision experiments, and provides a promising arena for numerical simulations of QCD. Recent numerical work seems to be consistent with expectations suggested by renormalization group analysis of the potential universality classes of the QCD chiral phase transition; specifically, that the transition is second-order for two species of massless quarks but first order otherwise. There is an interesting possibility of long-range correlations in heavy ion collisions due to the creation of

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-06-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Some functional limit theorems for compound Cox processes

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

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

QCD: Quantum Chromodynamics

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

Lincoln, Don

The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilab’s Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.

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.

Massive QCD Amplitudes at Higher Orders

NASA Astrophysics Data System (ADS)

Moch, S.; Mitov, A.

2007-11-01

We consider the factorisation properties of on-shell QCD amplitudes with massive partons in the limit when all kinematical invariants are large compared to the parton mass and discuss the structure of their infrared singularities. The dimensionally regulated soft poles and the large collinear logarithms of the parton masses exponentiate to all orders. Based on this factorisation a simple relation between massless and massive scattering amplitudes in gauge theories can be established. We present recent applications of this relation for the calculation of the two-loop virtual QCD corrections to the hadro-production of heavy quarks.

QCD Physics with the CMS Experiment

NASA Astrophysics Data System (ADS)

Cerci, S.

2017-12-01

Jets which are the signatures of quarks and gluons in the detector can be described by Quantum Chromodynamics (QCD) in terms of parton-parton scattering. Jets are abundantly produced at the LHC's high energy scales. Measurements of inclusive jets, dijets and multijets can be used to test perturbative QCD predictions and to constrain parton distribution functions (PDF), as well as to measure the strong coupling constant αS . The measurements use the samples of proton-proton collisions collected with the CMS detector at the LHC at various center-of-mass energies of 7, 8 and 13 TeV.

Hadron mass spectrum from lattice QCD.

PubMed

Majumder, Abhijit; Müller, Berndt

2010-12-17

Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T(c) ≈ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing mass spectrum up to a temperature T=155 MeV. Using simple parametrizations of the hadron mass spectrum we show how one may estimate the total spectral weight in these yet undermined states.

Conformal Symmetry as a Template for QCD

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

Brodsky, S

2004-08-04

Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadronmore » phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized.« 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.

Generalized reciprocity theorem for semiconductor devices

NASA Technical Reports Server (NTRS)

Misiakos, K.; Lindholm, F. A.

1985-01-01

A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.

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.

Discovering Theorems in Abstract Algebra Using the Software "GAP"

ERIC Educational Resources Information Center

Blyth, Russell D.; Rainbolt, Julianne G.

2010-01-01

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Observables of QCD diffraction

NASA Astrophysics Data System (ADS)

Mieskolainen, Mikael; Orava, Risto

2017-03-01

A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of diffraction, Regge phenomenology together with AGK cutting rules and random fluctuations.

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

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.

QCD: Quantum Chromodynamics

ScienceCinema

Lincoln, Don

2018-01-16

The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilab’s Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.

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.

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

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.

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.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

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.

Systematic Approaches to Experimentation: The Case of Pick's Theorem

ERIC Educational Resources Information Center

Papadopoulos, Ioannis; Iatridou, Maria

2010-01-01

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

A uniform Tauberian theorem in dynamic games

NASA Astrophysics Data System (ADS)

Khlopin, D. V.

2018-01-01

Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.

Hybrid baryons in QCD

DOE PAGES

Dudek, Jozef J.; Edwards, Robert G.

2012-03-21

In this study, we present the first comprehensive study of hybrid baryons using lattice QCD methods. Using a large basis of composite QCD interpolating fields we extract an extensive spectrum of baryon states and isolate those of hybrid character using their relatively large overlap onto operators which sample gluonic excitations. We consider the spectrum of Nucleon and Delta states at several quark masses finding a set of positive parity hybrid baryons with quantum numbersmore » $$N_{1/2^+},\\,N_{1/2^+},\\,N_{3/2^+},\\, N_{3/2^+},\\,N_{5/2^+},\\,$$ and $$\\Delta_{1/2^+},\\, \\Delta_{3/2^+}$$ at an energy scale above the first band of `conventional' excited positive parity baryons. This pattern of states is compatible with a color octet gluonic excitation having $$J^{P}=1^{+}$$ as previously reported in the hybrid meson sector and with a comparable energy scale for the excitation, suggesting a common bound-state construction for hybrid mesons and baryons.« less

Computer Algebra Systems and Theorems on Real Roots of Polynomials

ERIC Educational Resources Information Center

Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

2010-01-01

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

Instanton liquid properties from lattice QCD

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

Athenodorou, A.; Boucaud, Philippe; De Soto, F.

Here, we examined the instanton contribution to the QCD configurations generated from lattice QCD for N F = 0, N F = 2 + 1 and N F = 2 + 1 + 1 dynamical quark flavors from two different and complementary approaches. First via the use of Gradient flow, we computed instanton liquid properties using an algorithm to localize instantons in the gauge field configurations and studied their evolution with flow time. Then, the analysis of the running at low momenta of gluon Green's functions serves as an independent confirmation of the instanton density which can also be derivedmore » without the use of the Gradient flow.« less

Instanton liquid properties from lattice QCD

DOE PAGES

Athenodorou, A.; Boucaud, Philippe; De Soto, F.; ...

2018-02-22

Here, we examined the instanton contribution to the QCD configurations generated from lattice QCD for N F = 0, N F = 2 + 1 and N F = 2 + 1 + 1 dynamical quark flavors from two different and complementary approaches. First via the use of Gradient flow, we computed instanton liquid properties using an algorithm to localize instantons in the gauge field configurations and studied their evolution with flow time. Then, the analysis of the running at low momenta of gluon Green's functions serves as an independent confirmation of the instanton density which can also be derivedmore » without the use of the Gradient flow.« less

Flux tubes in the QCD vacuum

NASA Astrophysics Data System (ADS)

Cea, Paolo; Cosmai, Leonardo; Cuteri, Francesca; Papa, Alessandro

2017-06-01

The hypothesis that the QCD vacuum can be modeled as a dual superconductor is a powerful tool to describe the distribution of the color field generated by a quark-antiquark static pair and, as such, can provide useful clues for the understanding of confinement. In this work we investigate, by lattice Monte Carlo simulations of the S U (3 ) pure gauge theory and of (2 +1 )-flavor QCD with physical mass settings, some properties of the chromoelectric flux tube at zero temperature and their dependence on the physical distance between the static sources. We draw some conclusions about the validity domain of the dual superconductor picture.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

Visualization Tools for Lattice QCD - Final Report

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

Massimo Di Pierro

2012-03-15

Our research project is about the development of visualization tools for Lattice QCD. We developed various tools by extending existing libraries, adding new algorithms, exposing new APIs, and creating web interfaces (including the new NERSC gauge connection web site). Our tools cover the full stack of operations from automating download of data, to generating VTK files (topological charge, plaquette, Polyakov lines, quark and meson propagators, currents), to turning the VTK files into images, movies, and web pages. Some of the tools have their own web interfaces. Some Lattice QCD visualization have been created in the past but, to our knowledge,more » our tools are the only ones of their kind since they are general purpose, customizable, and relatively easy to use. We believe they will be valuable to physicists working in the field. They can be used to better teach Lattice QCD concepts to new graduate students; they can be used to observe the changes in topological charge density and detect possible sources of bias in computations; they can be used to observe the convergence of the algorithms at a local level and determine possible problems; they can be used to probe heavy-light mesons with currents and determine their spatial distribution; they can be used to detect corrupted gauge configurations. There are some indirect results of this grant that will benefit a broader audience than Lattice QCD physicists.« less

Lattice QCD and nucleon resonances

NASA Astrophysics Data System (ADS)

Edwards, R. G.; Fiebig, H. R.; Fleming, G.; Richards, D. G.; LHP Collaboration

2004-06-01

Lattice calculations provide an ab initio means for the study of QCD. Recent progress at understanding the spectrum and structure of nucleons from lattice QCD studies is reviewed. Measurements of the masses of the lightest particles for the lowest spin values are described and related to predictions of the quark model. Measurements of the mass of the first radial excitation of the nucleon, the so-called Roper resonance, obtained using Bayesian statistical analyses, are detailed. The need to perform calculations at realistically light values of the pion mass is emphasised, and the exciting progress at attaining such masses is outlined. The talk concludes with future prospects, emphasising the importance of constructing a basis of interpolating operators that is sensitive to three-quark states, to multi-quark states, and to excited glue.

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

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.

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

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.

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.

Generalized entropy production fluctuation theorems for quantum systems

NASA Astrophysics Data System (ADS)

Rana, Shubhashis; Lahiri, Sourabh; Jayannavar, A. M.

2013-02-01

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

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].

QCD for Postgraduates (4/5)

ScienceCinema

Zanderighi, Giulia

2018-05-23

Modern QCD - Lecture 4. We will consider some processes of interest at the LHC and will discuss the main elements of their cross-section calculations. We will also summarize the current status of higher order calculations.

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.

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

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.

Phenomenology of Semileptonic B-Meson Decays with Form Factors from Lattice QCD

DOE PAGES

Du, Daping; El-Khadra, A. X.; Gottlieb, Steven; ...

2016-02-03

We study the exclusive semileptonic B-meson decays B→K(π)ℓ +ℓ -, B→K(π)νν¯, and B→πτν, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control. The resulting partially-integrated branching fractions for B→πμ +μ - and B→Kμ +μ - outside the charmonium resonance region are 1-2σ higher than the LHCb Collaboration's recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7σ. Combining the Standard-Modelmore » rates with LHCb's measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V td|=7.45(69)×10 -3, |V ts|=35.7(1.5)×10 -3, and |V td/V ts|=0.201(20), which are compatible with the values obtained from neutral B (s)-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. Furthermore, the constraints on the Wilson coefficients Re(C 9) and Re(C 10) from B→πμ +μ - and B→Kμ +μ - are competitive with those from B→K*μ +μ -, and display a 2.0σ tension with the Standard Model. Our predictions for B→K(π)νν¯ and B→πτν are close to the current experimental limits.« less

Twelve years before the quantum no-cloning theorem

NASA Astrophysics Data System (ADS)

Ortigoso, Juan

2018-03-01

The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.

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

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.

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.

Angle Defect and Descartes' Theorem

ERIC Educational Resources Information Center

Scott, Paul

2006-01-01

Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)

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.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

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

Generalized Bezout's Theorem and its applications in coding theory

NASA Technical Reports Server (NTRS)

Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

A new blackhole theorem and its applications to cosmology and astrophysics

NASA Astrophysics Data System (ADS)

Wang, Shouhong; Ma, Tian

2015-04-01

We shall present a blackhole theorem and a theorem on the structure of our Universe, proved in a recently published paper, based on 1) the Einstein general theory of relativity, and 2) the cosmological principle that the universe is homogeneous and isotropic. These two theorems are rigorously proved using astrophysical dynamical models coupling fluid dynamics and general relativity based on a symmetry-breaking principle. With the new blackhole theorem, we further demonstrate that both supernovae explosion and AGN jets, as well as many astronomical phenomena including e.g. the recent reported are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Benard type convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to a huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.

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

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.

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.

Fixed point theorems for generalized contractions in ordered metric spaces

NASA Astrophysics Data System (ADS)

O'Regan, Donal; Petrusel, Adrian

2008-05-01

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

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.

Guided discovery of the nine-point circle theorem and its proof

NASA Astrophysics Data System (ADS)

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 investigation in a dynamic geometry environment, and consequently prove it using a method of guided discovery. The paper concludes with a variety of suggestions for the ways in which the whole set of activities can be implemented in geometry classrooms.

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

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.

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

Expanding the Interaction Equivalency Theorem

ERIC Educational Resources Information Center

Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro

2015-01-01

Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…

The Geometric Mean Value Theorem

ERIC Educational Resources Information Center

de Camargo, André Pierro

2018-01-01

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…

Luttinger theorem and imbalanced Fermi systems

NASA Astrophysics Data System (ADS)

Pieri, Pierbiagio; Strinati, Giancarlo Calvanese

2017-04-01

The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "Φ-derivable" approximation, and illustrate it in particular for the self-consistent t-matrix approximation.

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Global QCD Analysis of the Nucleon Tensor Charge with Lattice QCD Constraints

NASA Astrophysics Data System (ADS)

Shows, Harvey, III; Melnitchouk, Wally; Sato, Nobuo

2017-09-01

By studying the parton distribution functions (PDFs) of a nucleon, we probe the partonic scale of nature, exploring what it means to be a nucleon. In this study, we are interested in the transversity PDF-the least studied of the three collinear PDFs. By conducting a global analysis on experimental data from semi-inclusive deep inelastic scattering (SIDIS), as well as single-inclusive e+e- annihilation (SIA), we extract the fit parameters needed to describe the transverse moment dependent (TMD) transversity PDF, as well as the Collins fragmentation function. Once the collinear transversity PDF is obtained by integrating the extracted TMD PDF, we wish to resolve discrepancies between lattice QCD calculations and phenomenological extractions of the tensor charge from data. Here we show our results for the transversity distribution and tensor charge. Using our method of iterative Monte Carlo, we now have a more robust understanding of the transversity PDF. With these results we are able to progress in our understanding of TMD PDFs, as well as testify to the efficacy of current lattice QCD calculations. This work is made possible through support from NSF award 1659177 to Old Dominion University.

Fixed-point theorems for families of weakly non-expansive maps

NASA Astrophysics Data System (ADS)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

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".

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".

Hard QCD processes in the nuclear medium

NASA Astrophysics Data System (ADS)

Freese, Adam

The environment inside the atomic nucleus is one of the most fascinating arenas for the study of quantum chromodynamics (QCD). The strongly-interacting nature of the nuclear medium a?ects the nature of both QCD processes and the quark-gluon structure of hadrons, allowing several unique aspects of the strong nuclear force to be investigated in reactions involving nuclear targets. The research presented in this dissertation explores two aspects of nuclear QCD: firstly, the partonic structure of the nucleus itself; and secondly, the use of the nucleus as a micro-laboratory in which QCD processes can be studied. The partonic structure of the nucleus is calculated in this work by deriving and utilizing a convolution formula. The hadronic structure of the nucleus and the quark-gluon structure of its constituent nucleons are taken together to determine the nuclear partonic structure. Light cone descriptions of short range correlations, in terms of both hadronic and partonic structure, are derived and taken into account. Medium modifications of the bound nucleons are accounted for using the color screening model, and QCD evolution is used to connect nuclear partonic structure at vastly di?erent energy scales. The formalism developed for calculating nuclear partonic structure is applied to inclusive dijet production from proton-nucleus collisions at LHC kinematics, and novel predictions are calculated and presented for the dijet cross section. The nucleus is investigated as a micro-laboratory in vector meson photoproduction reactions. In particular, the deuteron is studied in the break-up reaction gammad → Vpn, for both the φ(1020) and J/v vector mesons. The generalized eikonal approximation is utilized, allowing unambiguous separation of the impulse approximation and final state interactions (FSIs). Two peaks or valleys are seen in the angular distribution of the reaction cross section, each of which is due to an FSI between either the proton and neutron, or the

Trace theorem for quasi-Fuchsian groups

NASA Astrophysics Data System (ADS)

Connes, A.; Sukochev, F. A.; Zanin, D. V.

2017-10-01

We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322-325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.

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.

QCD with Chiral Imbalance: models vs. lattice

NASA Astrophysics Data System (ADS)

Andrianov, Alexander; Andrianov, Vladimir; Espriu, Domenec

2017-03-01

In heavy ion collisions (HIC) at high energies there may appear new phases of matter which must be described by QCD. These phases may have different color and flavour symmetries associated with the constituents involved in collisions as well as various space-time symmetries of hadron matter. Properties of the QCD medium in such a matter can be approximately described, in particular, by a number of right-handed (RH) and left-handed (LH) light quarks. The chiral imbalance (ChI) is characterized by the difference between the numbers of RH and LH quarks and supposedly occurs in the fireball after HIC. Accordingly we have to introduce a quark chiral (axial) chemical potential which simulates a ChI emerging in such a phase. In this report we discuss the possibility of a phase with Local spatial Parity Breaking (LPB) in such an environment and outline conceivable signatures for the registration of LPB as well as the appearance of new states in the spectra of scalar, pseudoscalar and vector particles as a consequence of local ChI. The comparison of the results obtained in the effective QCD- motivated models with lattice data is also performed.

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)

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

Refinement of Representation Theorems for Context-Free Languages

NASA Astrophysics Data System (ADS)

Fujioka, Kaoru

In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.

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.

QCD equation of state to O (μB6) from lattice QCD

NASA Astrophysics Data System (ADS)

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

2017-03-01

We calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon, strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range T ∈[135 MeV ,330 MeV ] using up to four different sets of lattice cutoffs corresponding to lattices of size Nσ3×Nτ with aspect ratio Nσ/Nτ=4 and Nτ=6 - 16 . The strange quark mass is tuned to its physical value, and we use two strange to light quark mass ratios ms/ml=20 and 27, which in the continuum limit correspond to a pion mass of about 160 and 140 MeV, respectively. Sixth-order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth-order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (μB≤2 T ). The fourth-order equation of state thus is suitable for the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to √{sN N}˜12 GeV . We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth-order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure, energy and entropy densities in the T -μB plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freeze-out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. We argue that results on sixth-order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for μB/T ≤2 and T /Tc(μB=0 )>0.9 .

QCD equation of state to O ( μ B 6 ) from lattice QCD

DOE PAGES

Bazavov, A.; Ding, H. -T.; Hegde, P.; ...

2017-03-07

In this work, we calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon, strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range T ϵ [135 MeV, 330 MeV] using up to four different sets of lattice cut-offs corresponding to lattices of size Nmore » $$3\\atop{σ}$$ × N τ with aspect ratio N σ/N τ = 4 and N τ = 6-16. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios m s/m l = 20 and 27, which in the continuum limit correspond to a pion mass of about 160 MeV and 140 MeV respectively. Sixth-order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth-order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (µ B ≤ 2T ). The fourth-order equation of state thus is suitable for √the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to √sNN ~ 12 GeV. We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure, energy and entropy densities in the T -µ B plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freeze-out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. Lastly, we argue that results on sixth order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for µ B/T ≤ 2 and T/T c(µ B = 0) > 0.9.« less

η and η' mesons from lattice QCD.

PubMed

Christ, N H; Dawson, C; Izubuchi, T; Jung, C; Liu, Q; Mawhinney, R D; Sachrajda, C T; Soni, A; Zhou, R

2010-12-10

The large mass of the ninth pseudoscalar meson, the η', is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1-flavor, lattice QCD calculation of the η and η' masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of θ=-14.1(2.8)°. Extrapolation to the physical light quark mass gives, with statistical errors only, mη=573(6) MeV and mη'=947(142) MeV, consistent with the experimental values of 548 and 958 MeV.

The Steep Nekhoroshev's Theorem

NASA Astrophysics Data System (ADS)

Guzzo, M.; Chierchia, L.; Benettin, G.

2016-03-01

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

Reduction theorems for optimal unambiguous state discrimination of density matrices

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

Raynal, Philippe; Luetkenhaus, Norbert; Enk, Steven J. van

2003-08-01

We present reduction theorems for the problem of optimal unambiguous state discrimination of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank n and are described in a Hilbert space of dimensions 2n. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N{>=}2)

Merging weak and QCD showers with matrix elements

DOE PAGES

Christiansen, Jesper Roy; Prestel, Stefan

2016-01-22

In this study, we present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell–Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton-shower resummation into a single framework. The new merging strategy is implemented in the P ythia event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.

Merging weak and QCD showers with matrix elements

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

Christiansen, Jesper Roy; Prestel, Stefan

In this study, we present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell–Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton-shower resummation into a single framework. The new merging strategy is implemented in the P ythia event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

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

Noether’s second theorem and Ward identities for gauge symmetries

DOE PAGES

Avery, Steven G.; Schwab, Burkhard U. W.

2016-02-04

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Resonances from lattice QCD

DOE PAGES

Briceno, Raul A.

2018-03-26

The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows formore » the determination of resonant electroweak amplitudes from finite-volume matrix elements. I use the recent calculation of the πγ* → ππ amplitude as an example illustrating the power of this formalism. From such amplitudes one can determine transition form factors of resonances. I close by reviewing on-going efforts to generalize these ideas to increasingly complex reactions and I then give a outlook of the field.« less

Resonances from lattice QCD

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

Briceno, Raul A.

The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows formore » the determination of resonant electroweak amplitudes from finite-volume matrix elements. I use the recent calculation of the πγ* → ππ amplitude as an example illustrating the power of this formalism. From such amplitudes one can determine transition form factors of resonances. I close by reviewing on-going efforts to generalize these ideas to increasingly complex reactions and I then give a outlook of the field.« less

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

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.

Tetraquarks in holographic QCD

NASA Astrophysics Data System (ADS)

Gutsche, Thomas; Lyubovitskij, Valery E.; Schmidt, Ivan

2017-08-01

Using a soft-wall AdS/QCD approach we derive the Schrödinger-type equation of motion for the tetraquark wave function, which is dual to the dimension-4 AdS bulk profile. The latter coincides with the number of constituents in the leading Fock state of the tetraquark. The obtained equation of motion is solved analytically, providing predictions for both the tetraquark wave function and its mass. A low mass limit for possible tetraquark states is given by M ≥2 κ =1 GeV , where κ =0.5 GeV is the typical value of the scale parameter in soft-wall AdS/QCD. We confirm results of the COMPASS Collaboration recently reported on the discovery of the a1(1414 ) state, interpreted as a tetraquark state composed of light quarks and having JP C=1++. Our prediction for the mass of this state, Ma1=√{2 } GeV ≃1.414 GeV , is in good agreement with the COMPASS result Ma1=1.41 4-0.013+0.015 GeV . Next we included finite quark mass effects, which are essential for the tetraquark states involving heavy quarks.

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.

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.

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 ).

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.

General self-tuning solutions and no-go theorem

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

Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min, E-mail: forste@th.physik.uni-bonn.de, E-mail: jihnekim@gmail.com, E-mail: hyun.min.lee@kias.re.kr

2013-03-01

We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodoxmore » Lagrangians.« less

Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

ERIC Educational Resources Information Center

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Model Checking Failed Conjectures in Theorem Proving: A Case Study

NASA Technical Reports Server (NTRS)

Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

2004-01-01

Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

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.

Experimenting with Langevin lattice QCD

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

Gavai, R.V.; Potvin, J.; Sanielevici, S.

1987-05-01

We report on the status of our investigations of the effects of systematic errors upon the practical merits of Langevin updating in full lattice QCD. We formulate some rules for the safe use of this updating procedure and some observations on problems which may be common to all approximate fermion algorithms.

Enter the reverend: introduction to and application of Bayes' theorem in clinical ophthalmology.

PubMed

Thomas, Ravi; Mengersen, Kerrie; Parikh, Rajul S; Walland, Mark J; Muliyil, Jayprakash

2011-12-01

Ophthalmic practice utilizes numerous diagnostic tests, some of which are used to screen for disease. Interpretation of test results and many clinical management issues are actually problems in inverse probability that can be solved using Bayes' theorem. Use two-by-two tables to understand Bayes' theorem and apply it to clinical examples. Specific examples of the utility of Bayes' theorem in diagnosis and management. Two-by-two tables are used to introduce concepts and understand the theorem. The application in interpretation of diagnostic tests is explained. Clinical examples demonstrate its potential use in making management decisions. Positive predictive value and conditional probability. The theorem demonstrates the futility of testing when prior probability of disease is low. Application to untreated ocular hypertension demonstrates that the estimate of glaucomatous optic neuropathy is similar to that obtained from the Ocular Hypertension Treatment Study. Similar calculations are used to predict the risk of acute angle closure in a primary angle closure suspect, the risk of pupillary block in a diabetic undergoing cataract surgery, and the probability that an observed decrease in intraocular pressure is due to the medication that has been started. The examples demonstrate how data required for management can at times be easily obtained from available information. Knowledge of Bayes' theorem helps in interpreting test results and supports the clinical teaching that testing for conditions with a low prevalence has a poor predictive value. In some clinical situations Bayes' theorem can be used to calculate vital data required for patient management. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

NΩ interaction from two approaches in lattice QCD

NASA Astrophysics Data System (ADS)

Etminan, Faisal; Firoozabadi, Mohammad Mehdi

2014-10-01

We compare the standard finite volume method by Lüscher with the potential method by HAL QCD collaboration, by calculating the ground state energy of N(nucleon)-Ω(Omega) system in 5 S2 channel. We employ 2+1 flavor full QCD configurations on a (1.9 fm)3×3.8 fm lattice at the lattice spacing a≃0.12 fm, whose ud(s) quark mass corresponds to mπ = 875(1) (mK = 916(1)) MeV. We have found that both methods give reasonably consistent results that there is one NΩ bound state at this parameter.

Exploring Flavor Physics with Lattice QCD

NASA Astrophysics Data System (ADS)

Du, Daping; Fermilab/MILC Collaborations Collaboration

2016-03-01

The Standard Model has been a very good description of the subatomic particle physics. In the search for physics beyond the Standard Model in the context of flavor physics, it is important to sharpen our probes using some gold-plated processes (such as B rare decays), which requires the knowledge of the input parameters, such as the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and other nonperturbative quantities, with sufficient precision. Lattice QCD is so far the only first-principle method which could compute these quantities with competitive and systematically improvable precision using the state of the art simulation techniques. I will discuss the recent progress of lattice QCD calculations on some of these nonpurturbative quantities and their applications in flavor physics. I will also discuss the implications and future perspectives of these calculations in flavor physics.

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.

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.

Abel's Theorem Simplifies Reduction of Order

ERIC Educational Resources Information Center

Green, William R.

2011-01-01

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

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.

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

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.

Entanglement, space-time and the Mayer-Vietoris theorem

NASA Astrophysics Data System (ADS)

Patrascu, Andrei T.

2017-06-01

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

Volumes of critical bubbles from the nucleation theorem

NASA Astrophysics Data System (ADS)

Wilemski, Gerald

2006-09-01

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V* of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the pT,x form of the nucleation theorem as a sum rule is noted.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Nucleon PDFs and TMDs from Continuum QCD

NASA Astrophysics Data System (ADS)

Bednar, Kyle; Cloet, Ian; Tandy, Peter

2017-09-01

The parton structure of the nucleon is investigated in an approach based upon QCD's Dyson-Schwinger equations. The method accommodates a variety of QCD's dynamical outcomes including: the running mass of quark propagators and formation of non-pointlike di-quark correlations. All needed elements, including the nucleon wave function solution from a Poincaré covariant Faddeev equation, are encoded in spectral-type representations in the Nakanishi style to facilitate Feynman integral procedures and allow insight into key underlying mechanisms. Results will be presented for spin-independent PDFs and TMDs arising from a truncation to allow only scalar di-quark correlations. The influence of axial-vector di-quark correlations may be discussed if results are available. Supported by NSF Grant No. PHY-1516138.

Using Bayes' theorem for free energy calculations

NASA Astrophysics Data System (ADS)

Rogers, David M.

Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.

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.

Nuclear Physics and Lattice QCD

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

Beane, Silas

2003-11-01

Impressive progress is currently being made in computing properties and interac- tions of the low-lying hadrons using lattice QCD. However, cost limitations will, for the foreseeable future, necessitate the use of quark masses, Mq, that are signif- icantly larger than those of nature, lattice spacings, a, that are not significantly smaller than the physical scale of interest, and lattice sizes, L, that are not sig- nificantly larger than the physical scale of interest. Extrapolations in the quark masses, lattice spacing and lattice volume are therefore required. The hierarchy of mass scales is: L 1 j Mq j â ºC jmore » a 1 . The appropriate EFT for incorporating the light quark masses, the finite lattice spacing and the lattice size into hadronic observables is C-PT, which provides systematic expansions in the small parame- ters e m L, 1/ Lâ ºC, p/â ºC, Mq/â ºC and aâ ºC . The lattice introduces other unphysical scales as well. Lattice QCD quarks will increasingly be artificially separated« less

On Leighton's comparison theorem

NASA Astrophysics Data System (ADS)

Ghatasheh, Ahmed; Weikard, Rudi

2017-06-01

We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.

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.

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.

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).

Two-gluon and trigluon glueballs from dynamical holography QCD

NASA Astrophysics Data System (ADS)

Chen, Yi-dian; Huang, Mei

2016-12-01

We study the scalar, vector and tensor two-gluon and trigluon glueball spectra in the framework of the 5-dimension dynamical holographic QCD model, where the metric structure is deformed self-consistently by the dilaton field. For comparison, the glueball spectra are also calculated in the hard-wall and soft-wall holographic QCD models. In order to distinguish glueballs with even and odd parities, we introduce a positive and negative coupling between the dilaton field and glueballs, and for higher spin glueballs, we introduce a deformed 5-dimension mass. With this set-up, there is only one free parameter from the quadratic dilaton profile in the dynamical holographic QCD model, which is fixed by the scalar glueball spectra. It is found that the two-gluon glueball spectra produced in the dynamical holographic QCD model are in good agreement with lattice data. Among six trigluon glueballs, the produced masses for 1±- and 2-- are in good agreement with lattice data, and the produced masses for 0--, 0+- and 2+- are around 1.5 GeV lighter than lattice results. This result might indicate that the three trigluon glueballs of 0--, 0+- and 2+- are dominated by the three-gluon condensate contribution. Supported by the NSFC (11175251, 11621131001), DFG and NSFC (CRC 110), CAS Key Project KJCX2-EW-N01, K.C.Wong Education Foundation, and Youth Innovation Promotion Association of CAS

Testing subleading multiple soft graviton theorem for CHY prescription

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

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.

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Sharp comparison theorems for the Klein-Gordon equation in d dimensions

NASA Astrophysics Data System (ADS)

Hall, Richard L.; Zorin, Petr

2016-06-01

We establish sharp (or ’refined’) comparison theorems for the Klein-Gordon equation. We show that the condition Va ≤ Vb, which leads to Ea ≤ Eb, can be replaced by the weaker assumption Ua ≤ Ub which still implies the spectral ordering Ea ≤ Eb. In the simplest case, for d = 1, Ui(x) =∫0xV i(t)dt, i = a or b and for d > 1, Ui(r) =∫0rV i(t)td-1dt, i = a or b. We also consider sharp comparison theorems in the presence of a scalar potential S (a ‘variable mass’) in addition to the vector term V (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.

Basics of QCD perturbation theory

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

Soper, D.E.

1997-06-01

This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.

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.

Pythagoras Theorem and Relativistic Kinematics

NASA Astrophysics Data System (ADS)

Mulaj, Zenun; Dhoqina, Polikron

2010-01-01

In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.

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)

Student Research Project: Goursat's Other Theorem

ERIC Educational Resources Information Center

Petrillo, Joseph

2009-01-01

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

Fluctuation theorem for channel-facilitated membrane transport of interacting and noninteracting solutes.

PubMed

Berezhkovskii, Alexander M; Bezrukov, Sergey M

2008-05-15

In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.

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.

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.

Current matrix element in HAL QCD's wavefunction-equivalent potential method

NASA Astrophysics Data System (ADS)

Watanabe, Kai; Ishii, Noriyoshi

2018-04-01

We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

Bs and Ds decay constants in three-flavor lattice QCD.

PubMed

Wingate, Matthew; Davies, Christine T H; Gray, Alan; Lepage, G Peter; Shigemitsu, Junko

2004-04-23

Capitalizing on recent advances in lattice QCD, we present a calculation of the leptonic decay constants f(B(s)) and f(D(s)) that includes effects of one strange sea quark and two light sea quarks via an improved staggered action. By shedding the quenched approximation and the associated lattice scale uncertainty, lattice QCD greatly increases its predictive power. Nonrelativistic QCD is used to simulate heavy quarks with masses between 1.5m(c) and m(b). We arrive at the following results: f(B(s))=260+/-7+/-26+/-8+/-5 and f(D(s))=290+/-20+/-29+/-29+/-6 MeV. The first quoted error is the statistical uncertainty, and the rest estimate the sizes of higher order terms neglected in this calculation. All of these uncertainties are systematically improvable by including another order in the weak coupling expansion, the nonrelativistic expansion, or the Symanzik improvement program.

Electrostatic Hellmann-Feynman theorem applied to long-range interatomic forces - The hydrogen molecule.

NASA Technical Reports Server (NTRS)

Steiner, E.

1973-01-01

The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.

Explorations of the Gauss-Lucas Theorem

ERIC Educational Resources Information Center

Brilleslyper, Michael A.; Schaubroeck, Beth

2017-01-01

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

QCD triple Pomeron coupling from string amplitudes

NASA Astrophysics Data System (ADS)

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

1998-06-01

Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

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.

Testing ground for fluctuation theorems: The one-dimensional Ising model

NASA Astrophysics Data System (ADS)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems

PubMed Central

Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok

2018-01-01

Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target’s trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes. PMID:29562621

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

Determination of the chiral condensate from (2+1)-flavor lattice QCD.

PubMed

Fukaya, H; Aoki, S; Hashimoto, S; Kaneko, T; Noaki, J; Onogi, T; Yamada, N

2010-03-26

We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16{3}x48 lattice at a lattice spacing approximately 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in (2+1)-flavor QCD with strange quark mass fixed at its physical value as Sigma;{MS[over ]}(2 GeV)=[242(04)(+19/-18) MeV]{3} where the errors are statistical and systematic, respectively.

The Pythagorean Theorem and the Solid State

ERIC Educational Resources Information Center

Kelly, Brenda S.; Splittgerber, Allan G.

2005-01-01

Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.

Hyperasymptotics and quark-hadron duality violations in QCD

NASA Astrophysics Data System (ADS)

Boito, Diogo; Caprini, Irinel; Golterman, Maarten; Maltman, Kim; Peris, Santiago

2018-03-01

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex q2 plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality-violating contributions. Starting with the assumption that for QCD at Nc=∞ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite Nc.

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.

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.

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.

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.

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.

QCD sum rules study of meson-baryon sigma terms

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

Erkol, Gueray; Oka, Makoto; Turan, Guersevil

2008-11-01

The pion-baryon sigma terms and the strange-quark condensates of the octet and the decuplet baryons are calculated by employing the method of QCD sum rules. We evaluate the vacuum-to-vacuum transition matrix elements of two baryon interpolating fields in an external isoscalar-scalar field and use a Monte Carlo-based approach to systematically analyze the sum rules and the uncertainties in the results. We extract the ratios of the sigma terms, which have rather high accuracy and minimal dependence on QCD parameters. We discuss the sources of uncertainties and comment on possible strangeness content of the nucleon and the Delta.

A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone

ERIC Educational Resources Information Center

Stupel, Moshe; Ben-Chaim, David

2013-01-01

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

Charmed tetraquarks Tcc and Tcs from dynamical lattice QCD simulations

NASA Astrophysics Data System (ADS)

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

2014-02-01

Charmed tetraquarks Tcc=(ccubardbar) and Tcs=(csubardbar) are studied through the S-wave meson-meson interactions, D-D, Kbar-D, D-D* and Kbar-D*, on the basis of the (2+1)-flavor lattice QCD simulations with the pion mass mπ≃410, 570 and 700 MeV. For the charm quark, the relativistic heavy quark action is employed to treat its dynamics on the lattice. Using the HAL QCD method, we extract the S-wave potentials in lattice QCD simulations, from which the meson-meson scattering phase shifts are calculated. The phase shifts in the isospin triplet (I=1) channels indicate repulsive interactions, while those in the I=0 channels suggest attraction, growing as mπ decreases. This is particularly prominent in the Tcc (JP=1+,I=0) channel, though neither bound state nor resonance are found in the range mπ=410-700 MeV. We make a qualitative comparison of our results with the phenomenological diquark picture.

Searching for beauty-fully bound tetraquarks using lattice nonrelativistic QCD

NASA Astrophysics Data System (ADS)

Hughes, Ciaran; Eichten, Estia; Davies, Christine T. H.

2018-03-01

Motivated by multiple phenomenological considerations, we perform the first search for the existence of a b ¯b ¯b b tetraquark bound state with a mass below the lowest noninteracting bottomonium-pair threshold using the first-principles lattice nonrelativistic QCD methodology. We use a full S -wave color/spin basis for the b ¯b ¯b b operators in the three 0++, 1+- and 2++ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from a =0.06 - 0.12 fm , all of which include u , d , s and c quarks in the sea, and one ensemble which has physical light-quark masses. Additionally, we perform novel exploratory work with the objective of highlighting any signal of a near threshold tetraquark, if it existed, by adding an auxiliary potential into the QCD interactions. With our results we find no evidence of a QCD bound tetraquark below the lowest noninteracting thresholds in the channels studied.

Searching for beauty-fully bound tetraquarks using lattice nonrelativistic QCD

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

Hughes, Ciaran; Eichten, Estia; Davies, Christine T. H.

Motivated by multiple phenomenological considerations, we perform the first search for the existence of amore » $$\\bar{bb}bb$$ tetraquark bound state with a mass below the lowest noninteracting bottomonium-pair threshold using the first-principles lattice nonrelativistic QCD methodology. Here, we use a full S-wave color/spin basis for the $$\\bar{bb}bb$$ operators in the three 0 ++, 1 +- and 2 ++ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from a=0.06–0.12 fm, all of which include u, d, s and c quarks in the sea, and one ensemble which has physical light-quark masses. Additionally, we perform novel exploratory work with the objective of highlighting any signal of a near threshold tetraquark, if it existed, by adding an auxiliary potential into the QCD interactions. With our results we find no evidence of a QCD bound tetraquark below the lowest noninteracting thresholds in the channels studied.« less

Searching for beauty-fully bound tetraquarks using lattice nonrelativistic QCD

DOE PAGES

Hughes, Ciaran; Eichten, Estia; Davies, Christine T. H.

2018-03-14

Motivated by multiple phenomenological considerations, we perform the first search for the existence of amore » $$\\bar{bb}bb$$ tetraquark bound state with a mass below the lowest noninteracting bottomonium-pair threshold using the first-principles lattice nonrelativistic QCD methodology. Here, we use a full S-wave color/spin basis for the $$\\bar{bb}bb$$ operators in the three 0 ++, 1 +- and 2 ++ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from a=0.06–0.12 fm, all of which include u, d, s and c quarks in the sea, and one ensemble which has physical light-quark masses. Additionally, we perform novel exploratory work with the objective of highlighting any signal of a near threshold tetraquark, if it existed, by adding an auxiliary potential into the QCD interactions. With our results we find no evidence of a QCD bound tetraquark below the lowest noninteracting thresholds in the channels studied.« less

Cosmological abundance of the QCD axion coupled to hidden photons

NASA Astrophysics Data System (ADS)

Kitajima, Naoya; Sekiguchi, Toyokazu; Takahashi, Fuminobu

2018-06-01

We study the cosmological evolution of the QCD axion coupled to hidden photons. For a moderately strong coupling, the motion of the axion field leads to an explosive production of hidden photons by tachyonic instability. We use lattice simulations to evaluate the cosmological abundance of the QCD axion. In doing so, we incorporate the backreaction of the produced hidden photons on the axion dynamics, which becomes significant in the non-linear regime. We find that the axion abundance is suppressed by at most O (102) for the decay constant fa =1016GeV, compared to the case without the coupling. For a sufficiently large coupling, the motion of the QCD axion becomes strongly damped, and as a result, the axion abundance is enhanced. Our results show that the cosmological upper bound on the axion decay constant can be relaxed by a few hundred for a certain range of the coupling to hidden photons.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Generalized Friedland's theorem for C0-semigroups

NASA Astrophysics Data System (ADS)

Cichon, Dariusz; Jung, Il Bong; Stochel, Jan

2008-07-01

Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.

On Viviani's Theorem and Its Extensions

ERIC Educational Resources Information Center

Abboud, Elias

2010-01-01

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…

Fixed Point Theorems for Hybrid Mappings

PubMed Central

Kamran, Tayyab; Karapinar, Erdal

2015-01-01

We obtain some fixed point theorems for two pairs of hybrid mappings using hybrid tangential property and quadratic type contractive condition. Our results generalize some results by Babu and Alemayehu and those contained therein. In the sequel, we introduce a new notion to generalize occasionally weak compatibility. Moreover, two concrete examples are established to illuminate the generality of our results. PMID:25629089

Representations of the language recognition problem for a theorem prover

NASA Technical Reports Server (NTRS)

Minker, J.; Vanderbrug, G. J.

1972-01-01

Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.

The QCD corrections of the process h → ηbZ

NASA Astrophysics Data System (ADS)

Zhu, Rong-Fei; Feng, Tai-Fu; Zhang, Hai-Bin

2018-05-01

We investigate the 125 GeV Higgs boson decay to a pseudoscalar quarkonium ηb and Z boson. We calculate the quantum chromodynamics (QCD) one-loop corrections to the branching ratio of the process, Br(h → ηbZ), both in the Standard Model (SM) and in the two Higgs double models (THDM). Adding the QCD one-loop corrections, the branching ratio of h → ηbZ in the SM is Br(h → ηbZ) = (4.739‑0.244+0.276) × 10‑5. The relative correction of that QCD one-loop level relative to the tree level of Br(h → ηbZ) is around 76% in the SM. Similarly, the relative correction in the THDM also can be around 75%. The key parameter, tan β, can affect the relative correction in the THDM.

Constructing a neutron star from the lattice in G2-QCD

NASA Astrophysics Data System (ADS)

Hajizadeh, Ouraman; Maas, Axel

2017-10-01

The inner structure of neutron stars is still an open question. One obstacle is the infamous sign problem of lattice QCD, which bars access to the high-density equation of state. A possibility to make progress and understand the qualitative impact of gauge interactions on the neutron star structure is to study a modified version of QCD without the sign problem. In the modification studied here the gauge group of QCD is replaced by the exceptional Lie group G_2 , which keeps neutrons in the spectrum. Using an equation of state from lattice calculations only we determine the mass-radius-relation for a neutron star using the Tolman-Oppenheimer-Volkoff equation. This allows us to understand the challenges and approximations currently necessary to use lattice data for this purpose. We discuss in detail the particular uncertainties and systematic problems of this approach.

Broken chiral symmetry on a null plane

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

Beane, Silas R., E-mail: silas@physics.unh.edu

2013-10-15

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-planemore » description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.« less

Topics in QCD at Nonzero Temperature and Density

NASA Astrophysics Data System (ADS)

Pangeni, Kamal

Understanding the behavior of matter at ultra-high density such as neutron stars require the knowledge of ground state properties of Quantum chromodynamics (QCD) at finite chemical potential. However, this task has turned out to be very difficult because of two main reasons: 1) QCD may still be strongly coupled at those regimes making perturbative calculations unreliable and 2) QCD at finite density suffers from the sign problem that makes the use of lattice simulation problematic and it even affects phenomenological models. In the first part of this thesis, we show that the sign problem in analytical calculations of finite density models can be solved by considering the CK-symmetric, where C is charge conjugation and K is complex conjugation, complex saddle points of the effective action. We then explore the properties and consequences of such complex saddle points at non-zero temperature and density. Due to CK symmetry, the mass matrix eigenvalues in these models are not always real but can be complex, which results in damped oscillation of the density-density correlation function, a new feature of finite density models. To address the generality of such behavior, we next consider a lattice model of QCD with static quarks at strong-coupling. Computation of the mass spectrum confirms the existence of complex eigenvalues in much of temperature-chemical potential plane. This provides an independent confirmation of our results obtained using phenomenological models of QCD. The existence of regions in parameter space where density-density correlation function exhibit damped oscillation is one of the hallmarks of typical liquid-gas system. The formalism developed to tackle the sign problem in QCD models actually gives a simple understanding for the existence of such behavior in liquid-gas system. To this end, we develop a generic field theoretic model for the treatment of liquid-gas phase transition. An effective field theory at finite density derived from a

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Stochastic thermodynamics, fluctuation theorems and molecular machines.

PubMed

Seifert, Udo

2012-12-01

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

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.

openQ*D simulation code for QCD+QED

NASA Astrophysics Data System (ADS)

Campos, Isabel; Fritzsch, Patrick; Hansen, Martin; Krstić Marinković, Marina; Patella, Agostino; Ramos, Alberto; Tantalo, Nazario

2018-03-01

The openQ*D code for the simulation of QCD+QED with C* boundary conditions is presented. This code is based on openQCD-1.6, from which it inherits the core features that ensure its efficiency: the locally-deflated SAP-preconditioned GCR solver, the twisted-mass frequency splitting of the fermion action, the multilevel integrator, the 4th order OMF integrator, the SSE/AVX intrinsics, etc. The photon field is treated as fully dynamical and C* boundary conditions can be chosen in the spatial directions. We discuss the main features of openQ*D, and we show basic test results and performance analysis. An alpha version of this code is publicly available and can be downloaded from http://rcstar.web.cern.ch/.

Mixing rates and limit theorems for random intermittent maps

NASA Astrophysics Data System (ADS)

Bahsoun, Wael; Bose, Christopher

2016-04-01

We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.

Reasoning by analogy as an aid to heuristic theorem proving.

NASA Technical Reports Server (NTRS)

Kling, R. E.

1972-01-01

When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.

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

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

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.

Tennis Rackets and the Parallel Axis Theorem

ERIC Educational Resources Information Center

Christie, Derek

2014-01-01

This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.

QCD and Multiparticle Production - Proceedings of the XXIX International Symposium on Multiparticle Dynamics

NASA Astrophysics Data System (ADS)

Sarcevic, Ina; Tan, Chung-I.

2000-07-01

-hard Components in Multiplicity Distributions in the TeV Region * Qualitative Difference Between Particle Production Dynamics in Soft and Hard Processes * Session Chairman: M. Tannenbaum -- Bose-Einstein Correlations * Questions in Bose-Einstein Correlations * The Source Size Dependence on the mhadron Applying Fermi and Bose Statistics and I-Spin Invariance * Signal of Partial UA(1) Symmetry Restoration from Two-Pion Bose-Einstein Correlations * Multiparticle Bose-Einstein Correlations in Heavy-Ion Collisions * Tuesday afternoon session: Heavy Ion Collisions - Conveners: B. Müller and J. Statchel * Session Chairman: J. Stachel * Probing Baryon Freeze-out Density at the AGS with Proton Correlations * Centrality Dependence of Hadronic Observables at CERN SPS * Study of Transverse Momentum Spectra in pp Collisions with a Statistical Model of Hadronisation * Session Chairman: B. Brower * Production of Light (Anti-)Nuclei with E864 at the AGS * QCD Critical Point in Heavy-Ion Collision Experiments * Tuesday evening session * Session Chairman: H. M. Fried * Oscillating Hq, Event Shapes, and QCD * Critical Behavior of Quark-Hadron Phase Transition * Shadowing of Gluons at RHIC and LHC * Parton Distributions in Nuclei at Small x * Wednesday morning session: Diffraction and Small x - Conveners: M. Derrick and A. White * Session Chairman: C. Pajares * High-Energy Effective Action from Scattering of Shock Waves in QCD * The Triangle Anomaly in the Triple-Regge Limit * CDF Results on Hard Diffraction and Rapidity Gap Physics * DØ Results on Hard Diffraction * Interjet Rapidity Gaps in Perturbative QCD * Pomeron: Beyond the Standard Approach * Factorization and Diffractive Production at Collider Energies * Thursday morning session: Heavy Ion Collisions - Conveners: B. Müller and J. B. Stachel * Session Chairman: N. Schmitz * Summary of J/ψ Suppression Data and Preliminary Results on Multiplicity Distributions in PB-PB Collisions from the NA50 Experiment * Duality and Chiral Restoration

Fluctuations in the quark-meson model for QCD with isospin chemical potential

NASA Astrophysics Data System (ADS)

Kamikado, Kazuhiko; Strodthoff, Nils; von Smekal, Lorenz; Wambach, Jochen

2013-01-01

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, μB and μI. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite μB = 3 μ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (μI, μ) plane of this phase diagram is strongly constrained by the "Silver Blaze problem." In particular, the onset of pion condensation must occur at μI =mπ / 2, independent of μ as long as μ +μI stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.

Learning-assisted theorem proving with millions of lemmas☆

PubMed Central

Kaliszyk, Cezary; Urban, Josef

2015-01-01

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck. PMID:26525678

Berry Phase in Lattice QCD.

PubMed

Yamamoto, Arata

2016-07-29

We propose the lattice QCD calculation of the Berry phase, which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.

Hadron electric polarizability from lattice QCD

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Lujan, Michael; Freeman, Walter; Lee, Frank

2015-04-01

Electric polarizability measures the ability of the electric field to deform a particle. Experimentally, electric and magnetic polarizabilities can be measured in Compton scattering experiments. To compute these quantities theoretically we need to understand the internal structure of the scatterer and the dynamics of its constituents. For hadrons - bound stated of quarks and gluons - this is a very difficult problem. Lattice QCD can be used to compute the polarizabilities directly in terms of quark and gluons degrees of freedom. In this talk we focus on the neutron. We present results for the electric polarizability for two different quark masses, light enough to connect to chiral perturbation theory. These are currently the lightest quark masses used in lattice QCD polarizability studies. For each pion mass we compute the polarizability at four different volumes and perform an infinite volume extrapolation. For one ensemble, we also discuss the effect of turning on the coupling between the background field and the sea quarks. We compare our results to chiral perturbation theory expectations.

Searching for the QCD Axion with Gravitational Microlensing

NASA Astrophysics Data System (ADS)

Fairbairn, Malcolm; Marsh, David J. E.; Quevillon, Jérémie

2017-07-01

The phase transition responsible for axion dark matter (DM) production can create large amplitude isocurvature perturbations, which collapse into dense objects known as axion miniclusters. We use microlensing data from the EROS survey and from recent observations with the Subaru Hyper Suprime Cam to place constraints on the minicluster scenario. We compute the microlensing event rate for miniclusters, treating them as spatially extended objects. Using the published bounds on the number of microlensing events, we bound the fraction of DM collapsed into miniclusters fMC. For an axion with temperature-dependent mass consistent with the QCD axion, we find fMC<0.083 (ma/100 μ eV )0.12 , which represents the first observational constraint on the minicluster fraction. We forecast that a high-efficiency observation of around ten nights with Subaru would be sufficient to constrain fMC≲0.004 over the entire QCD axion mass range. We make various approximations to derive these constraints, and dedicated analyses by the observing teams of EROS and Subaru are necessary to confirm our results. If accurate theoretical predictions for fMC can be made in the future, then microlensing can be used to exclude or discover the QCD axion. Further details of our computations are presented in a companion paper [M. Fairbairn, D. J. E. Marsh, J. Quevillon, and S. Rozier (to be published)].

Quenching parameter in a holographic thermal QCD

NASA Astrophysics Data System (ADS)

Patra, Binoy Krishna; Arya, Bhaskar

2017-01-01

We have calculated the quenching parameter, q ˆ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS black hole metric for which the dual gauge theory becomes conformally invariant unlike QCD. Therefore we use a metric which incorporates the fundamental quarks by embedding the coincident D7 branes in the Klebanov-Tseytlin background and a finite temperature is switched on by inserting a black hole into the background, known as OKS-BH metric. Further inclusion of an additional UV cap to the metric prepares the dual gauge theory to run similar to thermal QCD. Moreover q ˆ is usually defined in the literature from the Glauber model perturbative QCD evaluation of the Wilson loop, which has no reasons to hold if the coupling is large and is thus against the main idea of gauge-gravity duality. Thus we use an appropriate definition of q ˆ : q ˆ L- = 1 /L2, where L is the separation for which the Wilson loop is equal to some specific value. The above two refinements cause q ˆ to vary with the temperature as T4 always and to depend linearly on the light-cone time L- with an additional (1 /L-) correction term in the short-distance limit whereas in the long-distance limit, q ˆ depends only linearly on L- with no correction term. These observations agree with other holographic calculations directly or indirectly.

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.

Communication. Kinetics of scavenging of small, nucleating clusters. First nucleation theorem and sum rules

DOE PAGES

Malila, Jussi; McGraw, Robert; Laaksonen, Ari; ...

2015-01-07

Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less

Effective model approach to the dense state of QCD matter

NASA Astrophysics Data System (ADS)

Fukushima, Kenji

2011-12-01

The first-principle approach to the dense state of QCD matter, i.e. the lattice-QCD simulation at finite baryon density, is not under theoretical control for the moment. The effective model study based on QCD symmetries is a practical alternative. However the model parameters that are fixed by hadronic properties in the vacuum may have unknown dependence on the baryon chemical potential. We propose a new prescription to constrain the effective model parameters by the matching condition with the thermal Statistical Model. In the transitional region where thermal quantities blow up in the Statistical Model, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from hadrons and resonances. We use the Polyakov-loop coupled Nambu-Jona-Lasinio (PNJL) model as an effective description in the quark side and show how the matching condition is satisfied by a simple ansäatz on the Polyakov loop potential. Our results favor a phase diagram with the chiral phase transition located at slightly higher temperature than deconfinement which stays close to the chemical freeze-out points.

Freeze-out conditions in heavy ion collisions from QCD thermodynamics.

PubMed

Bazavov, A; Ding, H-T; Hegde, P; Kaczmarek, O; Karsch, F; Laermann, E; Mukherjee, Swagato; Petreczky, P; Schmidt, C; Smith, D; Soeldner, W; Wagner, M

2012-11-09

We present a determination of freeze-out conditions in heavy ion collisions based on ratios of cumulants of net electric charge fluctuations. These ratios can reliably be calculated in lattice QCD for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. From a computation of up to fourth order cumulants and charge correlations we first determine the strangeness and electric charge chemical potentials that characterize freeze-out conditions in a heavy ion collision and confirm that in the temperature range 150 MeV ≤ T ≤ 170 MeV the hadron resonance gas model provides good approximations for these parameters that agree with QCD calculations on the 5%-15% level. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature.

QCD nature of dark energy at finite temperature: Cosmological implications

NASA Astrophysics Data System (ADS)

Azizi, K.; Katırcı, N.

2016-05-01

The Veneziano ghost field has been proposed as an alternative source of dark energy, whose energy density is consistent with the cosmological observations. In this model, the energy density of the QCD ghost field is expressed in terms of QCD degrees of freedom at zero temperature. We extend this model to finite temperature to search the model predictions from late time to early universe. We depict the variations of QCD parameters entering the calculations, dark energy density, equation of state, Hubble and deceleration parameters on temperature from zero to a critical temperature. We compare our results with the observations and theoretical predictions existing at different eras. It is found that this model safely defines the universe from quark condensation up to now and its predictions are not in tension with those of the standard cosmology. The EoS parameter of dark energy is dynamical and evolves from -1/3 in the presence of radiation to -1 at late time. The finite temperature ghost dark energy predictions on the Hubble parameter well fit to those of Λ CDM and observations at late time.

Symmetries and mass splittings QCD 2 coupled to adjoint fermions

NASA Astrophysics Data System (ADS)

Boorstein, Joshua; Kutasov, David

1994-06-01

Two-dimensional QCD coupled to fermions in the adjoint representation of the gauge group SU( N), a useful toy model of QCD strings, is supersymmetric for a certain ratio of quark mass and gauge coupling constant. Here we study the theory in the vicinity of the supersymmetric point; in particular we exhibit the algebraic structure of the model and show that the mass splittings as one moves away from the supersymmetric point obey a universal relation of the form Mi2(B)- Mi2(F) = Miδm + O( δm3). We discuss the connection of this relation to string and quark model expectations and verify it numerically for large N. At least for low lying states the O( δm3) corrections are extremely small. We also discuss a natural generalization of QCD 2 with an infinite number of couplings, which preserves SUSY. This leads to a Landau-Ginzburg description of the theory, and may be useful for defining a scaling limit in which smooth worldsheets appear.

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.

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

QCD studies in ep collisions

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

Smith, W.H.

1997-06-01

These lectures describe QCD physics studies over the period 1992--1996 from data taken with collisions of 27 GeV electrons and positrons with 820 GeV protons at the HERA collider at DESY by the two general-purpose detectors H1 and ZEUS. The focus of these lectures is on structure functions and jet production in deep inelastic scattering, photoproduction, and diffraction. The topics covered start with a general introduction to HERA and ep scattering. Structure functions are discussed. This includes the parton model, scaling violation, and the extraction of F{sub 2}, which is used to determine the gluon momentum distribution. Both low andmore » high Q{sup 2} regimes are discussed. The low Q{sup 2} transition from perturbative QCD to soft hadronic physics is examined. Jet production in deep inelastic scattering to measure {alpha}{sub s}, and in photoproduction to study resolved and direct photoproduction, is also presented. This is followed by a discussion of diffraction that begins with a general introduction to diffraction in hadronic collisions and its relation to ep collisions, and moves on to deep inelastic scattering, where the structure of diffractive exchange is studied, and in photoproduction, where dijet production provides insights into the structure of the Pomeron. 95 refs., 39 figs.« less

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

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

Ohashi, Y.

2004-12-01

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theorymore » developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.« less

Applying the multivariate time-rescaling theorem to neural population models

PubMed Central

Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon

2011-01-01

Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436

Gauge Invariance and the Goldstone Theorem

NASA Astrophysics Data System (ADS)

Guralnik, Gerald S.

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

Special relativity theorem and Pythagoras’s magic

NASA Astrophysics Data System (ADS)

Korkmaz, S. D.; Aybek, E. C.; Örücü, M.

2016-03-01

In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.

Answering Junior Ant's "Why" for Pythagoras' Theorem

ERIC Educational Resources Information Center

Pask, Colin

2002-01-01

A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

Fermat's Last Theorem for Factional and Irrational Exponents

ERIC Educational Resources Information Center

Morgan, Frank

2010-01-01

Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

PubMed Central

Zhang, Likun; Marston, Philip L.

2013-01-01

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam. PMID:24049681

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.