Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations
NASA Astrophysics Data System (ADS)
Jadach, S.; Płaczek, W.; Skrzypek, M.; Stokłosa, P.
2010-02-01
We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5×10. This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summaryProgram title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions:Limited to the case of massless partons. Implemented in the LO and NLO approximations only. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5×10. Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C-type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
NASA Astrophysics Data System (ADS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-03-01
We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)SJNCAS0038-5506][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)SPHJAR0038-5646] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)EPCFFB1434-604410.1140/epjc/s10052-009-1195-8][M. M. Block, Eur. Phys. J. C 68, 683 (2010)EPCFFB1434-604410.1140/epjc/s10052-010-1374-7] allow us to write fully decoupled solutions for the singlet structure function Fs(x,Q2) and G(x,Q2) as Fs(x,Q2)=Fs(Fs0(x0),G0(x0)) and G(x,Q2)=G(Fs0(x0),G0(x0)), where the x0 are the Bjorken x values at Q02. Here Fs and G are known functions—found using LO DGLAP splitting functions—of the initial boundary conditions Fs0(x)≡Fs(x,Q02) and G0(x)≡G(x,Q02), i.e., the chosen starting functions at the virtuality Q02. For both G(x) and Fs(x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy—a computational fractional precision of O(10-9). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet Fs distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)EPCFFB1434-604410.1140/epjc/s10052-009-1072-5], starting from their initial values at Q02=1GeV2 and 1.69GeV2, respectively, using their choice of αs(Q2). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and Fs satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of
A new approach to parton recombination in the QCD evolution equations
NASA Astrophysics Data System (ADS)
Wei Zhu
1999-06-01
Parton recombination is reconsidered in perturbation theory without using the AGK cutting rules in the leading order of the recombination. We use time-ordered perturbation theory to sum the cut diagrams, which are neglected in the GLR evolution equation. We present a set of new evolution equations including parton recombination.
NASA Astrophysics Data System (ADS)
These are the proceedings of the QCD Evolution 2015 Workshop which was held 26-30 May, 2015 at Jefferson Lab, Newport News, Virginia, USA. The workshop is a continuation of a series of workshops held during four consecutive years 2011, 2012, 2013 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 with great enthusiasm to the 2015 meeting. A special attention was also paid to participation of experimentalists as the topics discussed are of immediate importance for the JLab 12 experimental program and a future Electron Ion Collider.
Jet quenching from QCD evolution
NASA Astrophysics Data System (ADS)
Chien, Yang-Ting; Emerman, Alexander; Kang, Zhong-Bo; Ovanesyan, Grigory; Vitev, Ivan
2016-04-01
Recent advances in soft-collinear effective theory with Glauber gluons have led to the development of a new method that gives a unified description of inclusive hadron production in reactions with nucleons and heavy nuclei. We show how this approach, based on the generalization of the DGLAP evolution equations to include final-state medium-induced parton shower corrections for large Q2 processes, can be combined with initial-state effects for applications to jet quenching phenomenology. We demonstrate that the traditional parton energy loss calculations can be regarded as a special soft-gluon emission limit of the general QCD evolution framework. We present phenomenological comparison of the SCETG -based results on the suppression of inclusive charged hadron and neutral pion production in √{sNN }=2.76 TeV lead-lead collisions at the Large Hadron Collider to experimental data. We also show theoretical predictions for the upcoming √{sNN }≃5.1 TeV Pb +Pb run at the LHC.
Sivers Asymmetry with QCD Evolution
NASA Astrophysics Data System (ADS)
Echevarria, Miguel G.; Idilbi, Ahmad; Kang, Zhong-Bo; Vitev, Ivan
2015-02-01
We analyze the Sivers asymmetry in both Drell-Yan (DY) production and semi-inclusive deep inelastic scattering (SIDIS), while considering properly defined transverse momentum dependent parton distribution and fragmentation functions and their QCD evolution. After finding a universal non-perturbative spin-independent Sudakov factor that can describe reasonably well the world's data of SIDIS, DY lepton pair and W/Z production in unpolarized scatterings, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. Then we make predictions for the asymmetry in DY lepton pair and W boson production, which could be compared to the future experimental data in order to test the sign change of the Sivers function.
Evolution of fluctuations near QCD critical point
Stephanov, M. A.
2010-03-01
We propose to describe the time evolution of quasistationary fluctuations near QCD critical point by a system of stochastic Boltzmann-Langevin-Vlasov-type equations. We derive the equations and study the system analytically in the linearized regime. Known results for equilibrium stationary fluctuations as well as the critical scaling of diffusion coefficient are reproduced. We apply the approach to the long-standing question of the fate of the critical point fluctuations during the hadronic rescattering stage of the heavy-ion collision after chemical freeze-out. We find that if conserved particle number fluctuations survive the rescattering, so do, under a certain additional condition, the fluctuations of nonconserved quantities, such as mean transverse momentum. We derive a simple analytical formula for the magnitude of this memory effect.
Correlations and discreteness in nonlinear QCD evolution
Armesto, N.; Milhano, J.
2006-06-01
We consider modifications of the standard nonlinear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities y=({alpha}{sub s}N{sub c}/{pi})Y<10. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cutoff evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cutoff. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients.
QCDNUM: Fast QCD evolution and convolution
NASA Astrophysics Data System (ADS)
Botje, M.
2011-02-01
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by feeding alternative sets of evolution kernels into the program. A versatile convolution engine provides tools to compute parton luminosities, cross-sections in hadron-hadron scattering, and deep inelastic structure functions in the zero-mass scheme or in generalised mass schemes. Input to these calculations are either the QCDNUM evolved densities, or those read in from an external parton density repository. Included in the software distribution are packages to calculate zero-mass structure functions in un-polarised deep inelastic scattering, and heavy flavour contributions to these structure functions in the fixed flavour number scheme. Program summaryProgram title: QCDNUM version: 17.00 Catalogue identifier: AEHV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public Licence No. of lines in distributed program, including test data, etc.: 45 736 No. of bytes in distributed program, including test data, etc.: 911 569 Distribution format: tar.gz Programming language: Fortran-77 Computer: All Operating system: All RAM: Typically 3 Mbytes Classification: 11.5 Nature of problem: Evolution of the strong coupling constant and parton densities, up to next-to-next-to-leading order in perturbative QCD. Computation of observable quantities by Mellin convolution of the evolved densities with partonic cross-sections. Solution method: Parametrisation of the parton densities as linear or quadratic splines on a discrete grid, and evolution of the spline
QCD Evolution of the Transverse Momentum Dependent Correlations
Zhou, Jian; Liang, Zuo-Tang; Yuan, Feng
2008-12-10
We study the QCD evolution for the twist-three quark-gluon correlation functions associated with the transverse momentum odd quark distributions. Different from that for the leading twist quark distributions, these evolution equations involve more general twist-three functions beyond the correlation functions themselves. They provide important information on nucleon structure, and can be studied in the semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in pp scattering process.
QCD Evolution of Helicity and Transversity TMDs
Prokudin, Alexei
2014-01-01
We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.
R evolution: Improving perturbative QCD
Hoang, Andre H.; Jain, Ambar; Stewart, Iain W.; Scimemi, Ignazio
2010-07-01
Perturbative QCD results in the MS scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ''MSR scheme'' which achieves this in a Lorentz and gauge invariant way and has a very simple relation to MS. Results in MSR depend on a cutoff parameter R, in addition to the {mu} of MS. R variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like {mu} in MS). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q{approx}1 GeV, and power corrections are reduced compared to MS.
R evolution: Improving perturbative QCD
NASA Astrophysics Data System (ADS)
Hoang, André H.; Jain, Ambar; Scimemi, Ignazio; Stewart, Iain W.
2010-07-01
Perturbative QCD results in the MS¯ scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the “MSR scheme” which achieves this in a Lorentz and gauge invariant way and has a very simple relation to MS¯. Results in MSR depend on a cutoff parameter R, in addition to the μ of MS¯. R variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like μ in MS¯). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q˜1GeV, and power corrections are reduced compared to MS¯.
Wong's equations and the small x effective action in QCD
Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju
2000-07-13
We propose a new form for the small x effective action in QCD. This form of the effective action is motivated by Wong's equations for classical, colored particles in non-Abelian background fields. We show that the BFKL equation, which sums leading logarithms in x, is efficiently reproduced with this form of the action. We argue that this form of the action may be particularly useful in computing next-to-leading-order results in QCD at small x.
Wong's equations and the small x effective action in QCD
Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju
2001-02-01
We propose a new form for the small x effective action in QCD. This form of the effective action is motivated by Wong's equations for classical, colored particles in non-Abelian background fields. We show that the BFKL equation, which sums leading logarithms in x, is efficiently reproduced with this form of the action. We argue that this form of the action may be particularly useful in computing next-to-leading-order results in QCD at small x.
Hadron properties from QCD bound-state equations
NASA Astrophysics Data System (ADS)
Eichmann, Gernot
2009-09-01
This thesis presents an investigation of meson and baryon properties in the framework of covariant bound-state equations based on the Dyson-Schwinger equations of QCD. Pion and rho-meson, diquark, nucleon and delta-baryon masses are obtained as self-consistent solutions of the respective equations for qbar{q}, qq, qqq and q(qq) systems. The common parenthesis is given by a rainbow-ladder truncation in the quark-(anti-)quark channel. It includes an effective quark-gluon coupling as the only phenomenological input and inherent link in the calculation of meson and baryon observables. Results for hadron masses and the pion's and nucleon's static electromagnetic properties as a function of a self-consistently calculated pion mass are presented and compared to lattice results and their chiral extrapolations. The evolution of the nucleon electromagnetic form factors with larger photon momentum is investigated. The impact of further contributions beyond rainbow-ladder, e.g. pionic corrections, and possible future applications are discussed.
The QCD evolution of TMD in the covariant approach
NASA Astrophysics Data System (ADS)
Efremov, A. V.; Teryaev, O. V.; Zavada, P.
2016-02-01
The procedure for calculation of the QCD evolution of transverse momentum dependent distributions within the covariant approach is suggested. The standard collinear QCD evolution together with the requirements of relativistic invariance and rotational symmetry of the nucleon in its rest frame represent the basic ingredients of our approach. The obtained results are compared with the predictions of some other approaches.
QCD EVOLUTION AND TMD/SPIN EXPERIMENTS
Jian-Ping Chen
2012-12-01
Transverse Spin and Transverse Momemtum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Incluisve Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. QCD factorization has been carefully studied. A SIDIS experiment on the neutron with a polarized 3He target was performed at JLab. Recently published results will be shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. The approved experiments with a new SoLID spectrometer on both the proton and neutron will be presented. Proper QCD evolution treatments beyond collinear cases become crucial for the precision study of the TMDs. Experimentally, Q2 evolution and higher-twist effects are often closely related. The experience of study higher-twist effects in the cases of moments of the spin structure functions will be discussed.
QCD evolution of the Sivers asymmetry
NASA Astrophysics Data System (ADS)
Echevarria, Miguel G.; Idilbi, Ahmad; Kang, Zhong-Bo; Vitev, Ivan
2014-04-01
We study the QCD evolution of the Sivers effect in both semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan production (DY). We pay close attention to the nonperturbative spin-independent Sudakov factor in the evolution formalism and find a universal form which can describe reasonably well the experimental data on the transverse momentum distributions in SIDIS, DY lepton pair and W/Z production. With this Sudakov factor at hand, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. We then make predictions for the Sivers asymmetry in DY lepton pair and W production that can be compared to the future experimental measurements to test the sign change of the Sivers functions between SIDIS and DY processes and constrain the sea quark Sivers functions.
How to impose initial conditions for QCD evolution of double parton distributions?
NASA Astrophysics Data System (ADS)
Golec-Biernat, Krzysztof; Lewandowska, Emilia
2014-07-01
Double parton distribution functions are used in the QCD description of double parton scattering. The double parton distributions evolve with hard scales through QCD evolution equations which obey nontrivial momentum and valence quark number sum rules. We describe an attempt to construct initial conditions for the evolution equations which exactly fulfill these sum rules and discuss its shortcomings. We also discuss the factorization of the double parton distributions into a product of two single parton distribution functions at small values of the parton momentum fractions.
Resumming double logarithms in the QCD evolution of color dipoles
NASA Astrophysics Data System (ADS)
Iancu, E.; Madrigal, J. D.; Mueller, A. H.; Soyez, G.; Triantafyllopoulos, D. N.
2015-05-01
The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.
Double distributions and evolution equations
A.V. Radyushkin
1998-05-01
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements < p{prime} {vert_bar}O(0,z){vert_bar}p > of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{sub {zeta}}(X;t). Here they discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the {zeta}-dependence of nonforward distributions. They show that, for small {zeta}, one can easily obtain nonforward distributions (in the X > {zeta} region) from the parton densities: F{sub {zeta}} (X;t=0) {approx} f(X{minus}{zeta}/2).
Supersymmetric fifth order evolution equations
Tian, K.; Liu, Q. P.
2010-03-08
This paper considers supersymmetric fifth order evolution equations. Within the framework of symmetry approach, we give a list containing six equations, which are (potentially) integrable systems. Among these equations, the most interesting ones include a supersymmetric Sawada-Kotera equation and a novel supersymmetric fifth order KdV equation. For the latter, we supply some properties such as a Hamiltonian structures and a possible recursion operator.
Mode decomposition evolution equations
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Vertex Sensitivity in the Schwinger-Dyson Equations of QCD
David J. Wilson, Michael R. Pennington
2012-01-01
The nonperturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the nonperturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a mass-like term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
The QCD equation of state with charm quarks from lattice QCD
NASA Astrophysics Data System (ADS)
Cheng, Michael
Recently, there have been several calculations of the QCD equation of state (EoS) on the lattice. These calculations take into account the two light quarks and the strange quark, but have ignored the effects of the charm quark, assuming that the charm mass (mc ≈ 1300 MeV) is exponentially suppressed at the temperatures which are explored. However, future heavy ion collisions, such as those planned at the LHC, may well probe temperature regimes where the charm quarks play an important role in the dynamics of the QGP. We present a calculation of the charm quark contribution to the QCD EoS using p4-improved staggered fermions at Nt = 4, 6, 8. This calculation is done with a quenched charm quark, i.e. the relevant operators are measured using a valence charm quark mass on a 2+1 flavor gauge field background. The charm quark masses are determined by calculating charmonium masses (metac and mJ/Psi) and fixing these mesons to their physical masses. The interaction measure, pressure, energy density, and entropy density are calculated. We find that the charm contribution makes a significant contribution, even down to temperatures as low as the pseudo-critical temperature, Tc. However, there are significant scaling corrections at the lattice spacings that we use, preventing a reliable continuum extrapolation.
Evolutions equations in computational anatomy.
Younes, Laurent; Arrate, Felipe; Miller, Michael I
2009-03-01
One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields. PMID:19059343
Renormalization group evolution of multi-gluon correlators in high energy QCD
Dumitru A.; Venugopalan R.; Jalilian-Marian, J.; Lappi, T.; Schenke, B.
2011-11-06
Many-body QCD in leading high energy Regge asymptotics is described by the Balitsky-JIMWLK hierarchy of renormalization group equations for the x evolution of multi-point Wilson line correlators. These correlators are universal and ubiquitous in final states in deeply inelastic scattering and hadronic collisions. For instance, recently measured di-hadron correlations at forward rapidity in deuteron-gold collisions at the Relativistic Heavy Ion Collider (RHIC) are sensitive to four and six point correlators of Wilson lines in the small x color fields of the dense nuclear target. We evaluate these correlators numerically by solving the functional Langevin equation that describes the Balitsky-JIMWLK hierarchy. We compare the results to mean-field Gaussian and large Nc approximations used in previous phenomenological studies. We comment on the implications of our results for quantitative studies of multi-gluon final states in high energy QCD.
Equation of state in two-, three-, and four-color QCD at nonzero temperature and density
NASA Astrophysics Data System (ADS)
Gorda, Tyler; Romatschke, Paul
2015-07-01
We calculate the equation of state at nonzero temperature and density from first principles in two-, three-, and four-color QCD with two fermion flavors in the fundamental and two-index, antisymmetric representation. By matching low-energy results (from a "hadron resonance gas") to high-energy results from (resummed) perturbative QCD, we obtain results for the pressure and trace anomaly that are in quantitative agreement with full lattice-QCD studies for three colors at zero chemical potential. Our results for nonzero chemical potential at zero temperature constitute predictions for the equation of state in QCD-like theories that can be tested by traditional lattice studies for two-color QCD with two fundamental fermions and four-color QCD with two two-index, antisymmetric fermions. We find that the speed of sound squared at zero temperature can exceed 1 /3 , which may be relevant for the phenomenology of high-mass neutron stars.
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Deur, Alexandre; Dosch, Hans Günter
2015-09-01
The valence Fock-state wavefunctions of the light-front (LF) QCD Hamiltonian satisfy a relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to LF Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic LF quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding LF Dirac equation provides a dynamical and spectroscopic model of nucleons. The same LF equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed LF time. LF holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of Anti-de Sitter (AdS) space and the boost-invariant LFWFs describing the internal structure of hadrons in physical space-time. We also show how the mass scale underlying confinement and the masses of light-quark hadrons determines the scale controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the LF and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The data for the effective coupling defined from the Bjorken sum rule are remarkably consistent with the
Efficient evolution of unpolarized and polarized parton distributions with QCD- PEGASUS
NASA Astrophysics Data System (ADS)
Vogt, A.
2005-07-01
The FORTRAN package QCD- PEGASUS is presented. This program provides fast, flexible and accurate solutions of the evolution equations for unpolarized and polarized parton distributions of hadrons in perturbative QCD. The evolution is performed using the symbolic moment-space solutions on a one-fits-all Mellin inversion contour. User options include the order of the evolution including the next-to-next-to-leading order in the unpolarized case, the type of the evolution including an emulation of brute-force solutions, the evolution with a fixed number n of flavors or in the variable- n scheme, and the evolution with a renormalization scale unequal to the factorization scale. The initial distributions are needed in a form facilitating the computation of the complex Mellin moments. Program summaryTitle of program: QCD- PEGASUS Version: 1.0 Catalogue identifier: ADVN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVN Program obtainable from: CPC Program Library Queen's University of Belfast, N. Ireland License: GNU Public License Computers: all Operating systems: all Program language:FORTRAN 77 (using the common compiler extension of procedure names with more than six characters) Memory required to execute: negligible ( <1 MB) Other programs called: none External files needed: none Number of lines in distributed program, including test data, etc.: 8157 Number of bytes in distributed program, including test data, etc.: 240 578 Distribution format: tar.gz Nature of the physical problem: Solution of the evolution equations for the unpolarized and polarized parton distributions of hadrons at leading order (LO), next-to-leading order and next-to-next-to-leading order of perturbative QCD. Evolution performed either with a fixed number n of effectively massless quark flavors or in the variable- n scheme. The calculation of observables from the parton distributions is not part of the present package. Method of solution: Analytic solution in Mellin space (beyond LO in
Evolution equation for quantum coherence
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2016-07-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.
Evolution equation for quantum coherence
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Evolution equation for quantum coherence.
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Real time evolution of non-Gaussian cumulants in the QCD critical regime
Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
2015-09-23
In this study, we derive a coupled set of equations that describe the nonequilibrium evolution of cumulants of critical fluctuations for spacetime trajectories on the crossover side of the QCD phase diagram. In particular, novel expressions are obtained for the nonequilibrium evolution of non-Gaussian skewness and kurtosis cumulants. UBy utilizing a simple model of the spacetime evolution of a heavy-ion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, skewness and kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories thatmore » skirt the edge of the critical regime. We use phenomenologically motivated parametrizations of freeze-out curves and of the beam-energy dependence of the net baryon chemical potential to explore the implications of our model study for the critical-point search in heavy-ion collisions.« less
Real time evolution of non-Gaussian cumulants in the QCD critical regime
Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
2015-09-23
In this study, we derive a coupled set of equations that describe the nonequilibrium evolution of cumulants of critical fluctuations for spacetime trajectories on the crossover side of the QCD phase diagram. In particular, novel expressions are obtained for the nonequilibrium evolution of non-Gaussian skewness and kurtosis cumulants. UBy utilizing a simple model of the spacetime evolution of a heavy-ion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, skewness and kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories that skirt the edge of the critical regime. We use phenomenologically motivated parametrizations of freeze-out curves and of the beam-energy dependence of the net baryon chemical potential to explore the implications of our model study for the critical-point search in heavy-ion collisions.
Calculation of equation of state of QCD at zero temperature and finite chemical potential
NASA Astrophysics Data System (ADS)
Jiang, Yu; Li, Ning; Sun, Wei-Min; Zong, Hong-Shi
2010-09-01
In this paper we calculate the equation of state (EOS) of QCD at zero temperature and finite chemical potential by using several models of quark propagators including the Dyson-Schwinger equations (DSEs) model, the hard-dense-loop (HDL) approximation and the quasi-particle model. The results are analyzed and compared with the known results in the literature.
Non-Markovian stochastic evolution equations
NASA Astrophysics Data System (ADS)
Costanza, G.
2014-05-01
Non-Markovian continuum stochastic and deterministic equations are derived from a set of discrete stochastic and deterministic evolution equations. Examples are given of discrete evolution equations whose updating rules depend on two or more previous time steps. Among them, the continuum stochastic evolution equation of the Newton second law, the stochastic evolution equation of a wave equation, the stochastic evolution equation for the scalar meson field, etc. are obtained as special cases. Extension to systems of evolution equations and other extensions are considered and examples are given. The concept of isomorphism and almost isomorphism are introduced in order to compare the coefficients of the continuum evolution equations of two different smoothing procedures that arise from two different approaches. Usually these discrepancies arising from two sources: On the one hand, the use of different representations of the generalized functions appearing in the models and, on the other hand, the different approaches used to describe the models. These new concept allows to overcome controversies that were appearing during decades in the literature.
Dumitru, Adrian; Jalilian-Marian, Jamal
2010-10-01
Present knowledge of QCD n-point functions of Wilson lines at high energies is rather limited. In practical applications, it is therefore customary to factorize higher n-point functions into products of two-point functions (dipoles) which satisfy the Balitsky-Kovchegov-evolution equation. We employ the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner formalism to derive explicit evolution equations for the 4- and 6-point functions of fundamental Wilson lines and show that if the Gaussian approximation is carried out before the rapidity evolution step is taken, then many leading order N{sub c} contributions are missed. Our evolution equations could specifically be used to improve calculations of forward dijet angular correlations, recently measured by the STAR Collaboration in deuteron-gold collisions at the RHIC collider. Forward dijets in proton-proton collisions at the LHC probe QCD evolution at even smaller light-cone momentum fractions. Such correlations may provide insight into genuine differences between the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner and Balitsky-Kovchegov approaches.
Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre P.; Dosch, Hans G.
2015-09-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale Λ_{{ovr MS}} controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value Λ_{{ovr MS}}=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
The IR sector of QCD: lattice versus Schwinger-Dyson equations
Binosi, Daniele
2010-12-22
Important information about the infrared dynamics of QCD is encoded in the behavior of its (of-shell) Green's functions, most notably the gluon and the ghost propagators. Due to recent improvements in the quality of lattice data and the truncation schemes employed for the Schwinger-Dyson equations we have now reached a point where the interplay between these two non-perturbative tools can be most fruitful. In this talk several of the above points will be reviewed, with particular emphasis on the implications for the ghost sector, the non-perturbative effective charge of QCD, and the Kugo-Ojima function.
QCD constraints on the equation of state for compact stars
NASA Astrophysics Data System (ADS)
Fraga, E. S.; Kurkela, A.; Schaffner-Bielich, J.; Vuorinen, A.
2016-01-01
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount - or even presence - of quark matter inside the stars. In this framework, we also present a simple effective equation of state for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an equation of state that is equally straightforward to use.
Dielectric polarization evolution equations and relaxation times
Baker-Jarvis, James; Riddle, Bill; Janezic, Michael D.
2007-05-15
In this paper we develop dielectric polarization evolution equations, and the resulting frequency-domain expressions, and relationships for the resulting frequency dependent relaxation times. The model is based on a previously developed equation that was derived using statistical-mechanical theory. We extract relaxation times from dielectric data and give illustrative examples for the harmonic oscillator and derive expressions for the frequency-dependent relaxation times and a time-domain integrodifferential equation for the Cole-Davidson model.
QCD chiral transition temperature in a Dyson-Schwinger-equation context
Blank, M.; Krassnigg, A.
2010-08-01
We analyze the chiral phase transition with the help of the QCD gap equation. Various models for the effective interaction in rainbow truncation are contrasted with regard to the resulting chiral transition temperatures. In particular, we investigate possible systematic relations of the details of the effective interaction and the value of T{sub c}. In addition, we quantify changes to the transition temperature beyond the rainbow truncation.
NASA Astrophysics Data System (ADS)
Fleming, Sean
In this talk I review recent experimental and theoretical results in QCD. Since the topic is too vast to cover within given time constraints I choose to highlight some of the subjects that I find particularly exciting. On the experimental side I focus on measurements made at the Tevatron. Specifically jet production rates, and the cross section for B meson production. In addition I discuss an interesting measurement made by the Belle collaboration of double exclusive charmonium production. On the theory side I quickly review recent advances in computing hadronic cross sections at subleading order in perturbation theory. I then move on to soft-collinear effective theory. After a lightning review of the formalism I discuss recently published results on color-suppressed B → D decays.
Statistical physics in QCD evolution towards high energies
NASA Astrophysics Data System (ADS)
Munier, Stéphane
2015-08-01
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies and at a fixed impact parameter is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In this review article, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.
Calculation of the equation of state of QCD at finite chemical and zero temperature
Zong Hongshi; Sun Weimin
2008-09-01
In this paper, we give a direct method for calculating the partition function, and hence the equation of state (EOS) of quantum chromodynamics (QCD) at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms: the first term P({mu})|{sub {mu}}{sub =0} (the pressure density at {mu}=0) is a {mu}-independent constant; the second term, which is totally determined by G{sub R}[{mu}](p) (the renormalized dressed quark propagator at finite {mu}), contains all the nontrivial {mu}-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71, 015205 (2005)], G{sub R}[{mu}](p) is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 70, 014014 (2004)]. From this the full analytic expression of the EOS of QCD at finite {mu} and zero T is obtained (apart from the constant term P({mu})|{sub {mu}}{sub =0} which can in principle be calculated from the Cornwall-Jackiw-Tomboulis effective action). A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski, and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.
Solution Methods for Certain Evolution Equations
NASA Astrophysics Data System (ADS)
Vega-Guzman, Jose Manuel
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value
Evolution equation for entanglement of assistance
Li Zongguo; Liu, W. M.; Zhao Mingjing; Fei Shaoming
2010-04-15
We investigate the time evolution of the entanglement of assistance when one subsystem undergoes the action of local noisy channels. A general factorization law is presented for the evolution equation of entanglement of assistance. Our results demonstrate that the dynamics of the entanglement of assistance is determined by the action of a noisy channel on the pure maximally entangled state, in which the entanglement reduction turns out to be universal for all quantum states entering the channel. This single quantity will make it easy to characterize the entanglement dynamics of entanglement of assistance under unknown channels in the experimental process of producing entangled states by assisted entanglement.
COLLINEAR SPLITTING, PARTON EVOLUTION AND THE STRANGE-QUARK ASYMMETRY OF THE NUCLEON IN NNLO QCD.
RODRIGO,G.CATANI,S.DE FLORIAN, D.VOGELSANG,W.
2004-04-25
We consider the collinear limit of QCD amplitudes at one-loop order, and their factorization properties directly in color space. These results apply to the multiple collinear limit of an arbitrary number of QCD partons, and are a basic ingredient in many higher-order computations. In particular, we discuss the triple collinear limit and its relation to flavor asymmetries in the QCD evolution of parton densities at three loops. As a phenomenological consequence of this new effect, and of the fact that the nucleon has non-vanishing quark valence densities, we study the perturbative generation of a strange-antistrange asymmetry s(x)-{bar s}(x) in the nucleon's sea.
Phenomenological neutron star equations of state. 3-window modeling of QCD matter
NASA Astrophysics Data System (ADS)
Kojo, Toru
2016-03-01
We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, nBlesssim 2ns (ns: nuclear saturation density), we utilize purely hadronic equations of state that are constrained by empirical observations at density n_B˜ n_s and neutron star radii. At high density, nBgtrsim 5ns, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2lesssim nB/ns lesssim 5 is described as neither purely hadronic nor percolated quark matter, and the equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, 0le cs2 le 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to nB˜ 10ns. The hyperon puzzle is also briefly discussed in light of quark descriptions.
Evolution equations for multi-time wavefunctions
NASA Astrophysics Data System (ADS)
Petrat, Soren Philipp
Multi-time wavefunctions are of particular interest in relativistic quantum mechanics. A multi-time wavefunction has separate time-variables for each particle; this makes it a manifestly Lorentz-invariant object. The time-evolution equations are systems of Schrodinger equations; one for each particle's time variable and each with a certain Hamiltonian. We derive conditions under which these systems of equations have a common solution. Also, we derive three main results about concrete multi-time models. First we show that a model proposed by Durr and Tumulka in 2001 is inconsistent. The second result is a consistent model for a constant number of particles with a cutoff pair potential. The third result is a consistent theory for a simple quantum field theoretic model with creation and annihilation of particles. Existence and uniqueness of solutions is proven for both models.
Evolution equations: Frobenius integrability, conservation laws and travelling waves
NASA Astrophysics Data System (ADS)
Prince, Geoff; Tehseen, Naghmana
2015-10-01
We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these equations. We also discuss ‘local’ conservations laws for evolution equations in general and demonstrate all the results for the Korteweg-de Vries equation.
Evolution equation for geometric quantum correlation measures
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2015-05-01
A simple relation is established for the evolution equation of quantum-information-processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation, and particularly the dynamics of geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks.
Analytic Evolution of Singular Distribution Amplitudes in QCD
Radyushkin, Anatoly V.; Tandogan Kunkel, Asli
2014-03-01
We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.
Dark soliton solutions of (N+1)-dimensional nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Demiray, Seyma Tuluce; Bulut, Hasan
2016-06-01
In this study, we investigate exact solutions of (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation by using generalized Kudryashov method. (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation can be returned to nonlinear ordinary differential equation by suitable transformation. Then, generalized Kudryashov method has been used to seek exact solutions of the (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation. Also, we obtain dark soliton solutions for these (N+1)-dimensional nonlinear evolution equations. Finally, we denote that this method can be applied to solve other nonlinear evolution equations.
Method of Analytic Evolution of Flat Distribution Amplitudes in QCD
Asli Tandogan, Anatoly V. Radyushkin
2011-11-01
A new analytical method of performing ERBL evolution is described. The main goal is to develop an approach that works for distribution amplitudes that do not vanish at the end points, for which the standard method of expansion in Gegenbauer polynomials is inefficient. Two cases of the initial DA are considered: a purely flat DA, given by the same constant for all x, and an antisymmetric DA given by opposite constants for x < 1/2 or x > 1/2. For a purely flat DA, the evolution is governed by an overall (x (1-x)){sup t} dependence on the evolution parameter t times a factor that was calculated as an expansion in t. For an antisymmetric flat DA, an extra overall factor |1-2x|{sup 2t} appears due to a jump at x = 1/2. A good convergence was observed in the t {approx}< 1/2 region. For larger t, one can use the standard method of the Gegenbauer expansion.
Kinematical and dynamical aspects of higher-spin bound-state equations in holographic QCD
de Téramond, Guy F.; Dosch, Hans Günter; Brodsky, Stanley J.
2013-04-01
In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti–de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the nontrivial geometry of pure AdS space encodes the kinematics, and the additional deformations of AdS space encode the dynamics, including confinement. It thus becomes possible to identify the features of holographic QCD, which are independent of the specific mechanisms of conformal symmetry breaking. In particular, we account for some aspects of the striking similarities and differences observed in the systematics of the meson and baryon spectra.
Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution
NASA Astrophysics Data System (ADS)
Aybat, S. Mert; Rogers, Ted C.
2011-06-01
We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution. Our goal is to initiate the process of establishing reliable, QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both to test TMD factorization and to search for evidence of the breakdown of TMD factorization that is expected for certain processes. In this article, we focus on spin-independent processes because they provide the simplest illustration of the basic steps and can already be used in direct tests of TMD factorization. Our calculations are based on the Collins-Soper-Sterman (CSS) formalism, supplemented by recent theoretical developments which have clarified the precise definitions of the TMD PDFs and TMD FFs needed for a valid TMD-factorization theorem. Starting with these definitions, we numerically generate evolved TMD PDFs and TMD FFs using as input existing parametrizations for the collinear PDFs, collinear FFs, nonperturbative factors in the CSS factorization formalism, and recent fixed-scale fits. We confirm that evolution has important consequences, both qualitatively and quantitatively, and argue that it should be included in future phenomenological studies of TMD functions. Our analysis is also suggestive of extensions to processes that involve spin-dependent functions such as the Boer-Mulders, Sivers, or Collins functions, which we intend to pursue in future publications. At our website [http://projects.hepforge.org/tmd/], we have made available the tables and calculations needed to obtain the TMD parametrizations presented herein.
Linear vs non-linear QCD evolution in the neutrino-nucleon cross section
NASA Astrophysics Data System (ADS)
Albacete, Javier L.; Illana, José I.; Soto-Ontoso, Alba
2016-03-01
Evidence for an extraterrestrial flux of ultra-high-energy neutrinos, in the order of PeV, has opened a new era in Neutrino Astronomy. An essential ingredient for the determination of neutrino fluxes from the number of observed events is the precise knowledge of the neutrino-nucleon cross section. In this work, based on [1], we present a quantitative study of σνN in the neutrino energy range 104 < Eν < 1014 GeV within two transversal QCD approaches: NLO DGLAP evolution using different sets of PDFs and BK small-x evolution with running coupling and kinematical corrections. Further, we translate this theoretical uncertainty into upper bounds for the ultra-high-energy neutrino flux for different experiments.
Fast wavelet based algorithms for linear evolution equations
NASA Technical Reports Server (NTRS)
Engquist, Bjorn; Osher, Stanley; Zhong, Sifen
1992-01-01
A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis. PMID:27347461
Invariant tori for a class of nonlinear evolution equations
Kolesov, A Yu; Rozov, N Kh
2013-06-30
The paper looks at quite a wide class of nonlinear evolution equations in a Banach space, including the typical boundary value problems for the main wave equations in mathematical physics (the telegraph equation, the equation of a vibrating beam, various equations from the elastic stability and so on). For this class of equations a unified approach to the bifurcation of invariant tori of arbitrary finite dimension is put forward. Namely, the problem of the birth of such tori from the zero equilibrium is investigated under the assumption that in the stability problem for this equilibrium the situation arises close to an infinite-dimensional degeneracy. Bibliography: 28 titles.
Probing QCD at high energy via correlations
Jalilian-Marian, Jamal
2011-04-26
A hadron or nucleus at high energy or small x{sub Bj} contains many gluons and may be described as a Color Glass Condensate. Angular and rapidity correlations of two particles produced in high energy hadron-hadron collisions is a sensitive probe of high gluon density regime of QCD. Evolution equations which describe rapidity dependence of these correlation functions are derived from a QCD effective action.
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1977-01-01
The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.
Karsch,F.; Kharzeev, D.; Molnar, K.; Petreczky, P.; Teaney, D.
2008-04-21
The interpretation of relativistic heavy-ion collisions at RHIC energies with thermal concepts is largely based on the relative success of ideal (nondissipative) hydrodynamics. This approach can describe basic observables at RHIC, such as particle spectra and momentum anisotropies, fairly well. On the other hand, recent theoretical efforts indicate that dissipation can play a significant role. Ideally viscous hydrodynamic simulations would extract, if not only the equation of state, but also transport coefficients from RHIC data. There has been a lot of progress with solving relativistic viscous hydrodynamics. There are already large uncertainties in ideal hydrodynamics calculations, e.g., uncertainties associated with initial conditions, freezeout, and the simplified equations of state typically utilized. One of the most sensitive observables to the equation of state is the baryon momentum anisotropy, which is also affected by freezeout assumptions. Up-to-date results from lattice quantum chromodynamics on the transition temperature and equation of state with realistic quark masses are currently available. However, these have not yet been incorporated into the hydrodynamic calculations. Therefore, the RBRC workshop 'Hydrodynamics in Heavy Ion Collisions and QCD Equation of State' aimed at getting a better understanding of the theoretical frameworks for dissipation and near-equilibrium dynamics in heavy-ion collisions. The topics discussed during the workshop included techniques to solve the dynamical equations and examine the role of initial conditions and decoupling, as well as the role of the equation of state and transport coefficients in current simulations.
Landscape evolution models: A review of their fundamental equations
NASA Astrophysics Data System (ADS)
Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel
2014-08-01
This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs
NLO Hierarchy of Wilson Lines Evolution
Balitsky, Ian
2015-03-01
The high-energy behavior of QCD amplitudes can be described in terms of the rapidity evolution of Wilson lines. I present the hierarchy of evolution equations for Wilson lines in the next-to-leading order.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1988-01-01
An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.
Supersymmetric QCD and high energy cosmic rays: Fragmentation functions of supersymmetric QCD
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Faraggi, Alon E.
2002-04-01
The supersymmetric evolution of the fragmentation functions (or timelike evolution) within N=1 QCD is discussed and predictions for the fragmentation functions of the theory (into final protons) are given. We use a backward running of the supersymmetric DGLAP equations, using a method developed in previous works. We start from the usual QCD parametrizations at low energy and run the DGLAP back, up to an intermediate scale-assumed to be supersymmetric-where we switch-on supersymmetry. From there on we assume the applicability of an N=1 supersymmetric evolution (ESAP). We elaborate on the possible application of these results to high energy cosmic rays near the GZK cutoff.
None
2011-10-06
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.
NASA Astrophysics Data System (ADS)
Kapusta, Joseph; Albright, Michael; Young, Clint
2015-10-01
We match hadronic equations of state at low energy densities to a perturbatively computed equation of state of quarks and gluons at high energy densities. The hadronic equations of state include all known hadrons; repulsive interactions are taken into account via two versions of the excluded volume approximation. A switching function is employed to make the crossover transition from one phase to another without introducing a thermodynamic phase transition. A fit to accurate lattice calculations of the pressure and trace anomaly, with temperature 100 < T < 1000 MeV and μ = 0 , determines the parameters. These parameters quantify the behavior of the QCD running gauge coupling and the hard core radius of the nucleon. With no new parameters, the pressure and trace anomaly from lattice calculations for μ = 400 MeV are equally well reproduced, as is the speed of sound. We then compute the skewness and kurtosis and compare to measurements of the fluctuations of the proton number distribution in central Au-Au collisions as measured by the STAR collaboration in a beam energy scan at RHIC. The crossover equations of state can reproduce the data if the fluctuations are frozen at a temperature significantly lower than the average chemical freeze-out. This work was supported by the US Department of Energy under Grant No. DE-FG02-87ER40328.
A Procedure to Construct Conservation Laws of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Yaşar, Emrullah; San, Sait
2016-05-01
In this article, we established abundant local conservation laws to some nonlinear evolution equations by a new combined approach, which is a union of multiplier and Ibragimov's new conservation theorem method. One can conclude that the solutions of the adjoint equations corresponding to the new conservation theorem can be obtained via multiplier functions. Many new families of conservation laws of the Pochammer-Chree (PC) equation and the Kaup-Boussinesq type of coupled KdV system are successfully obtained. The combined method presents a wider applicability for handling the conservation laws of nonlinear wave equations. The conserved vectors obtained here can be important for the explanation of some practical physical problems, reductions, and solutions of the underlying equations.
Fokker-Planck equation of Schramm-Loewner evolution.
Najafi, M N
2015-08-01
In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE(κ,ρc). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE(κ,ρc) traces and show that it is related to the higher-order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented. PMID:26382350
The effects of QCD equation of state on the relic density of WIMP dark matter
Drees, Manuel; Hajkarim, Fazlollah; Schmitz, Ernany Rossi
2015-06-12
Weakly Interactive Massive Particles (WIMPs) are the most widely studied candidate particles forming the cold dark matter (CDM) whose existence can be inferred from a wealth of astrophysical and cosmological observations. In the framework of the minimal cosmological model detailed measurements on the cosmic microwave background by the PLANCK collaboration fix the scaled CDM relic density to Ω{sub c}h{sup 2}=0.1193±0.0014, with an error of less than 1.5%. In order to fully exploit this observational precision, theoretical calculations should have a comparable or smaller error. In this paper we use recent lattice QCD calculations to improve the description of the thermal plasma. This affects the predicted relic density of “thermal WIMPs”, which once were in chemical equilibrium with Standard Model particles. For WIMP masses between 3 and 15 GeV, where QCD effects are most important, our predictions differ from earlier results by up to 9% (12%) for pure S-wave (P-wave) annihilation. We use these results to compute the thermally averaged WIMP annihilation cross section that reproduces the correct CDM relic density, for WIMP masses between 0.1 GeV and 10 TeV.
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1975-01-01
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.
NASA Astrophysics Data System (ADS)
Borsányi, Sz.; Endrődi, G.; Fodor, Z.; Katz, S. D.; Krieg, S.; Ratti, C.; Szabó, K. K.
2012-08-01
We determine the equation of state of QCD for nonzero chemical potentials via a Taylor expansion of the pressure. The results are obtained for N f = 2 + 1 flavors of quarks with physical masses, on various lattice spacings. We present results for the pressure, interaction measure, energy density, entropy density, and the speed of sound for small chemical potentials. At low temperatures we compare our results with the Hadron Resonance Gas model. We also express our observables along trajectories of constant entropy over particle number. A simple parameterization is given (the Matlab/Octave script parameterization.m, submitted to the arXiv along with the paper), which can be used to reconstruct the observables as functions of T and μ, or as functions of T and S/N.
An evolution equation modeling inversion of tulip flames
Dold, J.W.; Joulin, G.
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
Multi-soliton rational solutions for some nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Osman, Mohamed S.
2016-01-01
The Korteweg-de Vries equation (KdV) and the (2+ 1)-dimensional Nizhnik-Novikov-Veselov system (NNV) are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially) integrable equations. Compared with Hirota's method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.
Mimicking the QCD equation of state with a dual black hole
Gubser, Steven S.; Nellore, Abhinav
2008-10-15
We present numerical and analytical studies of the equation of state of translationally invariant black hole solutions to five-dimensional gravity coupled to a single scalar. As an application, we construct a family of black holes that closely mimics the equation of state of quantum chromodynamics at zero chemical potential.
A Harnack's inequality for mixed type evolution equations
NASA Astrophysics Data System (ADS)
Paronetto, Fabio
2016-03-01
We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is μ (x)∂ u/∂ t - Δu = 0 where μ can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.
On an evolution equation in a cell motility model
NASA Astrophysics Data System (ADS)
Mizuhara, Matthew S.; Berlyand, Leonid; Rybalko, Volodymyr; Zhang, Lei
2016-04-01
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and net motion. This issue can be addressed both qualitatively and quantitatively by studying the evolution equation of the sharp interface limit for this system. However, this equation is non-linear and non-local and existence of solutions presents a significant analytical challenge. We establish existence of solutions for a wide class of initial data in the so-called subcritical regime. Existence is proved in a two step procedure. First, for smooth (H2) initial data we use a regularization technique. Second, we consider non-smooth initial data that are more relevant from the application point of view. Here, uniform estimates on the time when solutions exist rely on a maximum principle type argument. We also explore the long time behavior of the model using both analytical and numerical tools. We prove the nonexistence of traveling wave solutions with nonzero velocity. Numerical experiments show that presence of non-linearity and asymmetry of the initial curve results in a net motion which distinguishes it from classical volume preserving curvature motion. This is done by developing an algorithm for efficient numerical resolution of the non-local term in the evolution equation.
Evolution equation for non-linear cosmological perturbations
Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch
2011-11-01
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
Integral equation for gauge invariant quark two-point Green's function in QCD
Sazdjian, H.
2008-02-15
Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with different numbers of path segments are established. An integral equation is obtained for the Green's function defined with a phase factor along a single straight line. The equation implicates an infinite series of two-point Green's functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green's function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.
Parameterization and Monte Carlo solutions to PDF evolution equations
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2015-04-01
The probability density function (PDF) of the chemical species concentrations transported in random environments is governed by unclosed evolution equations. The PDF is transported in the physical space by drift and diffusion processes described by coefficients derived by standard upscaling procedures. Its transport in the concentration space is described by a drift determined by reaction rates, in a closed form, as well as a term accounting for the sub-grid mixing process due to molecular diffusion and local scale hydrodynamic dispersion. Sub-grid mixing processes are usually described by models of the conditionally averaged diffusion flux or models of the conditional dissipation rate. We show that in certain situations mixing terms can also be derived, in the form of an Itô process, from simulated or measured concentration time series. Monte Carlo solutions to PDF evolution equations are usually constructed with systems of computational particles, which are well suited for highly dimensional advection-dominated problems. Such solutions require the fulfillment of specific consistency conditions relating the statistics of the random concentration field, function of both space and time, to that of the time random function describing an Itô process in physical and concentration spaces which governs the evolution of the system of particles. We show that the solution of the Fokker-Planck equation for the concentration-position PDF of the Itô process coincides with the solution of the PDF equation only for constant density flows in spatially statistically homogeneous systems. We also find that the solution of the Fokker-Planck equation is still equivalent to the solution of the PDF equation weighted by the variable density or by other conserved scalars. We illustrate the parameterization of the sub-grid mixing by time series and the Monte Carlo solution for a problem of contaminant transport in groundwater. The evolution of the system of computational particles whose
Evolution equation for soft physics at high energy
NASA Astrophysics Data System (ADS)
Brogueira, P.; Dias de Deus, J.
2010-07-01
Based on the nonlinear logistic equation we study, in a qualitative and semi-quantitative way, the evolution with energy and saturation of the elastic differential cross-section in pp(\\bar{p}p) collisions at high energy. Geometrical scaling occurs at the black disc limit, and scaling develops first for small values of the scaling variable |t|σtot.. Our prediction for dσ/dt at LHC, with two zeros and a minimum at large |t| differs, as far as we know, from all existing ones.
NASA Astrophysics Data System (ADS)
Aoki, Ken-Ichi; Sato, Daisuke
The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DχSB) in QCD. We show that the DχSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.
Kawamura, Hiroyuki; Tanaka, Kazuhiro
2010-06-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.
NASA Astrophysics Data System (ADS)
Kawamura, Hiroyuki; Tanaka, Kazuhiro
2010-06-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the “quasilocal” kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale μ with smaller interquark separations zt (z≤1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale ˜mbΛQCD for t less than ˜1GeV-1, using the recently obtained operator product expansion of the DA as the input at μ˜1GeV. We also derive the master formula, which reexpresses the integrals of the DA at μ˜mbΛQCD for the factorization formula by the compact integrals of the DA at μ˜1GeV.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Central equation of state in spherical characteristic evolutions
Barreto, W.; Castillo, L.; Barrios, E.
2009-10-15
We study the evolution of a perfect-fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state {rho}{sub c}+3p{sub c}=const at the center of the sphere, where the energy {rho}{sub c} density and the pressure p{sub c} do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and nonradiative at the center of the sphere. These results are currently being considered to build up a numerical relativistic hydrodynamic solver.
Entropy production and the geometry of dissipative evolution equations.
Reina, Celia; Zimmer, Johannes
2015-11-01
Purely dissipative evolution equations are often cast as gradient flow structures, z ̇=K(z)DS(z), where the variable z of interest evolves towards the maximum of a functional S according to a metric defined by an operator K. While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator K and the associated geometry does not necessarily do so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator K and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the steepest entropy ascent formalism. This variational principle is exemplified here for the simultaneous evolution of conserved and nonconserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure K is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement. PMID:26651657
Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio
2014-01-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530
Construction of rogue wave and lump solutions for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Lü, Zhuosheng; Chen, Yinnan
2015-07-01
Based on symbolic computation and an ansatz, we present a constructive algorithm to seek rogue wave and lump solutions for nonlinear evolution equations. As illustrative examples, we consider the potential-YTSF equation and a variable coefficient KP equation, and obtain nonsingular rational solutions of the two equations. The solutions can be rogue wave or lump solutions under different parameter conditions. We also present graphic illustration of some special solutions which would help better understand the evolution of solution waves.
Calculation of the nucleon axial charge in lattice QCD
D. B. Renner; R. G. Edwards; G. Fleming; Ph. Hagler; J. W. Negele; K. Orginos; A. V. Pochinsky; D. G. Richards; W. Schroers
2006-09-01
Protons and neutrons have a rich structure in terms of their constituents, the quarks and gluons. Understanding this structure requires solving Quantum Chromodynamics (QCD). However QCD is extremely complicated, so we must numerically solve the equations of QCD using a method known as lattice QCD. Here we describe a typical lattice QCD calculation by examining our recent computation of the nucleon axial charge.
Bornyakov, V.G.
2005-06-01
Possibilities that are provided by a lattice regularization of QCD for studying nonperturbative properties of QCD are discussed. A review of some recent results obtained from computer calculations in lattice QCD is given. In particular, the results for the QCD vacuum structure, the hadron mass spectrum, and the strong coupling constant are considered.
Equations of State: Gateway to Planetary Origin and Evolution (Invited)
NASA Astrophysics Data System (ADS)
Melosh, J.
2013-12-01
Research over the past decades has shown that collisions between solid bodies govern many crucial phases of planetary origin and evolution. The accretion of the terrestrial planets was punctuated by planetary-scale impacts that generated deep magma oceans, ejected primary atmospheres and probably created the moons of Earth and Pluto. Several extrasolar planetary systems are filled with silicate vapor and condensed 'tektites', probably attesting to recent giant collisions. Even now, long after the solar system settled down from its violent birth, a large asteroid impact wiped out the dinosaurs, while other impacts may have played a role in the origin of life on Earth and perhaps Mars, while maintaining a steady exchange of small meteorites between the terrestrial planets and our moon. Most of these events are beyond the scale at which experiments are possible, so that our main research tool is computer simulation, constrained by the laws of physics and the behavior of materials during high-speed impact. Typical solar system impact velocities range from a few km/s in the outer solar system to 10s of km/s in the inner system. Extrasolar planetary systems expand that range to 100s of km/sec typical of the tightly clustered planetary systems now observed. Although computer codes themselves are currently reaching a high degree of sophistication, we still rely on experimental studies to determine the Equations of State (EoS) of materials critical for the correct simulation of impact processes. The recent expansion of the range of pressures available for study, from a few 100 GPa accessible with light gas guns up to a few TPa from current high energy accelerators now opens experimental access to the full velocity range of interest in our solar system. The results are a surprise: several groups in both the USA and Japan have found that silicates and even iron melt and vaporize much more easily in an impact than previously anticipated. The importance of these findings is
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Motsa, S. S.; Magagula, V. M.; Sibanda, P.
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution
Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng
2016-01-13
In this paper, we study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in e+e- annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins- Soper-Sterman (CSS) formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in e+e- annihilations measured by BELLE and BABAR Collaborations and SIDIS datamore » from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. Finally, we give predictions and discuss impact of future experiments.« less
Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution
NASA Astrophysics Data System (ADS)
Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng
2016-01-01
We study the transverse-momentum-dependent (TMD) evolution of the Collins azimuthal asymmetries in e+e- annihilations and semi-inclusive hadron production in deep inelastic scattering processes. All the relevant coefficients are calculated up to the next-to-leading-logarithmic-order accuracy. By applying the TMD evolution at the approximate next-to-leading-logarithmic order in the Collins-Soper-Sterman formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back dihadron productions in e+e- annihilations measured by BELLE and BABAR collaborations and semi-inclusive hadron production in deep inelastic scattering data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation, and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
-front QCD Hamiltonian 'Light-Front Holography'. Light-Front Holography is in fact one of the most remarkable features of the AdS/CFT correspondence. The Hamiltonian equation of motion in the light-front (LF) is frame independent and has a structure similar to eigenmode equations in AdS space. This makes a direct connection of QCD with AdS/CFT methods possible. Remarkably, the AdS equations correspond to the kinetic energy terms of the partons inside a hadron, whereas the interaction terms build confinement and correspond to the truncation of AdS space in an effective dual gravity approximation. One can also study the gauge/gravity duality starting from the bound-state structure of hadrons in QCD quantized in the light-front. The LF Lorentz-invariant Hamiltonian equation for the relativistic bound-state system is P{sub {mu}}P{sup {mu}}|{psi}(P)> = (P{sup +}P{sup -} - P{sub {perpendicular}}{sup 2})|{psi}(P)> = M{sup 2}|{psi}(P)>, P{sup {+-}} = P{sup 0} {+-} P{sup 3}, where the LF time evolution operator P{sup -} is determined canonically from the QCD Lagrangian. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a LF Hamiltonian equation which describes the bound-state dynamics of light hadrons in terms of an invariant impact variable {zeta} which measures the separation of the partons within the hadron at equal light-front time {tau} = x{sup 0} + x{sup 3}. This allows us to identify the holographic variable z in AdS space with an impact variable {zeta}. The resulting Lorentz-invariant Schroedinger equation for general spin incorporates color confinement and is systematically improvable. Light-front holographic methods were originally introduced by matching the electromagnetic current matrix elements in AdS space with the corresponding expression using LF theory in physical space time. It was also shown that one obtains identical holographic mapping using the matrix elements of the energy-momentum tensor by perturbing
LATTICE QCD THERMODYNAMICS WITH WILSON QUARKS.
EJIRI,S.
2007-11-20
We review studies of QCD thermodynamics by lattice QCD simulations with dynamical Wilson quarks. After explaining the basic properties of QCD with Wilson quarks at finite temperature including the phase structure and the scaling properties around the chiral phase transition, we discuss the critical temperature, the equation of state and heavy-quark free energies.
QCD evolution of (un)polarized gluon TMDPDFs and the Higgs q T -distribution
NASA Astrophysics Data System (ADS)
Echevarria, Miguel G.; Kasemets, Tomas; Mulders, Piet J.; Pisano, Cristian
2015-07-01
We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them. We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy. Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unpolarized ( f {1/ g }), linearly polarized ( h {1/⊥ g }) and helicity ( g {1/L g }) gluon TMDPDFs, and show that, as expected, they are free from rapidity divergences. As a byproduct, we obtain the Wilson coefficients of the refactorization of these TMDPDFs at large transverse momentum. In particular, the coefficient of g {1/L g }, which has never been calculated before, constitutes a new and necessary ingredient for a reliable phenomenological extraction of this quantity, for instance at RHIC or the future AFTER@LHC or Electron-Ion Collider. The coefficients of f {1/ g } and h {1/⊥ g } have never been calculated in the present formalism, although they could be obtained by carefully collecting and recasting previous results in the new TMD formalism. We apply these results to analyze the contribution of linearly polarized gluons at different scales, relevant, for instance, for the inclusive production of the Higgs boson and the C-even pseudoscalar bottomonium state η b . Applying our resummation scheme we finally provide predictions for the Higgs boson q T -distribution at the LHC.
Solving nonlinear evolution equation system using two different methods
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.
2015-12-01
This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.
On the 'delta-equations' for vortex sheet evolution
NASA Technical Reports Server (NTRS)
Rottman, James W.; Stansby, Peter K.
1993-01-01
We use a set of equations, sometimes referred to as the 'delta-equations', to approximate the two-dimensional inviscid motion of an initially circular vortex sheet released from rest in a cross-flow. We present numerical solutions of these equations for the case with delta-square = 0 (for which the equations are exact) and for delta-square greater than 0. For small values of the smoothing parameter delta, a spectral filter must be used to eliminate spurious instabilities due to round-off error. Two singularities appear simultaneously in the vortex sheet when delta-square = 0 at a critical time t(c). After t(c), the solutions do not converge as the computational mesh is refined. With delta-square greater than 0, converged solutions were found for all values of delta-square when t is less than t(c), and for all but the two smallest values of delta-square used when t is greater than t(c). Our results show that, when delta-square is greater than 0, the vortex sheet deforms into two doubly branched spirals some time after t(c). The limiting solution as delta approaching 0 clearly exists and equals the delta = 0 solution when t is less than t(c).
NASA Astrophysics Data System (ADS)
Tanaka, Hiroshi; Nakajima, Asumi; Nishiyama, Akinobu; Tokihiro, Tetsuji
2009-03-01
A differential equation exhibiting replicative time-evolution patterns is derived by inverse ultradiscretizatrion of Fredkin’s game, which is one of the simplest replicative cellular automaton (CA) in two dimensions. This is achieved by employing a certain filter and a clock function in the equation. These techniques are applicable to the inverse ultra-discretization (IUD) of other CA and stabilize the time-evolution of the obtained differential equation. Application to the game of life, another CA in two dimensions, is also presented.
Binarization method based on evolution equation for document images produced by cameras
NASA Astrophysics Data System (ADS)
Wang, Yan; He, Chuanjiang
2012-04-01
We present an evolution equation-based binarization method for document images produced by cameras. Unlike the existing thresholding techniques, the idea behind our method is that a family of gradually binarized images is obtained by the solution of an evolution partial differential equation, starting with an original image. In our formulation, the evolution is controlled by a global force and a local force, both of which have opposite sign inside and outside the object of interests in the original image. A simple finite difference scheme with a significantly larger time step is used to solve the evolution equation numerically; the desired binarization is typically obtained after only one or two iterations. Experimental results on 122 camera document images show that our method yields good visual quality and OCR performance.
Dromion interactions of (2+1)-dimensional nonlinear evolution equations
Ruan; Chen
2000-10-01
Starting from two line solitons, the solution of integrable (2+1)-dimensional mKdV system and KdV system in bilinear form yields a dromion solution or a "Solitoff" solution. Such a dromion solution is localized in all directions and the Solitoff solution decays exponentially in all directions except a preferred one for the physical field or a suitable potential. The interactions between two dromions and between the dromion and Solitoff are studied by the method of figure analysis for a (2+1)-dimensional modified KdV equation and a (2+1)-dimensional KdV type equation. Our analysis shows that the interactions between two dromions may be elastic or inelastic for different forms of solutions. PMID:11089133
NASA Astrophysics Data System (ADS)
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-09-01
dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of αs(Q2) in order to bring better unity to the subject.
Decoupling of the DGLAP evolution equations by Laplace method
NASA Astrophysics Data System (ADS)
Boroun, G. R.; Zarrin, S.; Teimoury, F.
2015-10-01
In this paper we derive two second-order differential equations for the gluon and singlet distribution functions by using the Laplace transform method. We decoupled the solutions of the singlet and gluon distributions into the initial conditions (function and derivative of the function) at the virtuality Q 0 2 separately as these solutions are defined by F 2 s ( x, Q 2) = F( F 0 ,∂ F s0 and G( x, Q 2)= G( G 0, ∂ G 0. We compared our results with the MSTW parameterization and the experimental measurements of F 2 p ( x, Q 2.
Roberts, C.D.
1994-09-01
The Dyson-Schwinger equations (DSEs) are a tower of coupled integral equations that relate the Green functions of QCD to one another. Solving these equations provides the solution of QCD. This tower of equations includes the equation for the quark self-energy, which is the analogue of the gap equation in superconductivity, and the Bethe-Salpeter equation, the solution of which is the quark-antiquark bound state amplitude in QCD. The application of this approach to solving Abelian and non-Abelian gauge theories is reviewed. The nonperturbative DSE approach is being developed as both: (1) a computationally less intensive alternative and; (2) a complement to numerical simulations of the lattice action of QCD. In recent years, significant progress has been made with the DSE approach so that it is now possible to make sensible and direct comparisons between quantities calculated using this approach and the results of numerical simulations of Abelian gauge theories. Herein the application of the DSE approach to the calculation of pion observables is described: the {pi}-{pi} scattering lengths (a{sub 0}{sup 0}, a{sub 0}{sup 2}, A{sub 1}{sup 1}, a{sub 2}{sup 2}) and associated partial wave amplitudes; the {pi}{sup 0} {yields} {gamma}{gamma} decay width; and the charged pion form factor, F{sub {pi}}(q{sup 2}). Since this approach provides a straightforward, microscopic description of dynamical chiral symmetry breaking (D{sub X}SB) and confinement, the calculation of pion observables is a simple and elegant illustrative example of its power and efficacy. The relevant DSEs are discussed in the calculation of pion observables and concluding remarks are presented.
Two-loop conformal generators for leading-twist operators in QCD
NASA Astrophysics Data System (ADS)
Braun, V. M.; Manashov, A. N.; Moch, S.; Strohmaier, M.
2016-03-01
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d = 4 - 2ɛ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d = 4 - 2ɛ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD β-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.
NASA Astrophysics Data System (ADS)
Echevarria, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio
2014-07-01
By considering semi-inclusive deep-inelastic scattering and the (complementary) qT-spectrum for Drell-Yan lepton pair production we derive the QCD evolution for all the leading-twist transverse momentum dependent distribution and fragmentation functions. We argue that all of those functions evolve with Q2 following a single evolution kernel. This kernel is independent of the underlying kinematics and it is also spin independent. Those features hold, in impact parameter space, to all values of bT. The evolution kernel presented has all of its large logarithms resummed up to next-to-next-to leading logarithmic accuracy, which is the highest possible accuracy given the existing perturbative calculations. As a study case we apply this kernel to investigate the evolution of the Collins function, one of the ingredients that have recently attracted much attention within the phenomenological studies of spin asymmetries. Our analysis can be readily implemented to revisit previously obtained fits that involve data at different scales for other spin-dependent functions. Such improved fits are important to get better predictions—with the correct evolution kernel—for certain upcoming experiments aiming to measure the Sivers function, Collins function, transversity, and other spin-dependent functions as well.
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano; Mugnolo, Delio
2009-10-15
We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
Eu, Byung Chan
2008-09-01
In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel. PMID:19044872
Soliton evolution and radiation loss for the Korteweg--de Vries equation
Kath, W.L.; Smyth, N.F. Department of Mathematics and Statistics, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH93JZ, Scotland )
1995-01-01
The time-dependent behavior of solutions of the Korteweg--de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution.
Periodic boundary value problems for nonlinear impulsive evolution equations on Banach spaces
NASA Astrophysics Data System (ADS)
Yu, Xiulan; Wang, JinRong
2015-05-01
In this paper, we consider periodic boundary value problems for two new type nonlinear impulsive evolution equations on Banach spaces. By using the theory of semigroup, a mixed type Gronwall inequality and fixed point methods, we establish several sufficient conditions on the existence of mild solutions for such problems. Finally, examples are given to illustrate our main results.
Long range two-particle rapidity correlations in A+A collisions from high energy QCD evolution
NASA Astrophysics Data System (ADS)
Dusling, Kevin; Gelis, François; Lappi, Tuomas; Venugopalan, Raju
2010-05-01
Long range rapidity correlations in A+A collisions are sensitive to strong color field dynamics at early times after the collision. These can be computed in a factorization formalism (Gelis, Lappi and Venugopalan (2009) [1]) which expresses the n-gluon inclusive spectrum at arbitrary rapidity separations in terms of the multi-parton correlations in the nuclear wavefunctions. This formalism includes all radiative and rescattering contributions, to leading accuracy in αΔY, where Δ Y is the rapidity separation between either one of the measured gluons and a projectile, or between the measured gluons themselves. In this paper, we use a mean field approximation for the evolution of the nuclear wavefunctions to obtain a compact result for inclusive two gluon correlations in terms of the unintegrated gluon distributions in the nuclear projectiles. The unintegrated gluon distributions satisfy the Balitsky-Kovchegov equation, which we solve with running coupling and with initial conditions constrained by existing data on electron-nucleus collisions. Our results are valid for arbitrary rapidity separations between measured gluons having transverse momenta p,q≳Q, where Q is the saturation scale in the nuclear wavefunctions. We compare our results to data on long range rapidity correlations observed in the near-side ridge at RHIC and make predictions for similar long range rapidity correlations at the LHC.
Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles
NASA Astrophysics Data System (ADS)
Korennoy, Ya. A.; Man'ko, V. I.
2016-07-01
The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q-function, and Glauber-Sudarshan P-function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.
NASA Astrophysics Data System (ADS)
Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet
2016-08-01
In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).
NASA Astrophysics Data System (ADS)
Kirsch, Andreas; Rieder, Andreas
2016-08-01
It is common knowledge—mainly based on experience—that parameter identification problems in partial differential equations are ill-posed. Yet, a mathematical sound argumentation is missing, except for some special cases. We present a general theory for inverse problems related to abstract evolution equations which explains not only their local ill-posedness but also provides the Fréchet derivative and its adjoint of the corresponding parameter-to-solution map which are needed, e.g., in Newton-like solvers. Our abstract results are applied to inverse problems related to the following first order hyperbolic systems: Maxwell’s equation (electromagnetic scattering in conducting media) and elastic wave equation (seismic imaging).
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-05-09
regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $Q_0$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less
The Sturm-Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data
NASA Astrophysics Data System (ADS)
Johnson, Russell; Zampogni, Luca
2014-03-01
The Sturm-Liouville hierarchy of evolution equations was introduced in [Adv. Nonlinear Stud. 11 (2011), 555-591] and includes the Korteweg-de Vries and the Camassa-Holm hierarchies. We discuss some solutions of this hierarchy which are obtained as limits of algebro-geometric solutions. The initial data of our solutions are (generalized) reflectionless Sturm-Liouville potentials [Stoch. Dyn. 8 (2008), 413-449].
Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil
Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.
1986-09-10
For a generalized Zakharov-Shabat system in which the matrix potential is a polynomial in the spectral parameter a generating operator is constructed which makes it possible to compactly write out the nonlinear evolution equations (NEE) connected with the system. The eigenfunctions of the generating operator - the squares of solutions of the original system - are found. The Hamiltonian property of the NEE and the existence of a hierarchy of Hamiltonian structures are established.
Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle
Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.
1987-05-20
For the generalized Zakharov-Shabat system with the matrix potential a polynomial in the spectral parameter, they construct a generating operator which leads to a compact representation of the nonlinear evolution equations (NEE) associated with the system. The eigenfunctions of the generating operator are obtained as the squares of the solutions of the original system. The Hamiltonian nature of the NEE and the existence of a hierarchy of Hamiltonian structures is established.
Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil
Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.
1986-09-01
For a generalized Zakharov-Shabat system in which the matrix potential is a polynomial in the spectral parameter a generating operator is constructed which makes it possible to compactly write out the nonlinear evolution equations (NEE) connected with the system. The eigenfunctions of the generating operator - the ''squares'' of solutions of the original system - are found. The Hamiltonian property of the NEE and the existence of a hierachy of Hamiltonian structures are established.
Schüler, D.; Alonso, S.; Bär, M.; Torcini, A.
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Saturation and universality in QCD at small /x
NASA Astrophysics Data System (ADS)
Iancu, E.; McLerran, L.
2001-06-01
We find approximate solutions to the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate. This is a functional Fokker-Planck equation which generates in particular the non-linear evolution equations previously derived by Balitsky and Kovchegov within perturbative QCD. In the limit where the transverse momentum of the external probe is large compared to the saturation momentum, our approximations yield the Gaussian ansatz for the effective action of the McLerran-Venugopalan model. In the opposite limit, of a small external momentum, we find that the effective theory is governed by a scale-invariant universal action which has the correct properties to describe gluon saturation.
An equation for the evolution of solar and stellar flare loops
NASA Technical Reports Server (NTRS)
Fisher, George H.; Hawley, Suzanne L.
1990-01-01
An ordinary differential equation describing the evolution of a coronal loop subjected to a spatially uniform but time-varying heating rate is discussed. It is assumed that the duration of heating is long compared to the sound transit time through the loop, which is assumed to have uniform cross section area. The form of the equation changes as the loop evolves through three states: 'strong evaporation', 'scaling law behavior', and 'strong condensation'. Solutions to the equation may be used to compute the time dependence of the average coronal temperature and emission measure for an assumed temporal variation of the flare heating rate. The results computed from the model agree reasonably well with recent published numerical simulations and may be obtained with far less computational effort. The model is then used to study the May 21, 1980, solar flare observed by SMM and the giant April 12, 1985, flare observed on the star AD Leo.
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern
2004-10-15
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.
Birth and death master equation for the evolution of complex networks
NASA Astrophysics Data System (ADS)
Alvarez-Martínez, R.; Cocho, G.; Rodríguez, R. F.; Martínez-Mekler, G.
2014-05-01
Master equations for the evolution of complex networks with positive (birth) and negative (death) transition probabilities per unit time are analyzed. Explicit equations for the time evolution of the total number of nodes and for the relative node frequencies are given. It is shown that, in the continuous limit, the master equation reduces to a Fokker-Planck equation (FPE). The basic dynamical function for its stationary solution is the ratio between its drift and diffusion coefficients. When this ratio is approximated by partial fractions (Padé's approximants), a hierarchy of stationary solutions of the FPE is obtained analytically, which are expressed as an exponential times the product of powers of monomials and binomials. It is also shown that if the difference between birth and death transition probabilities goes asymptotically to zero, the exponential factor in the solution is absent. Fits to real complex network probability distribution functions are shown. Comparison with rank-ordered data shows that, in general, the value of this exponential factor is close to unity, evidencing crossovers among power-law scale invariant regimes which might be associated to an underlying criticality and are related to a generalization of the beta distribution. The time dependent solution is also obtained analytically in terms of hyper-geometric functions. It is also shown that the FPE has similarity solutions. The limitations of the approach here presented are also discussed.
Nawa, Kanabu; Suganuma, Hideo; Kojo, Toru
2007-04-15
We study baryons in holographic QCD with D4/D8/D8 multi-D-brane system. In holographic QCD, the baryon appears as a topologically nontrivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton brane-induced Skyrmion. Some review of D4/D8/D8 holographic QCD is presented from the viewpoints of recent hadron physics and QCD phenomenologies. A four-dimensional effective theory with pions and {rho} mesons is uniquely derived from the non-Abelian Dirac-Born-Infeld (DBI) action of D8 brane with D4 supergravity background at the leading order of large N{sub c}, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and {rho}-meson fields, we derive the energy functional and the Euler-Lagrange equation of brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the soliton solution and figure out the pion profile F(r) and the {rho}-meson profile G-tilde(r) of the brane-induced Skyrmion with its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without {rho} mesons. We analyze interaction terms of pions and {rho} mesons in brane-induced Skyrmion, and find a significant {rho}-meson component appearing in the core region of a baryon.
Hess, Peter O.
2006-09-25
A review is presented on the contributions of Mexican Scientists to QCD phenomenology. These contributions range from Constituent Quark model's (CQM) with a fixed number of quarks (antiquarks) to those where the number of quarks is not conserved. Also glueball spectra were treated with phenomenological models. Several other approaches are mentioned.
Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum
2014-01-01
In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics. PMID:25674431
Frenkel, A.L.; Indireshkumar, K.
1999-10-01
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out. {copyright} {ital 1999} {ital The American Physical Society}
QCD at nonzero chemical potential: Recent progress on the lattice
NASA Astrophysics Data System (ADS)
Aarts, Gert; Attanasio, Felipe; Jäger, Benjamin; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu
2016-01-01
We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.
Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Villois, Alberto; Proment, Davide; Krstulovic, Giorgio
2016-06-01
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently developed accurate and robust tracking algorithm, all quantized vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in helium II is observed. The topology of the tangle is then investigated showing that linked rings may appear during the evolution. The tracking also allows for determining the statistics of small-scale quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.
Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation.
Villois, Alberto; Proment, Davide; Krstulovic, Giorgio
2016-06-01
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently developed accurate and robust tracking algorithm, all quantized vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in helium II is observed. The topology of the tangle is then investigated showing that linked rings may appear during the evolution. The tracking also allows for determining the statistics of small-scale quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade. PMID:27415198
An inverse problem for a class of conditional probability measure-dependent evolution equations
NASA Astrophysics Data System (ADS)
Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.
2016-09-01
We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by partial differential equation models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.
Neutron Star Evolutions Using Nuclear Equations of State with a New Execution Model
NASA Astrophysics Data System (ADS)
Neilsen, David; Anderson, Matthew; Sterling, Thomas; Kaiser, Hartmut
2015-01-01
The addition of nuclear and neutrino physics to general relativistic fluid codes allows for a more realistic description of hot nuclear matter in neutron star and black hole systems. This additional microphysics requires that each processor have access to large tables of data, such as equations of state. Modern many-tasking execution models contain special semantic constructs designed to simplify distributed access to such tables and to reduce the negative impact in distributed large table access through network latency hiding measures such as local control objects. We present evolutions of a neutron star obtained using a message driven multi-threaded execution model known as ParalleX.
Threefold Complementary Approach to Holographic QCD
Brodsky, Stanley J.; de Teramond, Guy F.; Dosch, Hans Gunter
2013-12-27
A complementary approach, derived from (a) higher-dimensional anti-de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group andSO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.
NASA Astrophysics Data System (ADS)
Cao, Shanshan; Qin, Guang-You; Bass, Steffen A.
2014-12-01
We study heavy flavor evolution and hadronization in relativistic heavy-ion collisions. The in-medium evolution of heavy quarks is described using our modified Langevin framework that incorporates both collisional and radiative energy loss mechanisms. The subsequent hadronization process for heavy quarks is calculated with a fragmentation plus recombination model. We find significant contribution from gluon radiation to heavy quark energy loss at high pT; the recombination mechanism can greatly enhance the D meson production at medium pT. Our calculation provides a good description of the D meson nuclear modification at the LHC. In addition, we explore the angular correlation functions of heavy flavor pairs which may provide us a potential candidate for distinguishing different energy loss mechanisms of heavy quarks inside the QGP.
The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation
NASA Technical Reports Server (NTRS)
Davis, Sanford S.
2005-01-01
The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.
Keanini, R.G.
2011-04-15
Research Highlights: > Systematic approach for physically probing nonlinear and random evolution problems. > Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. > Organization of near-molecular scale vorticity mediated by hydrodynamic modes. > Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion
Neutron star structure from QCD
NASA Astrophysics Data System (ADS)
Fraga, Eduardo S.; Kurkela, Aleksi; Vuorinen, Aleksi
2016-03-01
In this review article, we argue that our current understanding of the thermodynamic properties of cold QCD matter, originating from first principles calculations at high and low densities, can be used to efficiently constrain the macroscopic properties of neutron stars. In particular, we demonstrate that combining state-of-the-art results from Chiral Effective Theory and perturbative QCD with the current bounds on neutron star masses, the Equation of State of neutron star matter can be obtained to an accuracy better than 30% at all densities.
Mukherjee, Abhik Janaki, M. S. Kundu, Anjan
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations
NASA Astrophysics Data System (ADS)
Husa, Sascha; Hinder, Ian; Lechner, Christiane
2006-06-01
We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations. Program summaryTitle of program: Kranc Catalogue identifier: ADXS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under Linux Programming language used: Mathematica, C, Fortran 90 Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KB Has the code been vectorized or parallelized: The code is parallelized based on the Cactus framework. Number of bytes in distributed program, including test data, etc.: 1 578 142 Number of lines in distributed program, including test data, etc.: 11 711 Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared
Evolution equations for the joint probability of several compositions in turbulent combustion
Bakosi, Jozsef
2010-01-01
One-point statistical simulations of turbulent combustion require models to represent the molecular mixing of species mass fractions, which then determine the reaction rates. For multi-species mixing the Dirichlet distribution has been used to characterize the assumed joint probability density function (PDF) of several scalars, parametrized by solving modeled evolution equations for their means and the sum of their variances. The PDF is then used to represent the mixing state and to obtain the chemical reactions source terms in moment closures or large eddy simulation. We extend the Dirichlet PDF approach to transported PDF methods by developing its governing stochastic differential equation (SDE). The transport equation, as opposed to parametrizing the assumed PDF, enables (1) the direct numerical computation of the joint PDF (and therefore the mixing model to directly account for the flow dynamics (e.g. reaction) on the shape of the evolving PDF), and (2) the individual specification of the mixing timescales of each species. From the SDE, systems of equations are derived that govern the first two moments, based on which constraints are established that provide consistency conditions for material mixing. A SDE whose solution is the generalized Dirichlet PDF is also developed and some of its properties from the viewpoint of material mixing are investigated. The generalized Dirichlet distribution has the following advantages over the standard Dirichlet distribution due to its more general covariance structure: (1) its ability to represent differential diffusion (i.e. skewness) without affecting the scalar means, and (2) it can represent both negatively and positively correlated scalars. The resulting development is a useful representation of the joint PDF of inert or reactive scalars in turbulent flows: (1) In moment closures, the mixing physics can be consistently represented by one underlying modeling principle, the Dirichlet or the generalized Dirichlet PDF, and
NASA Astrophysics Data System (ADS)
Ablowitz, Mark J.; Curtis, Christopher W.
2011-05-01
The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.
On the interface between perturbative and nonperturbative QCD
NASA Astrophysics Data System (ADS)
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-06-01
The QCD running coupling αs (Q2) sets the strength of the interactions of quarks and gluons as a function of the momentum transfer Q. The Q2 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-Q2 analytic behavior of the strong coupling αs (Q2). The high-Q2 dependence of the coupling αs (Q2) is specified by perturbative QCD and its renormalization group equation. The matching of the high and low Q2 regimes of αs (Q2) then determines the scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics. The value of Q0 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 Q0 and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the MS ‾, g1, MOM and V renormalization schemes. Our results show that the discrepancies on the value of αs at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute αs (Q2) over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.
A multiscale asymptotic analysis of time evolution equations on the complex plane
NASA Astrophysics Data System (ADS)
Braga, Gastão A.; Conti, William R. P.
2016-07-01
Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
Most of us here know that the diffusion equation has also been used to describe the evolution through time of scarp-like landforms, including fault scarps, shoreline scarps, or a set of marine terraces. The methods, models, and data employed in such studies have been described in the literature many times over the past 25 years. For most situations, everything you will ever need (or want) to know can be found in Hanks et al. (1984) and Hanks (2000), the latter being a review of numerous studies of the 1980s and 1990s and a summary of available estimates of the mass diffusivity κ. The geometric parameterization of scarp-like landforms is shown in Figure 1.
NASA Astrophysics Data System (ADS)
Vrecica, Teodor; Toledo, Yaron
2015-04-01
One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes. PMID:24329934
Multidimensional extension of the continuity equation method for debris clouds evolution
NASA Astrophysics Data System (ADS)
Letizia, Francesca; Colombo, Camilla; Lewis, Hugh G.
2016-04-01
As the debris spatial density increases due to recent collisions and inoperative spacecraft, the probability of collisions in space grows. Even a collision involving small objects may produce thousands of fragments due to the high orbital velocity and the high energy released. The propagation of the trajectories of all the objects produced by a breakup would be prohibitive in terms of computational time; therefore, simplified models are needed to describe the consequences of a collision with a reasonable computational effort. The continuity approach can be applied to this purpose as it allows switching the point of view from the analysis of each single fragment to the study of the evolution of the debris cloud globally. Previous formulations of the continuity equation approach focussed on the representation of the drag effect on the fragment spatial density. This work proposes how the continuity equation approach can be extended to multiple dimensions in the phase space defined by the relevant orbital parameters. This novel approach allows including in the propagation also the effect of the Earth's oblateness and improving the description of the drag effect by considering the distribution of area-to-mass ratio and eccentricity among the fragments. Results for these three applications are shown and discussed in terms of accuracy compared to the numerical propagation and to the one-dimensional approach.
QCD thermodynamics and missing hadron states
NASA Astrophysics Data System (ADS)
Petreczky, Peter
2016-03-01
Equation of State and fluctuations of conserved charges in hot strongly interacting matter are being calculated with increasing accuracy in lattice QCD, and continuum results at physical quark masses become available. At sufficiently low temperature the thermodynamic quantities can be understood in terms of hadron resonance gas model that includes known hadrons and hadronic resonances from Particle Data Book. However, for some quantities it is necessary to include undiscovered hadronic resonances (missing states) that are, however, predicted by quark model and lattice QCD study of hadron spectrum. Thus, QCD thermodynamics can provide indications for the existence of yet undiscovered hadron states.
NASA Astrophysics Data System (ADS)
Gao, YingYing; He, Feng; Shen, MengYu
2011-04-01
Based on the idea of adjoint method and the dynamic evolution method, a new optimum aerodynamic design technique is presented in this paper. It can be applied to the optimum problems with a large number of design variables and is time saving. The key of the new method lies in that the optimization process is regarded as an unsteady evolution, i.e., the optimization is executed, simultaneously with solving the unsteady flow governing equations and adjoint equations. Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented, and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.
Random walk through recent CDF QCD results
C. Mesropian
2003-04-09
We present recent results on jet fragmentation, jet evolution in jet and minimum bias events, and underlying event studies. The results presented in this talk address significant questions relevant to QCD and, in particular, to jet studies. One topic discussed is jet fragmentation and the possibility of describing it down to very small momentum scales in terms of pQCD. Another topic is the studies of underlying event energy originating from fragmentation of partons not associated with the hard scattering.
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Zytkow, A. N.
1976-01-01
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.
2013-04-01
In the paper, existence conditions for Feynman integrals in the sense of analytic continuation of Gaussian integrals with respect to operator arguments are found. A representation of Feynman integrals in the form of Gaussian integrals is also constructed and, finally, the class of evolution equations having solutions representable by Feynman integrals is described.
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Nuclear reactions from lattice QCD
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 calculations 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.
Nuclear reactions from lattice QCD
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
Lattice QCD input for axion cosmology
NASA Astrophysics Data System (ADS)
Berkowitz, Evan; Buchoff, Michael I.; Rinaldi, Enrico
2015-08-01
One intriguing beyond-the-Standard-Model particle is the QCD axion, which could simultaneously provide a solution to the Strong C P Problem and account for some, if not all, of the dark matter density in the Universe. This particle is a pseudo-Nambu-Goldstone boson of the conjectured Peccei-Quinn symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry-breaking scale, fa, the value of which is roughly greater than 109 GeV (or, conversely, the axion mass, ma, is roughly less than 104 μ eV ). The density of axions in the Universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early Universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the C P -violating phase, θ . However, this quantity is generically nonperturbative, and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small θ from first-principle lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the Universe, which is required to be less than or equal to the dark matter density. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-θ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound ma≥(14.6 ±0.1 ) μ eV when Peccei-Quinn breaking occurs
NASA Astrophysics Data System (ADS)
Fratanduono, D.
2015-12-01
The thermal history of terrestrial planets depends upon the melt boundary as it represents the largest rheological transition a material can undergo. This change in rheological behavior with solidification corresponds to a dramatic change in the thermal and chemical transport properties. Because of this dramatic change in thermal transport, recent work by Stixrude et al.[1] suggests that the silicate melt curve sets the thermal profile within super-Earths during their early thermal evolution. Here we present recent decaying shock wave experiments studying both enstatite and forsterite. The continuously measured shock pressure and temperature in these studies ranged from 8 to 1.5 Mbar and 20,000-4,000 K, respectively. We find a point on the MgSiO3 liquidus at 6800 K and 285 GPa, which is nearly a factor of two higher pressure than previously measured and provides a strong constraint on the temperature profile within super-Earths. Our shock temperature measurements on forsterite and enstatite provide much needed equation of state information to the planetary impact modeling community since the shock temperature data can be used to constrain the initial entropy state of a growing planet. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. 1. Stixrude, L., Melting in super-earths. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2014. 372(2014).
Foundations of Perturbative QCD
NASA Astrophysics Data System (ADS)
Collins, John
2011-04-01
1. Introduction; 2. Why QCD?; 3. Basics of QCD; 4. Infra-red safety and non-safety; 5. Libby-Sterman analysis and power counting; 6. Parton model to parton theory I; 7. Parton model to parton theory II; 8. Factorization; 9. Corrections to the parton model in QCD; 10. Factorization and subtractions; 11. DIS in QCD; 12. Fragmentation; 13. TMD factorization; 14. Hadron-hadron collisions; 15. More advanced topics; Appendices; References; Index.
Foundations of Perturbative QCD
NASA Astrophysics Data System (ADS)
Collins, John
2013-11-01
1. Introduction; 2. Why QCD?; 3. Basics of QCD; 4. Infra-red safety and non-safety; 5. Libby-Sterman analysis and power counting; 6. Parton model to parton theory I; 7. Parton model to parton theory II; 8. Factorization; 9. Corrections to the parton model in QCD; 10. Factorization and subtractions; 11. DIS in QCD; 12. Fragmentation; 13. TMD factorization; 14. Hadron-hadron collisions; 15. More advanced topics; Appendices; References; Index.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
QCD with chiral 4-fermion interactions ({chi}QCD)
Kogut, J.B.; Sinclair, D.K.
1996-10-01
Lattice QCD with staggered quarks is augmented by the addition of a chiral 4-fermion interaction. The Dirac operator is now non-singular at m{sub q}=0, decreasing the computing requirements for light quark simulations by at least an order of magnitude. We present preliminary results from simulations at finite and zero temperatures for m{sub q}=0, with and without gauge fields. Chiral QCD enables simulations at physical u and d quark masses with at least an order of magnitude saving in CPU time. It also enables simulations with zero quark masses which is important for determining the equation of state. A renormalization group analysis will be needed to continue to the continuum limit. 7 refs., 2 figs.
APFEL: A PDF evolution library with QED corrections
NASA Astrophysics Data System (ADS)
Bertone, Valerio; Carrazza, Stefano; Rojo, Juan
2014-06-01
Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MS bar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD ⊗ QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O(αs2) . All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in FORTRAN 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.
Non-perturbative aspects of hadron structure in QCD
Thomas, Anthony W.
2012-09-26
We review recent developments in the understanding of hadron structure in the context of QCD. These developments build on the success of lattice QCD and discoveries in chiral perturbation theory. We focus particularly on tests of QCD through the strangeness content of the nucleon, the investigation of excited states of the nucleon, where lattice QCD, experiment and phenomenology meet. Lastly, we discuss the implications of these developments in hadron structure for our understanding of nuclear structure and the equation of state of dense matter.
Nucleon QCD sum rules in the instanton medium
Ryskin, M. G.; Drukarev, E. G. 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.
NLO evolution of color dipoles in N=4 SYM
Chirilli, Giovanni A.; Balitsky, Ian
2009-07-04
Here, high-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal ${\\cal N}$=4 SYM theory. We define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance.
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U. /SLAC
2007-02-21
The AdS/CFT correspondence between string theory in AdS space and conformal .eld theories in physical spacetime leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. Although QCD is not conformally invariant, one can nevertheless use the mathematical representation of the conformal group in five-dimensional anti-de Sitter space to construct a first approximation to the theory. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD, such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, and other exclusive scattering amplitudes. New relativistic lightfront equations in ordinary space-time are found which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess remarkable algebraic structures and integrability properties. Since they are complete and orthonormal, the AdS/CFT model wavefunctions can also be used as a basis for the diagonalization of the full light-front QCD Hamiltonian, thus systematically improving the AdS/CFT approximation.
Holographic models and the QCD trace anomaly
Jose L. Goity, Roberto C. Trinchero
2012-08-01
Five dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and non-perturbative {beta}-functions are studied. It is shown that in the perturbative case, where the {beta}-function is the QCD one at leading order, the resulting space is not asymptotically AdS. In the non-perturbative case, the model considered presents confinement of static quarks and leads to a non-vanishing gluon condensate, although it does not correspond to an asymptotically free theory. In both cases analyses based on the trace anomaly and on Wilson loops are carried out.
Recent progress in lattice QCD at finite temperature
Petreczky,P.
2009-02-01
I review recent progress in finite temperature lattice calculations,including the study of the nature of the deconfinement transition in QCD, equation of state, screening of static quarks and meson spectral functions.
LATTICE QCD AT HIGH TEMPERATURE AND THE QGP.
KARSCH, F.
2005-10-24
We review recent progress in studies of bulk thermodynamics of strongly interacting matter, present results on the QCD equation of state and discuss the status of studies of the phase diagram at non-vanishing quark chemical potential.
NASA Astrophysics Data System (ADS)
A. N., Dev; Sarma, J.; M. K., Deka; A. P., Misra; N. C., Adhikary
2014-12-01
We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev—Petviashivili—Burgers (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.
NASA Astrophysics Data System (ADS)
Wuchterl, G.; Tscharnuter, W. M.
2003-02-01
We present the first study of early stellar evolution with ``cloud'' initial conditions utilizing a system of equations that comprises a solar model solution. All previous studies of protostellar collapse either make numerous assumptions specifically tailored for different parts of the flow and different parts of the evolution or they do not reach the pre-main sequence phase. We calculate the pre-main sequence properties of marginally gravitationally unstable, isothermal, equilibrium ``Bonnor-Ebert'' spheres with an initial temperature of 10 K and masses of 0.05 to 10 Msun. The mass accretion rate is determined by the solution of the flow equations rather than being prescribed or neglected. In our study we determine the protostar's radii and the thermal structure together with the mass and mass accretion rate, luminosity and effective temperature during its evolution to a stellar pre-main sequence object. We calculate the time needed to accrete the final stellar masses, the corresponding mean mass accretion rates and median luminosities, and the corresponding evolutionary tracks in the theoretical Hertzsprung-Russell diagram. We derive these quantities from the gas flow resulting from cloud collapse. We do not assume a value for an ``initial'' stellar radius and an ``initial'' stellar thermal structure at the ``top of the track'', the Hayashi-line or any other instant of the evolution. Instead we solve the flow equations for a cloud fragment with spherical symmetry. The system of equations we use contains the equations of stellar structure and evolution as a limiting case and has been tested by a standard solar model and by classical stellar pulsations (Wuchterl & Feuchtinger \\cite{Wuchterl1998}; Feuchtinger \\cite{Feuchtinger1999a}; Dorfi & Feuchtinger \\cite{Dorfi1999}). When dynamical accretion effects have become sufficiently small so that a comparison to existing hydrostatic stellar evolution calculations for corresponding masses can be made, young stars of 2
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
Urban, Federico R.; Zhitnitsky, Ariel R.
2010-08-30
We review two mechanisms rooted in the infrared sector of QCD which, by exploiting the properties of the QCD ghost, as introduced by Veneziano, provide new insight on the cosmological dark energy problem, first, in the form of a Casimir-like energy from quantising QCD in a box, and second, in the form of additional, time-dependent, vacuum energy density in an expanding universe. Based on [1, 2].
Semistable extremal ground states for nonlinear evolution equations in unbounded domains
NASA Astrophysics Data System (ADS)
Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro
2008-02-01
In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their approximation by extremal equilibria in bounded domains is also studied. The results are then applied to the important case of logistic equations.
Neumann type integrable reduction for nonlinear evolution equations in 1+1 and 2+1 dimensions
NASA Astrophysics Data System (ADS)
Chen, Jinbing
2009-12-01
A family of new Neumann type systems is given in view of the nonlinearization technique, realizing the variable separation of the modified Jaulent-Miodek hierarchy and a new coupled modified Kadomtsev-Petviashvili equation on the symplectic submanifold TSN -1. By two Casimir functions and a special solution of the Lenard eigenvalue equation, we deduce the Lax-Moser matrix of the Neumann type systems that yields integrals of motion and the constrained Hamiltonians whose vector fields are tangent to TSN -1. Based on the Dirac-Poisson bracket and a Lax equation on TSN -1, a new systematic way is proposed to prove the Liouville integrability of a family of Neumann type systems synchronously. The Dirac-Poisson bracket and the generating function are used to reveal the explicit relation between infinite dimensional integrable systems and Neumann type systems, and then we point out that compatible solutions of Neumann type systems yield the finite parametric solutions of 1+1 and 2+1 dimensional integrable nonlinear evolution equations and the finite-gap solutions of the Novikov equation.
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
On the analytic solution of the Balitsky-Kovchegov evolution equation
NASA Astrophysics Data System (ADS)
Bondarenko, Sergey; Prygarin, Alex
2015-06-01
The study presents an analytic solution of the Balitsky-Kovchegov (BK) equa-tion in a particular kinematics. The solution is written in the momentum space and based on the eigenfunctions of the truncated Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in the gauge adjoint representation, which was used for calculation of the Regge (Mandel-stam) cut contribution to the planar helicity amplitudes. We introduce an eigenfunction of the singlet BFKL equation constructed of the adjoint eigenfunction multiplied by a factor, which restores the dual conformal symmetry present in the adjoint and broken in the sin-glet BFKL equations. The proposed analytic BK solution correctly reproduces the initial condition and the high energy asymptotics of the scattering amplitude.
Norniella, Olga; /Barcelona, IFAE
2005-01-01
Recent QCD measurements from the CDF collaboration at the Tevatron are presented, together with future prospects as the luminosity increases. The measured inclusive jet cross section is compared to pQCD NLO predictions. Precise measurements on jet shapes and hadronic energy flows are compared to different phenomenological models that describe gluon emissions and the underlying event in hadron-hadron interactions.
NASA Astrophysics Data System (ADS)
Li, Zhi-Bin; Liu, Yin-Ping
2004-11-01
In Maple 8, by taking advantage of the package RIF contained in DEtools, we developed a package RAEEM which is a comprehensive and complete implementation of such methods as the tanh-method, the extended tanh-method, the Jacobi elliptic function method and the elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions, including those of polynomial, exponential, triangular, hyperbolic, rational, Jacobi elliptic, Weierstrass elliptic type. The effectiveness of the package is illustrated by applying it to a large variety of equations. In addition to recovering previously known solutions, we also obtain more general forms of some solutions and new solutions. Program summaryTitle of program: RAEEM Catalogue identifier: ADUP Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUP Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: PC Pentium IV Installations: Copy Operating systems: Windows 98/2000/XP Program language used: Maple 8 Memory required to execute with typical data: depends on the problem, minimum about 8M words No. of bits in a word: 8 No. of lines in distributed program, including test data, etc.: 3163 No. of bytes in distributed program, including the test data, etc.: 26 720 Distribution format: tar.gz Nature of physical problem: Our program provides exact traveling wave solutions, which describe various phenomena in nature, and thus can give more insight into the physical aspects of problems. These solutions may be easily used in further applications. Restriction on the complexity of the problem: The program can handle system of nonlinear evolution equations with any number of independent and dependent variables, in which each equation is a polynomial (or can be converted to a polynomial) in the dependent variables and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For
Light-Front Holography: A First Approximation to QCD
Teramond, Guy F. de; Brodsky, Stanley J.
2009-02-27
Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate {zeta} which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wave functions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space.
Representation formula for stochastic Schrödinger evolution equations and applications
NASA Astrophysics Data System (ADS)
de Bouard, Anne; Fukuizumi, Reika
2012-11-01
We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L2 or in the energy space of model equations arising in Bose-Einstein condensation, Abdullaev et al (2001 Nonlinearity and Disorder: Theory and Applications (NATO Science Series vol 45) ed F Abdullaev et al (Dodrecht: Kluwer)), or in fiber optics, Abdullaev et al (2000 Physica D 135 369-86). Our results also give a justification of diffusion-approximation for stochastic nonlinear Schrödinger equations.
Quarkonium states in an anisotropic QCD plasma
Dumitru, Adrian; Guo Yun; Mocsy, Agnes; Strickland, Michael
2009-03-01
We consider quarkonium in a hot quantum chromodynamics (QCD) plasma which, due to expansion and nonzero viscosity, exhibits a local anisotropy in momentum space. At short distances the heavy-quark potential is known at tree level from the hard-thermal loop resummed gluon propagator in anisotropic perturbative QCD. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is nonzero and inversely proportional to the temperature. We obtain numerical solutions of the three-dimensional Schroedinger equation for this potential. We find that quarkonium binding is stronger at nonvanishing viscosity and expansion rate, and that the anisotropy leads to polarization of the P-wave states.
Evolution of Central Moments for a General-Relativistic Boltzmann Equation
NASA Astrophysics Data System (ADS)
Banach, Zbigniew; Larecki, Wieslaw
Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY) 150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau-Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.
Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
Cui, Zhu-Fang; Hou, Feng-Yao; Shi, Yuan-Mei; Wang, Yong-Long; Zong, Hong-Shi
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.
NASA Astrophysics Data System (ADS)
Filimonov, M.; Masih, A.
2016-06-01
One of the analytical methods of presenting solutions of nonlinear partial differential equations is the method of special series in powers of specially selected functions called basis functions. The coefficients of such series are found successively as solutions of linear differential equations. To find recurrence, the coefficient is achieved by the choice of basis functions, which may also contain arbitrary functions. By using such functional arbitrariness, it allows in some cases to prove the global convergence of the corresponding constructed series, as well as the solvability of the boundary value problem.
Time evolution of Rényi entropy under the Lindblad equation
NASA Astrophysics Data System (ADS)
Abe, Sumiyoshi
2016-08-01
In recent years, the Rényi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Rényi entropy is studied. A compact general formula is presented for the lower bound on the entropy rate.
The evolution equation for the flame surface density in turbulent premixed combustion
NASA Technical Reports Server (NTRS)
Trouve, Arnaud
1993-01-01
The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only
The evolution equation for the flame surface density in turbulent premixed combustion
NASA Technical Reports Server (NTRS)
Trouve, A.; Poinsot, T.
1992-01-01
One central ingredient in flamelet models for turbulent premixed combustion is the flame surface density. This quantity conveys most of the effects of the turbulence on the rate of energy release and is obtained via a modeled transport equation, called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact, but unclosed, formulation for the turbulent Sigma-equation. In this exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the flame surface density and the turbulent flame stretch are not available from experiments and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the obvious, complementary approach to get basic information on these fundamental quantities. Three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, the effects of the Lewis number on the rate of production of flame surface area are described in great detail and meaningful comparisons with flamelet models can be performed. The analysis reveals in particular the tendency of the models to overpredict flame surface dissipation as well as their inability to reproduce variations due to thermo-diffusive phenomena. Thanks to the detailed information produced by a DNS-based analysis, this type of comparison not only underscores the shortcomings of current models but also suggests ways to improve them.
Modeling QCD for Hadron Physics
NASA Astrophysics Data System (ADS)
Tandy, P. C.
2011-10-01
We review the approach to modeling soft hadron physics observables based on the Dyson-Schwinger equations of QCD. The focus is on light quark mesons and in particular the pseudoscalar and vector ground states, their decays and electromagnetic couplings. We detail the wide variety of observables that can be correlated by a ladder-rainbow kernel with one infrared parameter fixed to the chiral quark condensate. A recently proposed novel perspective in which the quark condensate is contained within hadrons and not the vacuum is mentioned. The valence quark parton distributions, in the pion and kaon, as measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
Modeling QCD for Hadron Physics
Tandy, P. C.
2011-10-24
We review the approach to modeling soft hadron physics observables based on the Dyson-Schwinger equations of QCD. The focus is on light quark mesons and in particular the pseudoscalar and vector ground states, their decays and electromagnetic couplings. We detail the wide variety of observables that can be correlated by a ladder-rainbow kernel with one infrared parameter fixed to the chiral quark condensate. A recently proposed novel perspective in which the quark condensate is contained within hadrons and not the vacuum is mentioned. The valence quark parton distributions, in the pion and kaon, as measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
Lattice QCD in rotating frames.
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. PMID:24010426
AdS/QCD and Its Holographic Light-Front Partonic Representation
de Teramond, Guy F.; Brodsky, Stanley J.; ,
2008-11-12
Starting from the Hamiltonian equation of motion in QCD we find a single variable light-front equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space.
AdS/QCD and its Holographic Light-Front Partonic Representation
Teramond, Guy F. de; Brodsky, Stanley J.
2009-03-23
Starting from the Hamiltonian equation of motion in QCD we find a single variable light-front equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space.
The Dirichlet problem for the fractional p-Laplacian evolution equation
NASA Astrophysics Data System (ADS)
Vázquez, Juan Luis
2016-04-01
We consider a model of fractional diffusion involving a natural nonlocal version of the p-Laplacian operator. We study the Dirichlet problem posed in a bounded domain Ω of RN with zero data outside of Ω, for which the existence and uniqueness of strong nonnegative solutions is proved, and a number of quantitative properties are established. A main objective is proving the existence of a special separate variable solution U (x , t) =t - 1 / (p - 2) F (x), called the friendly giant, which produces a universal upper bound and explains the large-time behaviour of all nontrivial nonnegative solutions in a sharp way. Moreover, the spatial profile F of this solution solves an interesting nonlocal elliptic problem. We also prove everywhere positivity of nonnegative solutions with any nontrivial data, a property that separates this equation from the standard p-Laplacian equation.
On the solution of evolution equations based on multigrid and explicit iterative methods
NASA Astrophysics Data System (ADS)
Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.
2015-08-01
Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.
Exclusive QCD processes, quark-hadron duality, and the transition to perturbative QCD
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Li, Hsiang-nan; Savkli, Cetin
1998-07-01
Experiments at CEBAF will scan the intermediate-energy region of the QCD dynamics for the nucleon form factors and for Compton Scattering. These experiments will definitely clarify the role of resummed perturbation theory and of quark-hadron duality (QCD sum rules) in this regime. With this perspective in mind, we review the factorization theorem of perturbative QCD for exclusive processes at intermediate energy scales, which embodies the transverse degrees of freedom of a parton and the Sudakov resummation of the corresponding large logarithms. We concentrate on the pion and proton electromagnetic form factors and on pion Compton scattering. New ingredients, such as the evolution of the pion wave function and the complete two-loop expression of the Sudakov factor, are included. The sensitivity of our predictions to the infrared cutoff for the Sudakov evolution is discussed. We also elaborate on QCD sum rule methods for Compton Scattering, which provide an alternative description of this process. We show that, by comparing the local duality analysis to resummed perturbation theory, it is possible to describe the transition of exclusive processes to perturbative QCD.
Dynamics of Vapour Bubbles in Nucleate Boiling. 1; Basic Equations of Bubble Evolution
NASA Technical Reports Server (NTRS)
Buyevich, Yu A.; Webbon, Bruce W.; Callaway, Robert (Technical Monitor)
1995-01-01
We consider the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. There is no forced convection of an ambient liquid, and the bubble is presumably separated from the wall by a thin liquid microlayer. The energy conservation law results in a variational equation for the mechanical energy of the whole system consisting of the bubble and liquid. It leads to a set of two strongly nonlinear equations which govern bubble expansion and motion of its centre of mass. A supplementary equation to find out the vapour temperature follows from consideration of heat transfer to the bubble, both from the bulk of surrounding liquid and through the microlayer. The average thickness of the microlayer is shown to increase monotonously with time as the bubble meniscus spreads along the wall. Bubble expansion is driven by the pressure head between vapour inside and liquid far away from the bubble, with due allowance for surface tension and gravity effects. It is resisted by inertia of liquid being placed into motion as the bubble grows. The inertia originates also a force that presses the bubble to the wall. This force is counteracted by the buoyancy and an effective surface tension force that tends to transform the bubble into a sphere. The analysis brings about quite a new formulation of the familiar problem of bubble growth and detachment under conditions of nucleate pool boiling.
Evolution of a network of vortex loops in He-II: exact solution of the rate equation.
Nemirovskii, Sergey K
2006-01-13
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection. PMID:16486471
Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation
Nemirovskii, Sergey K.
2006-01-13
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l){proportional_to}l{sup -5/2} obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.
Mapping the QCD Phase Transition with Accreting Compact Stars
Blaschke, D.; Poghosyan, G.; Grigorian, H.
2008-10-29
We discuss an idea for how accreting millisecond pulsars could contribute to the understanding of the QCD phase transition in the high-density nuclear matter equation of state (EoS). It is based on two ingredients, the first one being a ''phase diagram'' of rapidly rotating compact star configurations in the plane of spin frequency and mass, determined with state-of-the-art hybrid equations of state, allowing for a transition to color superconducting quark matter. The second is the study of spin-up and accretion evolution in this phase diagram. We show that the quark matter phase transition leads to a characteristic line in the {omega}-M plane, the phase border between neutron stars and hybrid stars with a quark matter core. Along this line a drop in the pulsar's moment of inertia entails a waiting point phenomenon in the accreting millisecond pulsar (AMXP) evolution: most of these objects should therefore be found along the phase border in the {omega}-M plane, which may be viewed as the AMXP analog of the main sequence in the Hertzsprung-Russell diagram for normal stars. In order to prove the existence of a high-density phase transition in the cores of compact stars we need population statistics for AMXPs with sufficiently accurate determination of their masses, spin frequencies and magnetic fields.
Next-to-leading order QCD factorization for semi-inclusive deep inelastic scattering at twist 4.
Kang, Zhong-Bo; Wang, Enke; Wang, Xin-Nian; Xing, Hongxi
2014-03-14
Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic e+A collisions, as well as lepton pair production in p+A collisions. With explicit calculations of both real and virtual contributions, we verify, for the first time, the factorization theorem at twist 4 in NLO for the nuclear-enhanced transverse momentum weighted differential cross section and demonstrate the universality of the associated twist-4 quark-gluon correlation function. We also identify the QCD evolution equation for the twist-4 quark-gluon correlation function in a large nucleus, which can be solved to determine the scale dependence of the jet transport parameter in the study of jet quenching. PMID:24679281
Next-to-Leading Order QCD Factorization for Semi-Inclusive Deep Inelastic Scattering at Twist 4
NASA Astrophysics Data System (ADS)
Kang, Zhong-Bo; Wang, Enke; Wang, Xin-Nian; Xing, Hongxi
2014-03-01
Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic e +A collisions, as well as lepton pair production in p +A collisions. With explicit calculations of both real and virtual contributions, we verify, for the first time, the factorization theorem at twist 4 in NLO for the nuclear-enhanced transverse momentum weighted differential cross section and demonstrate the universality of the associated twist-4 quark-gluon correlation function. We also identify the QCD evolution equation for the twist-4 quark-gluon correlation function in a large nucleus, which can be solved to determine the scale dependence of the jet transport parameter in the study of jet quenching.
NASA Astrophysics Data System (ADS)
Lutz, Matthias F. M.; Lange, Jens Sören; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B.; Metag, Volker; Nakano, Takashi; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Stephen L.; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram
2016-04-01
We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: What is needed to understand the physics of resonances in QCD? Where does QCD lead us to expect resonances with exotic quantum numbers? What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy-light and heavy-heavy meson systems, those with charm quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
NASA Astrophysics Data System (ADS)
Geiger, Klaus
1997-08-01
VNI is a general-purpose Monte Carlo event generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. On the basis of renormalization-group improved parton description and quantum-kinetic theory, it uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme that is governed by the dynamics itself. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons, in position space, momentum space and color space. The parton evolution is described in terms of a space-time generalization of the familiar momentum-space description of multiple (semi) hard interactions in QCD, involving 2 → 2 parton collisions, 2 → 1 parton fusion processes, and 1 → 2 radiation processes. The formation of color-singlet pre-hadronic clusters and their decays into hadrons, on the other hand, is treated by using a spatial criterion motivated by confinement and a non-perturbative model for hadronization. This article gives a brief review of the physics underlying VNI, which is followed by a detailed description of the program itself. The latter program description emphasizes easy-to-use pragmatism and explains how to use the program (including a simple example), annotates input and control parameters, and discusses output data provided by it.
Skands, Peter Z.; /Fermilab
2005-07-01
Recent developments in QCD phenomenology have spurred on several improved approaches to Monte Carlo event generation, relative to the post-LEP state of the art. In this brief review, the emphasis is placed on approaches for (1) consistently merging fixed-order matrix element calculations with parton shower descriptions of QCD radiation, (2) improving the parton shower algorithms themselves, and (3) improving the description of the underlying event in hadron collisions.
NASA Astrophysics Data System (ADS)
Chetyrkin, K. G.; Zoller, M. F.
2016-06-01
We present analytical results for the leading top-Yukawa and QCD contribution to the β-function for the Higgs self-coupling λ of the Standard Model at four-loop level, namely the part ∝ y t 4 g s 6 independently confirming a result given in [1]. We also give the contribution ∝ y t 2 g s 6 of the anomalous dimension of the Higgs field as well as the terms ∝ y t g s 8 to the top-Yukawa β-function which can also be derived from the anomalous dimension of the top quark mass. We compare the results with the RG functions of the correlators of two and four scalar currents in pure QCD and find a new relation between the anomalous dimension γ 0 of the QCD vacuum energy and the anomalous dimension γ m SS appearing in the RG equation of the correlator of two scalar currents. Together with the recently computed top-Yukawa and QCD contributions to β gs [2, 3] the β-functions presented here constitute the leading four-loop contributions to the evolution of the Higgs self-coupling. A numerical estimate of these terms at the scale of the top-quark mass is presented as well as an analysis of the impact on the evolution of λ up to the Planck scale and the vacuum stability problem.
Small-x Evolution of Structure Functions in the Next-to-Leading Order
Chirilli, Giovanni A.
2009-12-17
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the nonlinear Balitsky-Kovchegov (BK) equation. The NLO corrections define the scale of the running-coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the 'composite dipole operator' with the rapidity cutoff preserving conformal invariance, and the resulting Moebius invariant kernel for this operator agrees with the forward NLO BFKL calculation.In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part.
Small-x Evolution of Structure Functions in the Next-to-Leading Order
Giovanni Antonio Chirilli
2009-12-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the nonlinear Balitsky-Kovchegov (BK) equation. The NLO corrections define the scale of the running coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance, and the resulting Möbius invariant kernel for this operator agrees with the forward NLO BFKL calculation. In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part.
A non-local evolution equation model of cell–cell adhesion in higher dimensional space
Dyson, Janet; Gourley, Stephen A.; Webb, Glenn F.
2013-01-01
A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments. AMS Classifications: 35A01; 35B09; 35B40; 35K57; 92C17 PMID:23289870
An extended structure-based model based on a stochastic eddy-axis evolution equation
NASA Technical Reports Server (NTRS)
Kassinos, S. C.; Reynolds, W. C.
1995-01-01
We have proposed and implemented an extension of the structure-based model for weak deformations. It was shown that the extended model will correctly reduce to the form of standard k-e models for the case of equilibrium under weak mean strain. The realizability of the extended model is guaranteed by the method of its construction. The predictions of the proposed model were very good for rotating homogeneous shear flows and for irrotational axisymmetric contraction, but were seriously deficient in the case of plane strain and axisymmetric expansion. We have concluded that the problem behind these difficulties lies in the algebraic constitutive equation relating the Reynolds stresses to the structure parameters rather than in the slow model developed here. In its present form, this equation assumes that under irrotational strain the principal axes of the Reynolds stresses remain locked onto those of the eddy-axis tensor. This is correct in the RDT limit, but inappropriate under weaker mean strains, when the non-linear eddy-eddy interactions tend to misalign the two sets of principal axes and create some non-zero theta and gamma.
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 equal 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.
NASA Astrophysics Data System (ADS)
Lou, Sen-yue
1998-05-01
To study a nonlinear partial differential equation (PDE), the Painleve expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painleve analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is used for many nonlinear integrable and nonintegrable PDEs such as the Burgers, Korteweg de-Vries (KdV), Kadomtsev-Petviashvli (KP), Caudrey-Dodd-Gibbon-Sawada-Kortera (CDGSK), Nonlinear Schrödinger (NLS), Davey-Stewartson (DS), Broer-Kaup (BK), KdV-Burgers (KdVB), λf4 , sine-Gordon (sG) etc.
NASA Technical Reports Server (NTRS)
Ogallagher, J. J.; Maslyar, G. A., III
1975-01-01
A recently developed model predicts an energy dependent phase lag in the modulated cosmic ray density U(t) given by U(t) approximately equal to US (t - tau) where US is the solution to the Fokker-Planck equation under time independent conditions and tau is the average time spent by particles inside the modulating region. The delay times tau are functions of modulating parameters R (the radius of the modulating cavity), V (the solar wind velocity), and K (the effective average diffusion-coefficient which is a function of energy). This model is applied to predict the time evolution of the modulated cosmic ray proton spectrum over a simulated solar cycle. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations.
Ultrahigh energy neutrinos and nonlinear QCD dynamics
Machado, Magno V.T.
2004-09-01
The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the nonlinear QCD dynamics. Based on the color dipole framework, the results for the saturation model supplemented by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution as well as for the Balitskii-Fadin-Kuraev-Lipatov (BFKL) formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using next-to-leading order DGLAP and unified BFKL-DGLAP formalisms.
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
ERIC Educational Resources Information Center
Mayr, Ernst
1978-01-01
Traces the history of evolution theory from Lamarck and Darwin to the present. Discusses natural selection in detail. Suggests that, besides biological evolution, there is also a cultural evolution which is more rapid than the former. (MA)
Hot Compression of TC8M-1: Constitutive Equations, Processing Map, and Microstructure Evolution
NASA Astrophysics Data System (ADS)
Yue, Ke; Chen, Zhiyong; Liu, Jianrong; Wang, Qingjiang; Fang, Bo; Dou, Lijun
2016-06-01
Hot compression of TC8M-1 was carried out under isothermal working conditions with temperature from 1173 K to 1323 K (900 °C to 1050 °C), strain rate from 0.001 to 10/s, and height reduction from 20 to 80 pct (corresponding true strain from 0.22 to 1.61). Constitutive equations were constructed and apparent activation energies of 149.5 and 617.4 kJ/mol were obtained for deformation in the β and upper α/ β phase regions, respectively. Microstructure examination confirmed the dominant role of dynamic recrystallization in the α/ β phase region and that of dynamic recovery in the β phase region, with the occurrence of grain boundary sliding at very low strain rate (0.001/s) in both regions. Based on the dynamic materials model, processing maps were constructed, providing optimal domains for hot working at the temperature of 1253 K (980 °C) and the strain rate of 0.01 to 0.1/s, or at 1193 K to 1213 K (920 °C to 940 °C) and 0.001/s. Moreover, our results indicated that the initial temperature non-uniformity along the specimen axis before compression existed and influenced the strain distribution, which contributed to the abnormal oscillations and/or abrupt rise-up of true stress and inhomogeneous deformation.
Hot Compression of TC8M-1: Constitutive Equations, Processing Map, and Microstructure Evolution
NASA Astrophysics Data System (ADS)
Yue, Ke; Chen, Zhiyong; Liu, Jianrong; Wang, Qingjiang; Fang, Bo; Dou, Lijun
2016-04-01
Hot compression of TC8M-1 was carried out under isothermal working conditions with temperature from 1173 K to 1323 K (900 °C to 1050 °C), strain rate from 0.001 to 10/s, and height reduction from 20 to 80 pct (corresponding true strain from 0.22 to 1.61). Constitutive equations were constructed and apparent activation energies of 149.5 and 617.4 kJ/mol were obtained for deformation in the β and upper α/β phase regions, respectively. Microstructure examination confirmed the dominant role of dynamic recrystallization in the α/β phase region and that of dynamic recovery in the β phase region, with the occurrence of grain boundary sliding at very low strain rate (0.001/s) in both regions. Based on the dynamic materials model, processing maps were constructed, providing optimal domains for hot working at the temperature of 1253 K (980 °C) and the strain rate of 0.01 to 0.1/s, or at 1193 K to 1213 K (920 °C to 940 °C) and 0.001/s. Moreover, our results indicated that the initial temperature non-uniformity along the specimen axis before compression existed and influenced the strain distribution, which contributed to the abnormal oscillations and/or abrupt rise-up of true stress and inhomogeneous deformation.
Narayanan, Siva
2016-01-01
It is important to evaluate how the value of medicine is assessed, as it may have important implications for health technology and reimbursement assessments. The value equation could comprise 'incremental benefit/outcome' (relative results of care in terms of patient health, comparing the innovation to best available alternative(s)) in the numerator and 'cost' (relative costs involved in the full cycle of care (or a defined period) for the patient's medical condition, incorporating the relevant cost-offsets due to displacement of best available alternative(s)) in the denominator. This 'relative value' combined with the overall net budget impact (of including the drug in the formulary or reimbursed drug list) at the concerned population level in the given institution/region/country may better inform the usefulness of the new therapeutic option to the healthcare system. As product value messages are created, anticipating external stakeholder questions and information needs, including addressing three main categories of 'uncertainties', namely the scientific uncertainties, usage uncertainties, and financial uncertainties, could facilitate demonstration of optimal product value and help informed decision-making to benefit all stakeholders involved in the process. PMID:27489585
Narayanan, Siva
2016-01-01
It is important to evaluate how the value of medicine is assessed, as it may have important implications for health technology and reimbursement assessments. The value equation could comprise ‘incremental benefit/outcome’ (relative results of care in terms of patient health, comparing the innovation to best available alternative(s)) in the numerator and ‘cost’ (relative costs involved in the full cycle of care (or a defined period) for the patient's medical condition, incorporating the relevant cost-offsets due to displacement of best available alternative(s)) in the denominator. This ‘relative value’ combined with the overall net budget impact (of including the drug in the formulary or reimbursed drug list) at the concerned population level in the given institution/region/country may better inform the usefulness of the new therapeutic option to the healthcare system. As product value messages are created, anticipating external stakeholder questions and information needs, including addressing three main categories of ‘uncertainties’, namely the scientific uncertainties, usage uncertainties, and financial uncertainties, could facilitate demonstration of optimal product value and help informed decision-making to benefit all stakeholders involved in the process. PMID:27489585
The three-loop splitting functions in QCD: The helicity-dependent case
NASA Astrophysics Data System (ADS)
Moch, S.; Vermaseren, J. A. M.; Vogt, A.
2014-12-01
We present the next-to-next-to-leading order (NNLO) contributions to the main splitting functions for the evolution of longitudinally polarized parton densities of hadrons in perturbative QCD. The quark-quark and gluon-quark splitting functions have been obtained by extending our previous all Mellin-N calculations to the structure function g1 in electromagnetic deep-inelastic scattering (DIS). Their quark-gluon and gluon-gluon counterparts have been derived using third-order fixed-N calculations of structure functions in graviton-exchange DIS, relations to the unpolarized case and mathematical tools for systems of Diophantine equations. The NNLO corrections to the splitting functions are small outside the region of small momentum fractions x where they exhibit a large double-logarithmic enhancement, yet the corrections to the evolution of the parton densities can be unproblematic down to at least x ≈10-4.
Harris, R.
1992-05-01
We present measurements of jet production and isolated prompt photon production in p{bar p} collisions at {radical}s = 1.8 TeV from the 1988--89 run of the Collider Detector at Fermilab (CDF). To test QCD with jets, the inclusive jet cross section (p{bar p} {yields} J + X) and two jet angular distributions (p{bar P} {yields} JJ + X) are compared to QCD predictions and are used to search for composite quarks. The ratio of the scaled jet cross sections at two Tevatron collision energies ({radical}s= 546 and 1800 GeV) is compared to QCD predictions for X{sub T} scaling violations. Also, we present the first evidence for QCD interference effects (color coherence) in third jet production (p{bar p} {yields} JJJ + X). To test QCD with photons, we present measurements of the transverse momentum spectrum of single isolated prompt photon production (p{bar p} {yields} {gamma} + X), double isolated prompt photon production (p{bar p} {yields} {gamma}{gamma} + X), and the angular distribution of photon-jet events (p{bar p} {yields} {gamma} J + X). We have also measured the isolated production ratio of {eta} and {pi}{sup 0} mesons (p{bar p} {yields} {eta} + X)/(p{bar p} {yields} {pi}{sup 0} + X) = 1.02 {plus minus} .15(stat) {plus minus} .23(sys).
Harris, R.; The CDF Collaboration
1992-05-01
We present measurements of jet production and isolated prompt photon production in p{bar p} collisions at {radical}s = 1.8 TeV from the 1988--89 run of the Collider Detector at Fermilab (CDF). To test QCD with jets, the inclusive jet cross section (p{bar p} {yields} J + X) and two jet angular distributions (p{bar P} {yields} JJ + X) are compared to QCD predictions and are used to search for composite quarks. The ratio of the scaled jet cross sections at two Tevatron collision energies ({radical}s= 546 and 1800 GeV) is compared to QCD predictions for X{sub T} scaling violations. Also, we present the first evidence for QCD interference effects (color coherence) in third jet production (p{bar p} {yields} JJJ + X). To test QCD with photons, we present measurements of the transverse momentum spectrum of single isolated prompt photon production (p{bar p} {yields} {gamma} + X), double isolated prompt photon production (p{bar p} {yields} {gamma}{gamma} + X), and the angular distribution of photon-jet events (p{bar p} {yields} {gamma} J + X). We have also measured the isolated production ratio of {eta} and {pi}{sup 0} mesons (p{bar p} {yields} {eta} + X)/(p{bar p} {yields} {pi}{sup 0} + X) = 1.02 {plus_minus} .15(stat) {plus_minus} .23(sys).
Skartlien, R; Grimes, B; Meakin, P; Sjöblom, J; Sollum, E
2012-12-01
Lattice Boltzmann simulations were used to study the coalescence kinetics in emulsions with amphiphilic surfactant, under neutrally buoyant conditions, and with a significant kinematic viscosity contrast between the phases (emulating water in oil emulsions). The 3D simulation domain was large enough (256(3) ~ 10(7) grid points) to obtain good statistics with droplet numbers ranging from a few thousand at early times to a few hundred near equilibrium. Increased surfactant contents slowed down the coalescence rate between droplets due to the Gibbs-Marangoni effect, and the coalescence was driven by a quasi-turbulent velocity field. The kinetic energy decayed at a relatively slow rate at early times, due to conversion of interfacial energy to kinetic energy in the flow during coalescence. Phenomenological, coupled differential equations for the mean droplet diameter D(t) and the number density n(d)(t) were obtained from the simulation data and from film draining theories. Local (in time) power law exponents for the growth of the mean diameter (and for the concomitant decrease of n(d)) were established in terms of the instantaneous values of the kinetic energy, coalescence probability, Gibbs elasticity, and interfacial area. The model studies indicated that true power laws for the growth of the droplet size and decrease of the number of droplets with time may not be justified, since the exponents derived using the phenomenological model were time dependent. In contrast to earlier simulation results for symmetric blends with surfactant, we found no evidence for stretched logarithmic scaling of the form D ~ [ln (ct)](α) for the morphology length, or exponential scalings associated with arrested growth, on the basis of the phenomenological model. PMID:23231250
R. Skartlien; E. Sollum; A. Akselsen; P. Meakin; B. Grimes; J. Sjoblom
2012-12-01
Lattice Boltzmann simulations were used to study the coalescence kinetics in emulsions with amphiphilic surfactant, under neutrally buoyant conditions, and with a significant kinematic viscosity contrast between the phases (emulating water in oil emulsions). The 3D simulation domain was large enough (256 3rd power -- 10 7th power grid points) to obtain good statistics with droplet numbers ranging from a few thousand at early times to a few hundred near equilibrium. Increased surfactant contents slowed down the coalescence rate between droplets due to the Gibbs-Marangoni effect, and the coalescence was driven by a quasi-turbulent velocity field. The kinetic energy decayed at a relatively slow rate at early times, due to conversion of interfacial energy to kinetic energy in the flow during coalescence. Phenomenological, coupled differential equations for the mean droplet diameter D(t) and the number density nd(t) were obtained from the simulation data and from film draining theories. Local (in time) power law exponents for the growth of the mean diameter (and for the concomitant decrease of nd) were established in terms of the instantaneous values of the kinetic energy, coalescence probability, Gibbs elasticity, and interfacial area. The model studies indicated that true power laws for the growth of the droplet size and decrease of the number of droplets with time may not be justified, since the exponents derived using the phenomenological model were time dependent. In contrast to earlier simulation results for symmetric blends with surfactant, we found no evidence for stretched logarithmic scaling of the formD -- [ln (ct)]a for the morphology length, or exponential scalings associated with arrested growth, on the basis of the phenomenological model.
NASA Astrophysics Data System (ADS)
de Pater, Imke; Sromovsky, L. A.; Hammel, Heidi B.; Fry, P. M.; LeBeau, R. P.; Rages, Kathy; Showalter, Mark; Matthews, Keith
2011-09-01
We present observations of Uranus taken with the near-infrared camera NIRC2 on the 10-m W.M. Keck II telescope, the Wide Field Planetary Camera 2 (WFPC2) and the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) from July 2007 through November 2009. In this paper we focus on a bright southern feature, referred to as the "Berg." In Sromovsky et al. (Sromovsky, L.A., Fry, P.M., Hammel, H.B., Ahue, A.W., de Pater, I., Rages, K.A., Showalter, M.R., van Dam, M. [2009]. Icarus 203, 265-286), we reported that this feature, which oscillated between latitudes of -32° and -36° for several decades, suddenly started on a northward track in 2005. In this paper we show the complete record of observations of this feature's track towards the equator, including its demise. After an initially slow linear drift, the feature's drift rate accelerated at latitudes ∣ θ∣ < 25°. By late 2009 the feature, very faint by then, was spotted at a latitude of -5° before disappearing from view. During its northward track, the feature's morphology changed dramatically, and several small bright unresolved features were occasionally visible poleward of the main "streak." These small features were sometimes visible at a wavelength of 2.2 μm, indicative that the clouds reached altitudes of ˜0.6 bar. The main part of the Berg, which is generally a long sometimes multipart streak, is estimated to be much deeper in the atmosphere, near 3.5 bars in 2004, but rising to 1.8-2.5 bars in 2007 after it began its northward drift. Through comparisons with Neptune's Great Dark Spot and simulations of the latter, we discuss why the Berg may be tied to a vortex, an anticyclone deeper in the atmosphere that is visible only through orographic companion clouds.
Blazey, G.C.
1995-05-01
Selected recent Quantum Chromodynamics (QCD) results from the D0 and CDF experiments at the Fermilab Tevatron are presented and discussed. The inclusive jet and inclusive triple differential dijet cross sections are compared to next-to-leading order QCD calculations. The sensitivity of the dijet cross section to parton distribution functions (for hadron momentum fractions {approximately} 0.01 to {approximately} 0.4) will constrain the gluon distribution of the proton. Two analyses of dijet production at large rapidity separation are presented. The first analysis tests the contributions of higher order processes to dijet production and can be considered a test of BFKL or GLAP parton evolution. The second analysis yields a strong rapidity gap signal consistent with colorless exchange between the scattered partons. The prompt photon inclusive cross section is consistent with next-to-leading order QCD only at the highest transverse momenta. The discrepancy at lower momenta may be indicative of higher order processes impacting a transverse momentum or ``k{sub T}`` to the partonic interaction. The first measurement of the strong coupling constant from the Tevatron is also presented. The coupling constant can be determined from the ratio of W + 1jet to W + 0jet cross sections and a next-to-leading order QCD calculation.
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Hormuzdiar, J.N.; Hsu, S.D.
1999-02-01
We describe a class of pionic breather solutions (PBS) which appear in the chiral Lagrangian description of low-energy QCD. These configurations are long lived, with lifetimes greater than 10{sup 3} fm/c, and could arise as remnants of disoriented chiral condensate (DCC) formation at RHIC. We show that the chiral Lagrangian equations of motion for a uniformly isospin-polarized domain reduce to those of the sine-Gordon model. Consequently, our solutions are directly related to the breather solutions of sine-Gordon theory in 3+1 dimensions. We investigate the possibility of PBS formation from multiple domains of DCC, and show that the probability of formation is non-negligible. {copyright} {ital 1999} {ital The American Physical Society}
Unveiling the cosmological QCD phase transition through the eLISA/NGO detector
NASA Astrophysics Data System (ADS)
Mourão Roque, V. R. C.; Lugones, G.
2013-04-01
We study the evolution of turbulence in the early Universe at the QCD epoch using a state-of-the-art equation of state derived from lattice QCD simulations. Since the transition is a crossover we assume that temperature and velocity fluctuations were generated by some event in the previous history of the Universe and survive until the QCD epoch due to the extremely large Reynolds number of the primordial fluid. The fluid at the QCD epoch is assumed to be nonviscous, based on the fact that the viscosity per entropy density of the quark gluon plasma obtained from heavy-ion collision experiments at the Relativistic Heavy Ion Collider and the LHC is extremely small. Our hydrodynamic simulations show that the velocity spectrum is very different from the Kolmogorov power law considered in studies of primordial turbulence that focus on first order phase transitions. This is due to the fact that there is no continuous injection of energy into the system and the viscosity of the fluid is negligible. Thus, as kinetic energy cascades from the larger to the smaller scales, a large amount of kinetic energy is accumulated at the smallest scales due to the lack of dissipation. We have obtained the spectrum of the gravitational radiation emitted by the motion of the fluid finding that, if typical velocity and temperature fluctuations have an amplitude (Δv)/c≳10-2 and/or ΔT/Tc≳10-3, they would be detected by eLISA at frequencies larger than ˜10-4Hz.
Brodsky, Stanley J.; /SLAC
2007-07-06
I discuss a number of novel topics in QCD, including the use of the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. In particular, there is an exact correspondence between the fifth-dimension coordinate z of AdS space and a specific impact variable {zeta} which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. I also discuss a number of novel phenomenological features of QCD. Initial- and final-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and anomalous heavy quark effects. The presence of direct higher-twist processes where a proton is produced in the hard subprocess can explain the large proton-to-pion ratio seen in high centrality heavy ion collisions.
KOVCHEGOV,Y.V.
2000-04-25
The authors derive an equation determining the small-x evolution of the F{sub 2} structure function of a large nucleus which resumes a cascade of gluons in the leading logarithmic approximation using Mueller's color dipole model. In the traditional language it corresponds to resummation of the pomeron fan diagrams, originally conjectured in the GLR equation. The authors show that the solution of the equation describes the physics of structure functions at high partonic densities, thus allowing them to gain some understanding of the most interesting and challenging phenomena in small-x physics--saturation.
Lattice QCD for parallel computers
NASA Astrophysics Data System (ADS)
Quadling, Henley Sean
Lattice QCD is an important tool in the investigation of Quantum Chromodynamics (QCD). This is particularly true at lower energies where traditional perturbative techniques fail, and where other non-perturbative theoretical efforts are not entirely satisfactory. Important features of QCD such as confinement and the masses of the low lying hadronic states have been demonstrated and calculated in lattice QCD simulations. In calculations such as these, non-lattice techniques in QCD have failed. However, despite the incredible advances in computer technology, a full solution of lattice QCD may still be in the too-distant future. Much effort is being expended in the search for ways to reduce the computational burden so that an adequate solution of lattice QCD is possible in the near future. There has been considerable progress in recent years, especially in the research of improved lattice actions. In this thesis, a new approach to lattice QCD algorithms is introduced, which results in very significant efficiency improvements. The new approach is explained in detail, evaluated and verified by comparing physics results with current lattice QCD simulations. The new sub-lattice layout methodology has been specifically designed for current and future hardware. Together with concurrent research into improved lattice actions and more efficient numerical algorithms, the very significant efficiency improvements demonstrated in this thesis can play an important role in allowing lattice QCD researchers access to much more realistic simulations. The techniques presented in this thesis also allow ambitious QCD simulations to be performed on cheap clusters of commodity computers.
Radyushkin, Anatoly V.; Efremov, Anatoly Vasilievich; Ginzburg, Ilya F.
2013-04-01
We discuss some problems concerning the application of perturbative QCD to high energy soft processes. We show that summing the contributions of the lowest twist operators for non-singlet $t$-channel leads to a Regge-like amplitude. Singlet case is also discussed.
Brodsky, Stanley J.; Deshpande, Abhay L.; Gao, Haiyan; McKeown, Robert D.; Meyer, Curtis A.; Meziani, Zein-Eddine; Milner, Richard G.; Qiu, Jianwei; Richards, David G.; Roberts, Craig D.
2015-02-26
This White Paper presents the recommendations and scientific conclusions from the Town Meeting on QCD and Hadronic Physics that took place in the period 13-15 September 2014 at Temple University as part of the NSAC 2014 Long Range Planning process. The meeting was held in coordination with the Town Meeting on Phases of QCD and included a full day of joint plenary sessions of the two meetings. The goals of the meeting were to report and highlight progress in hadron physics in the seven years since the 2007 Long Range Plan (LRP07), and present a vision for the future by identifying the key questions and plausible paths to solutions which should define the next decade. The introductory summary details the recommendations and their supporting rationales, as determined at the Town Meeting on QCD and Hadron Physics, and the endorsements that were voted upon. The larger document is organized as follows. Section 2 highlights major progress since the 2007 LRP. It is followed, in Section 3, by a brief overview of the physics program planned for the immediate future. Finally, Section 4 provides an overview of the physics motivations and goals associated with the next QCD frontier: the Electron-Ion-Collider.
Andreas S. Kronfeld
2002-09-30
After reviewing some of the mathematical foundations and numerical difficulties facing lattice QCD, I review the status of several calculations relevant to experimental high-energy physics. The topics considered are moments of structure functions, which may prove relevant to search for new phenomena at the LHC, and several aspects of flavor physics, which are relevant to understanding CP and flavor violation.
Lincoln, Don
2016-06-28
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.
Devlin, T.; CDF Collaboration
1996-10-01
The CDF collaboration is engaged in a broad program of QCD measurements at the Fermilab Tevatron Collider. I will discuss inclusive jet production at center-of-mass energies of 1800 GeV and 630 GeV, properties of events with very high total transverse energy and dijet angular distributions.
Plunkett, R.; The CDF Collaboration
1991-10-01
Results are presented for hadronic jet and direct photon production at {radical}{bar s} = 1800 GeV. The data are compared with next-to-leading QCD calculations. A new limit on the scale of possible composite structure of the quarks is also reported. 12 refs., 4 figs.
Nathan Isgur
1997-03-01
The author presents an idiosyncratic view of baryons which calls for a marriage between quark-based and hadronic models of QCD. He advocates a treatment based on valence quark plus glue dominance of hadron structure, with the sea of q pairs (in the form of virtual hadron pairs) as important corrections.
On the possible role of zonal dynamics in the formation and evolution of F3 layers over equator
NASA Astrophysics Data System (ADS)
Mridula, N.; Pant, Tarun Kumar
2015-11-01
In the present study, occurrences of F3 layer over Thiruvananthapuram (8.5°N; 77°E; dip latitude ~0.5°N), a dip equatorial station in India have been investigated using ionosonde data for the years 2004-2007. The F3 layers appearing in the ionograms during the pre noon hours only have been included in the analysis. The result indicates that a weak EIA resulting in low ionospheric height and high ionization density prevails before the occurrence of F3 layer and serves as an essential condition for its occurrence. The relative Slant Total Electron Content (rSTEC) measured using collocated ground based coherent low earth orbiting (LEO) radio beacon receiver has also been used along with electron densities measured by CHAMP satellite for the year 2006 and 2007 to illustrate this difference in the evolution of Equatorial Ionization Anomaly (EIA) on F3 and non F3 days. A new mechanism for F3 generation has been proposed. It has been shown that the coupling of the thermospheric zonal wind jet over equator and enhanced ionospheric density at lower heights over Indian longitude can account for the generation of F3 layer through ion-drag. The vertical wind associated with the thermospheric heating resulting from ion-drag causes the generation of an additional eastward field which, along with the prevailing F-region electric field, leads to the upward excursion of the F3 layer.
Venturi, D.; Karniadakis, G.E.
2012-08-30
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.
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-spin 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 LHC
AdS/QCD and Light Front Holography: A New Approximation to QCD
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 the 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.
QCD with many fermions and QCD topology
NASA Astrophysics Data System (ADS)
Shuryak, Edward
2013-04-01
Major nonperturbative phenomena in QCD - confinement and chiral symmetry breaking - are known to be related with certain topological objects. Recent lattice advances into the domain of many Nf = O(10) fermion flavors have shown that both phase transitions had shifted in this case to much stronger coupling. We discuss confinement in terms of monopole Bose condensation, and discuss how it is affected by fermions "riding" on the monopoles, ending with the Nf dependence of the critical line. Chiral symmetry breaking is discussed in terms of the (anti)selfdual dyons, the instanton constituents. The fermionic zero modes of those have a different meaning and lead to strong interaction between dyons and antidyons. We report some qualitative consequences of this theory and also some information about our first direct numerical study of the dyonic ensemble, in respect to both chiral symmetry breaking and confinement (via back reaction to the holonomy potential).
NASA Technical Reports Server (NTRS)
Emukashvily, I. M.
1982-01-01
An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.
Small-x evolution of structure functions in the next-to-leading order
Giovanni A. Chirilli
2010-01-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In QCD the NLO kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the "composite dipole operator", and the resulting Mobius invariant kernel for this operator agrees with the forward NLO BFKL calculation.
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.
NASA Astrophysics Data System (ADS)
Dudek, Jozef J.
2016-03-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study ππ elastic scattering, including the ρ resonance, as well as coupled-channel πK, ηK scattering. The very recent extension to the case where an external current acts is also presented, considering the reaction πγ* → ππ, from which the unstable ρ → πγ transition form factor is extracted. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Exponentially modified QCD coupling
Cvetic, Gorazd; Valenzuela, Cristian
2008-04-01
We present a specific class of models for an infrared-finite analytic QCD coupling, such that at large spacelike energy scales the coupling differs from the perturbative one by less than any inverse power of the energy scale. This condition is motivated by the Institute for Theoretical and Experimental Physics operator product expansion philosophy. Allowed by the ambiguity in the analytization of the perturbative coupling, the proposed class of couplings has three parameters. In the intermediate energy region, the proposed coupling has low loop-level and renormalization scheme dependence. The present modification of perturbative QCD must be considered as a phenomenological attempt, with the aim of enlarging the applicability range of the theory of the strong interactions at low energies.
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 numbers $N_{1/2^+},\\,N_{1/2^+},\\,N_{3/2^+},\\, N_{3/2^+},\\,N_{5/2^+},\\,$ 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.
Gupta, R.
1998-12-31
The goal of the lectures on lattice QCD (LQCD) is to provide an overview of both the technical issues and the progress made so far in obtaining phenomenologically useful numbers. The lectures consist of three parts. The author`s charter is to provide an introduction to LQCD and outline the scope of LQCD calculations. In the second set of lectures, Guido Martinelli will discuss the progress they have made so far in obtaining results, and their impact on Standard Model phenomenology. Finally, Martin Luescher will discuss the topical subjects of chiral symmetry, improved formulation of lattice QCD, and the impact these improvements will have on the quality of results expected from the next generation of simulations.
Kovacs, E.; CDF Collaboration
1996-02-01
We present results for the inclusive jet cross section and the dijet mass distribution. The inclusive cross section and dijet mass both exhibit significant deviations from the predictions of NLO QCD for jets with E{sub T}>200 GeV, or dijet masses > 400 GeV/c{sup 2}. We show that it is possible, within a global QCD analysis that includes the CDF inclusive jet data, to modify the gluon distribution at high x. The resulting increase in the jet cross-section predictions is 25-35%. Owing to the presence of k{sub T} smearing effects, the direct photon data does not provide as strong a constraint on the gluon distribution as previously thought. A comparison of the CDF and UA2 jet data, which have a common range in x, is plagued by theoretical and experimental uncertainties, and cannot at present confirm the CDF excess or the modified gluon distribution.
NASA Astrophysics Data System (ADS)
Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene
2016-05-01
In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be approximated over a physically relevant timespan by solutions of the Nonlinear Schrödinger equation.
Bjorken, J.D.
1996-10-01
New directions for exploring QCD at future high-energy colliders are sketched. These include jets within jets. BFKL dynamics, soft and hard diffraction, searches for disoriented chiral condensate, and doing a better job on minimum bias physics. The new experimental opportunities include electron-ion collisions at HERA, a new collider detector at the C0 region of the TeVatron, and the FELIX initiative at the LHC.
Kronfeld, A.S.; Allison, I.F.; Aubin, C.; Bernard, C.; Davies, C.T.H.; DeTar, C.; Di Pierro, M.; Freeland, E.D.; Gottlieb, Steven; Gray, A.; Gregor, E.; Heller, U.M.; Hetrick, J.E.; El-Khadra, Aida X.; Levkova, L.; Mackenzie, P.B.; Maresca, F.; Menscher, D.; Nobes, M.; Okamoto, M.; Oktay, M.B.; /Fermilab /Glasgow U. /Columbia U. /Washington U., St. Louis /Utah U. /DePaul U. /Art Inst. of Chicago /Indiana U. /Ohio State U. /Arizona U. /APS, New York /U. Pacific, Stockton /Illinois U., Urbana /Cornell U., LEPP /Simon Fraser U. /UC, Santa Barbara
2005-09-01
In the past year, we calculated with lattice QCD three quantities that were unknown or poorly known. They are the q{sup 2} dependence of the form factor in semileptonic D {yields} K/{nu} decay, the decay constant of the D meson, and the mass of the B{sub c} meson. In this talk, we summarize these calculations, with emphasis on their (subsequent) confirmation by experiments.
Giannetti, P. )
1991-05-01
Recent analysis of jet data taken at the Fermilab Tevatron Collider at {radical}S = 1.8 Tev are presented. Inclusive jet, dijet, trijet and direct photon measurements are compared to QCD parton level calculations, at orders {alpha}{sub s}{sup 3} or {alpha}{sub s}{sup 2}. The large total transverse energy events are well described by the Herwig shower Montecarlo. 19 refs., 20 figs., 1 tab.
Polyakov loop, hadron resonance gas model and thermodynamics of QCD
Megías, E.; Arriola, E. Ruiz; Salcedo, L. L.
2014-11-11
We summarize recent results on the hadron resonance gas description of QCD. In particular, we apply this approach to describe the equation of state and the vacuum expectation value of the Polyakov loop in several representations. Ambiguities related to exactly which states should be included are discussed.
Hadronic Resonances from Lattice QCD
Lichtl, Adam C.; Bulava, John; Morningstar, Colin; Edwards, Robert; Mathur, Nilmani; Richards, David; Fleming, George; Juge, K. Jimmy; Wallace, Stephen J.
2007-10-26
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.
Hadronic Resonances from Lattice QCD
John Bulava; Robert Edwards; George Fleming; K. Jimmy Juge; Adam C. Lichtl; Nilmani Mathur; Colin Morningstar; David Richards; Stephen J. Wallace
2007-06-16
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.
Chiral and deconfining phase transitions from holographic QCD study
NASA Astrophysics Data System (ADS)
Fang, Zhen; He, Song; Li, Danning
2016-06-01
A preliminary quantitative study to match the lattice QCD simulation on the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field ϕ and metric warp factor Ae and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those background solutions. We find that the results are in good agreement with the two-flavor lattice results. All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which are consistent with the current understanding on the QCD phase transitions with physical quark mass. Furthermore, the extracted transition temperatures are comparable with the two-flavor lattice QCD results.
Gravitational waves from the cosmological QCD transition
NASA Astrophysics Data System (ADS)
Mourão Roque, V. R. C.; Roque, G. Lugones o.; Lugones, G.
2014-09-01
We determine the minimum fluctuations in the cosmological QCD phase transition that could be detectable by the eLISA/NGO gravitational wave observatory. To this end, we performed several hydrodynamical simulations using a state-of-the-art equation of state derived from lattice QCD simulations. Based on the fact that the viscosity per entropy density of the quark gluon plasma obtained from heavy-ion collision experiments at the RHIC and the LHC is extremely small, we considered a non-viscous fluid in our simulations. Several previous works about this transition considered a first order transition that generates turbulence which follows a Kolmogorov power law. We show that for the QCD crossover transition the turbulent spectrum must be very different because there is no viscosity and no source of continuous energy injection. As a consequence, a large amount of kinetic energy accumulates at the smallest scales. From the hydrodynamic simulations, we have obtained the spectrum of the gravitational radiation emitted by the motion of the fluid, finding that, if typical velocity and temperature fluctuations have an amplitude Δ v /c ≳ 10-2 and/or Δ T/T_c ≳ 10-3, they would be detected by eLISA/NGO at frequencies larger than ˜ 10-4 Hz.
Resource Letter QCD-1: Quantum chromodynamics
NASA Astrophysics Data System (ADS)
Kronfeld, Andreas S.; Quigg, Chris
2010-11-01
This Resource Letter provides a guide to the literature on quantum chromodynamics (QCD), the relativistic quantum field theory of the strong interactions. Journal articles, books, and other documents are cited for the following topics: Quarks and color, the parton model, Yang-Mills theory, experimental evidence for color, QCD as a color gauge theory, asymptotic freedom, QCD for heavy hadrons, QCD on the lattice, the QCD vacuum, pictures of quark confinement, early and modern applications of perturbative QCD, the determination of the strong coupling and quark masses, QCD and the hadron spectrum, hadron decays, the quark-gluon plasma, the strong nuclear interaction, and QCD's role in nuclear physics.
NLO evolution of color dipoles in N=4 SYM
Chirilli, Giovanni A.; Balitsky, Ian
2009-07-04
Here, high-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformalmore » $${\\cal N}$$=4 SYM theory. We define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance.« less
NLO evolution of color dipoles in N=4 SYM
Balitsky, Ian; Chirilli, Giovanni
2009-01-01
High-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal ${\\cal N}$=4 SYM theory. We define the ``composite dipole operator' with the rapidity cutoff preserving conformal invariance. The resulting M\\"obius invariant kernel agrees with the forward NLO BFKL calculation of Ref. 1
Multi-meson systems in lattice QCD / Many-body QCD
Detmold, William
2013-08-31
Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections
Light-Front Holographic QCD and the Confinement Potential
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter
2014-06-01
Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time τ = t + z / c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. In fact, the potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. We also show that the holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrödinger equation. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions of the LF equations of motion include a zero-mass pion in the chiral mq → 0 limit, and linear Regge trajectories M2 (n, L) ∝ n + L with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, and the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and
QCD dynamics in mesons at soft and hard scales
Nguyen, T.; Souchlas, N. A.; Tandy, P. C.
2010-07-27
Using a ladder-rainbow kernel previously established for the soft scale of light quark hadrons, we explore, within a Dyson-Schwinger approach, phenomena that mix soft and hard scales of QCD. The difference between vector and axial vector current correlators is examined to estimate the four quark chiral condensate and the leading distance scale for the onset of non-perturbative phenomena in QCD. The valence quark distributions, in the pion and kaon, defined in deep inelastic scattering, and measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
NASA Astrophysics Data System (ADS)
Bartels, Jochen
2006-06-01
I summarize the present status of the AGK cutting rules in perturbative QCD. Particular attention is given to the application of the AGK analysis to diffraction and multiple scattering in DIS at HERA and to pp collisions at the LHC. I also discuss the bootstrap conditions which appear in pQCD.
QCD: Questions, challenges, and dilemmas
Bjorken, J.
1996-11-01
An introduction to some outstanding issues in QCD is presented, with emphasis on work by Diakonov and co-workers on the influence of the instanton vacuum on low-energy QCD observables. This includes the calculation of input valence-parton distributions for deep-inelastic scattering. 35 refs., 3 figs.
QCD coupling constants and VDM
Erkol, G.; Ozpineci, A.; Zamiralov, V. S.
2012-10-23
QCD sum rules for coupling constants of vector mesons with baryons are constructed. The corresponding QCD sum rules for electric charges and magnetic moments are also derived and with the use of vector-meson-dominance model related to the coupling constants. The VDM role as the criterium of reciprocal validity of the sum rules is considered.
QCD Phase Diagram and the Constant Mass Approximation
NASA Astrophysics Data System (ADS)
Ahmad, A.; Ayala, A.; Bashir, A.; Gutiérrez, E.; Raya, A.
2015-11-01
Dynamical generation of quark masses in the infrared region of QCD plays an important role to understand the peculiar nature of the physics of hadrons. As it is known, the solution of QCD gap equation for the quark mass function is flat for low momentum, but smoothly evolves to the perturbative behavior at high momentum. In this work, we use an effective truncation of QCD gap equation valid up to 1 GeV, and implement it at finite temperature and chemical potential to understand the QCD phase diagram for chiral symmetry breaking-chiral symmetry restoration, and confinement-deconfinement phase transitions from the Schwinger-Dysin equations point of view. Our effective kernel contains a gluon dressing function with two light quark flavors Nf = 2, with current quark mass 0.0035 GeV. An effective coupling, adjusted to reproduce the behavior of the chiral condensate at finite T complements our truncation. We find the critical end point of the phase diagram located at the temperature TE = 0.1245 GeV and the baryonic chemical potential μEB = 0.211 GeV.
New advances in the hydrodynamic description of the QCD critical point in heavy-ion collisions
NASA Astrophysics Data System (ADS)
Nahrgang, Marlene
2013-04-01
Hydrodynamics has been very successful in explaining a variety of data from heavy-ion collision experiments. An essential ingredient is the equation of state, which allows for the study of the impact of different descriptions of the QCD medium and of the phase transition on the evolution of the bulk matter. At the critical point the correlation length of fluctuations of the order parameter diverges in thermodynamic systems. At the same time the relaxation times become infinite at the critical point, which in dynamic systems weakens critical phenomena. In order to provide solid predictions for event-by-event fluctuations of observables extensions of previous studies to dynamic systems are crucial to guide the search for the discovery of the critical point in heavy-ion collision experiments, like the beam energy scan at RHIC, BNL. A hydrodynamic description of the expanding matter, which takes further restrictions of the system like its inhomogeneity and finite size into account, is especially suitable because the order parameter oscillates slowly at the critical point and can thus be described as a collective variable within a hydrodynamic setup. First models, which propagate the fluctuations of the order parameter explicitly by a coupling to a hydrodynamically expanding heat bath, are able to see dynamic effects like critical slowing down at the critical point and supercooling at the first order phase transition. Latest results show that for the first order phase transition this leads to the phenomenon of domain formation. At the critical point the enhancement of event-by-event fluctuations can be observed. These explicitly dynamic models are thus a promising approach to a realistic description of the QCD critical point in heavy-ion collisions. In this talk I will review recent advances in our understanding of the phase transition obtained within hydrodynamic models and outline possible approaches to future contributions to the search for the QCD critical point.
Sekhar Chivukula
2010-01-08
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level. Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter.
Sakai, Tadakatsu; Sugimoto, Shigeki
2005-12-02
We propose a holographic dual of QCD with massless flavors on the basis of a D4/D8-brane configuration within a probe approximation. We are led to a five-dimensional Yang-Mills theory on a curved space-time along with a Chern-Simons five-form on it, both of which provide us with a unifying framework to study the massless pion and an infinite number of massive vector mesons. We make sample computations of the physical quantities that involve the mesons and compare them with the experimental data. It is found that most of the results of this model are compatible with the experiments.
NASA Astrophysics Data System (ADS)
Sakai, Tadakatsu; Sugimoto, Shigeki
2005-12-01
We propose a holographic dual of QCD with massless flavors on the basis of a D4/D8-brane configuration within a probe approximation. We are led to a five-dimensional Yang-Mills theory on a curved space-time along with a Chern-Simons five-form on it, both of which provide us with a unifying framework to study the massless pion and an infinite number of massive vector mesons. We make sample computations of the physical quantities that involve the mesons and compare them with the experimental data. It is found that most of the results of this model are compatible with the experiments.
Cool QCD: Hadronic Physics and QCD in Nuclei
NASA Astrophysics Data System (ADS)
Cates, Gordon
2015-10-01
QCD is the only strongly-coupled theory given to us by Nature, and it gives rise to a host of striking phenomena. Two examples in hadronic physics include the dynamic generation of mass and the confinement of quarks. Indeed, the vast majority of the mass of visible matter is due to the kinetic and potential energy of the massless gluons and the essentially massless quarks. QCD also gives rise to the force that binds protons and neutrons into nuclei, including subtle effects that have historically been difficult to understand. Describing these phenomena in terms of QCD has represented a daunting task, but remarkable progress has been achieved in both theory and experiment. Both CEBAF at Jefferson Lab and RHIC at Brookhaven National Lab have provided unprecedented experimental tools for investigating QCD, and upgrades at both facilities promise even greater opportunities in the future. Also important are programs at FermiLab as well as the LHC at CERN. Looking further ahead, an electron ion collider (EIC) has the potential to answer whole new sets of questions regarding the role of gluons in nuclear matter, an issue that lies at the heart of the generation of mass. On the theoretical side, rapid progress in supercomputers is enabling stunning progress in Lattice QCD calculations, and approximate forms of QCD are also providing deep new physical insight. In this talk I will describe both recent advances in Cool QCD as well as the exciting scientific opportunities that exist for the future.
Soltz, R; Vranas, P; Blumrich, M; Chen, D; Gara, A; Giampap, M; Heidelberger, P; Salapura, V; Sexton, J; Bhanot, G
2007-04-11
The theory of the strong nuclear force, Quantum Chromodynamics (QCD), can be numerically simulated from first principles on massively-parallel supercomputers using the method of Lattice Gauge Theory. We describe the special programming requirements of lattice QCD (LQCD) as well as the optimal supercomputer hardware architectures that it suggests. We demonstrate these methods on the BlueGene massively-parallel supercomputer and argue that LQCD and the BlueGene architecture are a natural match. This can be traced to the simple fact that LQCD is a regular lattice discretization of space into lattice sites while the BlueGene supercomputer is a discretization of space into compute nodes, and that both are constrained by requirements of locality. This simple relation is both technologically important and theoretically intriguing. The main result of this paper is the speedup of LQCD using up to 131,072 CPUs on the largest BlueGene/L supercomputer. The speedup is perfect with sustained performance of about 20% of peak. This corresponds to a maximum of 70.5 sustained TFlop/s. At these speeds LQCD and BlueGene are poised to produce the next generation of strong interaction physics theoretical results.
Nonperturbative QCD Calculations
NASA Astrophysics Data System (ADS)
Dellby, Niklas
1995-01-01
The research described in this thesis is an exact transformation of the Yang-Mills quantum chromodynamics (QCD) Lagrangrian into a form that is suitable for nonperturbative calculations. The conventional Yang-Mills Lagrangian has proven to be an excellent basis for perturbative calculations, but in nonperturbative calculations it is difficult to separate gauge problems from physical properties. To mitigate this problem, I develop a new equivalent Lagrangian that is not only expressed completely in terms of the field strengths ofthe gauge field but is also manifestly Lorentz and gauge invariant. The new Lagrangian is quadratic in derivatives, with non-linear local couplings, thus it is ideally suited for a numerical calculation. The field-strength Lagrangian is of such a form that it is possible to do a straightforward numerical stationary path expansion and find the fundamental QCD properties. This thesis examines several approximations analytically, investigating different ways to utilize the new Lagrangian. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
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
None
2011-10-06
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.
QCD Factorization and PDFs from Lattice QCD Calculation
NASA Astrophysics Data System (ADS)
Ma, Yan-Qing; Qiu, Jian-Wei
2015-02-01
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.
Double Parton Fragmentation Function and its Evolution in Quarkonium Production
NASA Astrophysics Data System (ADS)
Kang, Zhong-Bo
2014-01-01
We summarize the results of a recent study on a new perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum pT at collider energies. Such a new factorization formalism includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the mQ2/p_T^2 expansion for heavy quark mass mQ. For the NLP contribution, the so-called double parton fragmentation functions are involved, whose evolution equations have been derived. We estimate fragmentation functions in the non-relativistic QCD formalism, and found that their contribution reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization, in contrast to the single parton fragmentation function. This might shed some light on the heavy quarkonium polarization puzzle.
Goldstone bosons and fermions in QCD
Zwanziger, Daniel
2010-06-15
We consider the version of QCD in Euclidean Landau gauge in which the restriction to the Gribov region is implemented by a local, renormalizable action. This action depends on the Gribov parameter {gamma}, with dimensions of (mass){sup 4}, whose value is fixed in terms of {Lambda}{sub QCD}, by the gap equation, known as the horizon condition, ({partial_derivative}{Gamma}/{partial_derivative}{gamma})=0, where {Gamma} is the quantum effective action. The restriction to the Gribov region suppresses gluons in the infrared, which nicely explains why gluons are not in the physical spectrum, but this only makes more mysterious the origin of the long-range force between quarks. In the present article we exhibit the symmetries of {Gamma}, and show that the solution to the gap equation, which defines the classical vacuum, spontaneously breaks some of the symmetries of {Gamma}. This implies the existence of massless Goldstone bosons and fermions that do not appear in the physical spectrum. Some of the Goldstone bosons may be exchanged between quarks, and are candidates for a long-range confining force. As an exact result we also find that in the infrared limit the gluon propagator vanishes like k{sup 2}.
QCD and Light-Front Holography
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2010-10-27
The soft-wall AdS/QCD model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics. The model predicts a zero-mass pion for zero-mass quarks and 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. Light-Front Holography maps the amplitudes which are functions of the fifth dimension variable z of anti-de Sitter space to a corresponding hadron theory quantized on the light front. The resulting Lorentz-invariant relativistic light-front wave equations are functions of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. The result is to a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryon light-quark bound states, which in turn predict the behavior of the pion and nucleon form factors. The theory implements chiral symmetry in a novel way: the effects of chiral symmetry breaking increase as one goes toward large interquark separation, consistent with spectroscopic data, and the 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. The soft-wall model also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function which agrees with the effective coupling {alpha}{sub g1} extracted from the Bjorken sum rule. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also reviewed.
NASA Astrophysics Data System (ADS)
Basarab-Horwath, P.; Güngör, F.; Özemir, C.
2013-11-01
We consider generalized KP-Burgers equations and attempt to identify subclasses admitting Virasoro or Kac-Moody type algebras as their symmetries. We give reductions to ODEs constructed from invariance requirement under these infinite-dimensional Lie symmetry algebras and integrate them in cases where it is possible. We also look at the conditions under which the equation passes the Painlevé test and construct some exact solutions by truncation.
NASA Astrophysics Data System (ADS)
Peter, Ulmschneider
When we are looking for intelligent life outside the Earth, there is a fundamental question: Assuming that life has formed on an extraterrestrial planet, will it also develop toward intelligence? As this is hotly debated, we will now describe the development of life on Earth in more detail in order to show that there are good reasons why evolution should culminate in intelligent beings.
Lattice QCD and Nuclear Physics
Konstantinos Orginos
2007-03-01
A steady stream of developments in Lattice QCD have made it possible today to begin to address the question of how nuclear physics emerges from the underlying theory of strong interactions. Central role in this understanding play both the effective field theory description of nuclear forces and the ability to perform accurate non-perturbative calculations in lo w energy QCD. Here I present some recent results that attempt to extract important low energy constants of the effective field theory of nuclear forces from lattice QCD.
Hadron physics in holographic QCD
NASA Astrophysics Data System (ADS)
Santra, A. B.; Lombardo, U.; Bonanno, A.
2012-07-01
Hadron physics deals with the study of strongly interacting subatomic particles such as neutrons, protons, pions and others, collectively known as baryons and mesons. Physics of strong interaction is difficult. There are several approaches to understand it. However, in the recent years, an approach called, holographic QCD, based on string theory (or gauge-gravity duality) is becoming popular providing an alternative description of strong interaction physics. In this article, we aim to discuss development of strong interaction physics through QCD and string theory, leading to holographic QCD.
NASA Astrophysics Data System (ADS)
Chen, Jinbing
2010-08-01
Each soliton equation in the Korteweg-de Vries (KdV) hierarchy, the 2+1 dimensional breaking soliton equation, and the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation are reduced to two or three Neumann systems on the tangent bundle TSN -1 of the unit sphere SN -1. The Lax-Moser matrix for the Neumann systems of degree N -1 is deduced in view of the Mckean-Trubowitz identity and a bilinear generating function, whose favorite characteristic accounts for the problem of the genus of Riemann surface matching to the number of elliptic variables. From the Lax-Moser matrix, the constrained Hamiltonians in the sense of Dirac-Poisson bracket for all the Neumann systems are written down in a uniform recursively determined by integrals of motion. The involution of integrals of motion and constrained Hamiltonians is completed on TSN -1 by using a Lax equation and their functional independence is displayed over a dense open subset of TSN -1 by a direct calculation, which contribute to the Liouville integrability of a family of Neumann systems in a new systematical way. We also construct the hyperelliptic curve of Riemann surface and the Abel map straightening out the restricted Neumann flows that naturally leads to the Jacobi inversion problem on the Jacobian with the aid of the holomorphic differentials, from which some finite-gap solutions expressed by Riemann theta functions for the 2+1 dimensional breaking soliton equation, the 2+1 dimensional CDGKS equation, the KdV, and the fifth-order KdV equations are presented by means of the Riemann theorem.
QCD Corrections and New Physics - Proceedings of the International Symposium
NASA Astrophysics Data System (ADS)
Kodaira, Jiro; Onogi, Tetsuya; Sasaki, Ken
1998-09-01
The Table of Contents for the full book PDF is as follows: * Preface * Opening Address * Top Quark Physics * Threshold Resummation of Soft Gluons in Hadronic Reactions - An Introduction * Recent Results from CDF * Top Quark Physics: Overview * Complete Description of Polarization Effects in Top Quark Decays Including Higher Order QCD Corrections * Top Pair Production in e+e- and γγ Processes * Structure Functions I * Highlights of Physics at HERA * Some Aspects of the BFKL Evolution * Structure Functions II * New Result from SMC on g_{1}^ρ * Studies of the Nucleon Spin Structure by HERMES * Recent Developments in Perturbative QCD: Q2 Evolution of Chiral-Odd Distributions h1(x,Q2) and hL(x,Q2) * The Small x Behavior of g1 in the Resummed Approach * Jet Physics * QCD Results from LEP1 and LEP2 * Twenty Years of Jet Physics : Old and New * Multi-Parton Loop Amplitudes and Next-to-Leading Order Jet Cross-Sections * Heavy Meson * PQCD Analysis of Inclusive Heavy Hadrons Decays * Strong Coupling Constant from Lattice QCD * Heavy-Light Decay Constant from Lattice NRQCD * Concluding Remarks * Program * Organizing Committee * List of Participants
NASA Technical Reports Server (NTRS)
Nakagawa, Y.
1981-01-01
The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.
NASA Astrophysics Data System (ADS)
Sarcevic, Ina; Tan, Chung-I.
2000-07-01
The Table of Contents for the full book PDF is as follows: * Preface * Monday morning session: Hadronic Final States - Conveners: E. de Wolf and J. W. Gary * Session Chairman: J. W. Gary * Inclusive Jets at the Tevatron * Forward Jets, Dijets, and Subjets at the Tevatron * Inclusive Hadron Production and Dijets at HERA * Recent Opal Results on Photon Structure and Interactions * Review of Two-Photon Physics at LEP * Session Chairman: E. de Wolf * An Intriguing Area-Law-Based Hadron Production Scheme in e+e- Annihilation and Its Possible Extensions * Hyperfine Splitting in Hadron Production at High Energies * Event Selection Effects on Multiplicities in Quark and Gluon Jets * Quark and Gluon Jet Properties at LEP * Rapidity Gaps in Quark and Gluon Jets -- A Perturbative Approach * Monday afternoon session: Diffractive and Small-x - Conveners: M. Derrick and A. White * Session Chairman: A. White * Structure Functions: Low x, High y, Low Q2 * The Next-to-Leading Dynamics of the BFKL Pomeron * Renormalization Group Improved BFKL Equation * Session Chairman: G. Briskin * New Experimental Results on Diffraction at HERA * Diffractive Parton Distributions in Light-Cone QCD * The Logarithmic Derivative of the F2 Structure Function and Saturation * Spin Dependence of Diffractive DIS * Monday evening session * Session Chairman: M. Braun * Tests of QCD with Particle Production at HERA: Review and Outlook * Double Parton Scattering and Hadron Structure in Transverse Space * The High Density Parton Dynamics from Eikonal and Dipole Pictures * Hints of Higher Twist Effects in the Slope of the Proton Structure Function * Tuesday morning session: Correlations and Fluctuations - Conveners: R. Hwa and M. Tannenbaum * Session Chairman: A. Giovannini -- Fluctuations and Correlations * Bose-Einstein Results from L3 * Short-Range and Long-Range Correlations in DIS at HERA * Coior Mutation Model, Intermittency, and Erraticity * QCD Queuing and Hadron Multiplicity * Soft and Semi
Olson, Gordon L.
2011-08-20
Highlights: {yields} An existing multigroup transport algorithm is extended to be second-order in time. {yields} A new algorithm is presented that does not require a grey acceleration solution. {yields} The two algorithms are tested with 2D, multi-material problems. {yields} The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P{sub 1} forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.
NASA Astrophysics Data System (ADS)
Kravtsov, Yury A.; Chrzanowski, Janusz; Bieg, Bohdan
2012-02-01
New technique is suggested in plasma polarimetry: Differential equations for angular parameters of polarization ellipse, characterizing the amplitude ratio and the phase difference between orthogonal components of the wave field. Equations for angular variables ‘amplitude ratio-phase difference’ are derived, which allow direct calculation of the parameters of polarization ellipse, omitting solutions for the Stokes vector. The simplest analytical solutions are presented for the pure Faraday and the pure Cotton-Mouton effects. Behavior of angular parameters in the homogeneous and inhomogeneous plasmas is illustrated by numerical modeling in conditions when the Faraday and Cotton-Mouton effects are large enough and comparable in strength.
Excited Baryons in Holographic QCD
de Teramond, Guy F.; Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins
2011-11-08
The light-front holographic QCD approach is used to describe baryon spectroscopy and the systematics of nucleon transition form factors. Baryon spectroscopy and the excitation dynamics of nucleon resonances encoded in the nucleon transition form factors can provide fundamental insight into the strong-coupling dynamics of QCD. The transition from the hard-scattering perturbative domain to the non-perturbative region is sensitive to the detailed dynamics of confined quarks and gluons. Computations of such phenomena from first principles in QCD are clearly very challenging. The most successful theoretical approach thus far has been to quantize QCD on discrete lattices in Euclidean space-time; however, dynamical observables in Minkowski space-time, such as the time-like hadronic form factors are not amenable to Euclidean numerical lattice computations.
QCD analogy for quantum gravity
NASA Astrophysics Data System (ADS)
Holdom, Bob; Ren, Jing
2016-06-01
Quadratic gravity presents us with a renormalizable, asymptotically free theory of quantum gravity. When its couplings grow strong at some scale, as in QCD, then this strong scale sets the Planck mass. QCD has a gluon that does not appear in the physical spectrum. Quadratic gravity has a spin-2 ghost that we conjecture does not appear in the physical spectrum. We discuss how the QCD analogy leads to this conjecture and to the possible emergence of general relativity. Certain aspects of the QCD path integral and its measure are also similar for quadratic gravity. With the addition of the Einstein-Hilbert term, quadratic gravity has a dimensionful parameter that seems to control a quantum phase transition and the size of a mass gap in the strong phase.
RECENT LATTICE RESULTS ON FINITE TEMPERATURE AND DENSITY QCD, PART 1.
KARSCH,F.
2007-07-09
We discuss recent progress made studies of bulk thermodynamics of strongly interacting matter through lattice simulations of QCD with an almost physical light and strange quark mass spectrum. We present results on the QCD equation of state at vanishing and non-vanishing quark chemical potential and show first results on baryon number and strangeness fluctuations, which might be measured in event-by-event fluctuations in low energy runs at RHIC as well as at FAIR.
NASA Astrophysics Data System (ADS)
Markov, Yu. A.; Markova, M. A.
2007-03-01
In general line with our first work [Yu.A. Markov, M.A. Markova, Nucl. Phys. A 770 (2006) 162] within the framework of semiclassical approximation a general theory for the scattering processes of soft (anti)quark excitations off hard thermal particles in hot QCD-medium is thoroughly considered. The dynamical equations describing evolution for the usual classical color charge Q(t) and Grassmann color charges θ(t),θ(t) of hard particle taking into account the soft fermion degree of freedom of the system are suggested. On the basis of these equations and the Blaizot-Iancu equations iterative procedure of calculation of effective currents and sources generating the scattering processes under consideration is defined and their form up to third order in powers of free soft quark field, soft gluon one, and initial values of the color charges of hard particle is explicitly calculated. With use of the generalized Tsytovich principle a connection between matrix elements of the scattering processes and the effective currents and sources is established. In the context of the effective theory suggested for soft and hard fermion excitations new mechanisms of energy losses of high-energy parton propagating through QCD-medium are considered.
Small-x evolution in the next-to-leading order
Giovanni Antonio Chirilli
2009-12-01
After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. The NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part. The QCD and kernel of the BK equation is presented.
Meson Electro-/Photo-Production from QCD
NASA Astrophysics Data System (ADS)
Briceño, Raúl A.
2016-07-01
Recent results of meson photo-production at the existing electron machines with polarized real photon beams and the measurement of polarization observables of the final state baryons have provided high precision data that led to the discovery of new excited nucleon and Δ states using multi-channel partial wave analyses procedures. The internal structure of several prominent excited states has been revealed employing meson electroproduction processes. On the theoretical front, lattice QCD is now predicting the baryon spectrum with very similar characteristics as the constituent quark model, and continuum QCD, such as is represented in the Dyson-Schwinger equations approach and in light front relativistic quark models, describes the non-perturbative behavior of resonance excitations at photon virtuality of Q^2 > 1.5 GeV^2 . In this talk I discuss the need to continue a vigorous program of nucleon spectroscopy and the study of the internal structure of excited states as a way to reveal the effective degrees of freedom underlying the excited states and their dependence on the distance scale probed.
NASA Astrophysics Data System (ADS)
Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan
2012-06-01
Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).
Nuclear chromodynamics: applications of QCD to relativistic multiquark systems
Brodsky, S.J.; Ji, C.R.
1984-07-01
We review the applications of quantum chromodynamics to nuclear multiquark systems. In particular, predictions are given for the deuteron reduced form factor in the high momentum transfer region, hidden color components in nuclear wavefunctions, and the short distance effective force between nucleons. A new antisymmetrization technique is presented which allows a basis for relativistic multiquark wavefunctions and solutions to their evolution to short distances. Areas in which conventional nuclear theory conflicts with QCD are also briefly reviewed. 48 references.
Light-Front Holography and Non-Perturbative QCD
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2009-12-09
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 the 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.
High-Energy QCD Asymptotics of Photon--Photon Collisions
Brodsky, Stanley J.
2002-07-26
The high-energy behavior of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order (NLO) in QCD, is discussed. The NLO BFKL predictions, improved by the BLM optimal scale setting, are in good agreement with recent OPAL and L3 data at CERN LEP2. NLO BFKL predictions for future linear colliders are presented.
Renormalization in Coulomb-gauge QCD within the Lagrangian formalism
Niegawa, A.
2006-08-15
We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)
QCD measurements at the Tevatron
Bandurin, Dmitry; /Florida State U.
2011-12-01
Selected quantum chromodynamics (QCD) measurements performed at the Fermilab Run II Tevatron p{bar p} collider running at {radical}s = 1.96 TeV by CDF and D0 Collaborations are presented. The inclusive jet, dijet production and three-jet cross section measurements are used to test perturbative QCD calculations, constrain parton distribution function (PDF) determinations, and extract a precise value of the strong coupling constant, {alpha}{sub s}(m{sub Z}) = 0.1161{sub -0.0048}{sup +0.0041}. Inclusive photon production cross-section measurements reveal an inability of next-to-leading-order (NLO) perturbative QCD (pQCD) calculations to describe low-energy photons arising directly in the hard scatter. The diphoton production cross-sections check the validity of the NLO pQCD predictions, soft-gluon resummation methods implemented in theoretical calculations, and contributions from the parton-to-photon fragmentation diagrams. Events with W/Z+jets productions are used to measure many kinematic distributions allowing extensive tests and tunes of predictions from pQCD NLO and Monte-Carlo (MC) event generators. The charged-particle transverse momenta (p{sub T}) and multiplicity distributions in the inclusive minimum bias events are used to tune non-perturbative QCD models, including those describing the multiple parton interactions (MPI). Events with inclusive production of {gamma} and 2 or 3 jets are used to study increasingly important MPI phenomenon at high p{sub T}, measure an effective interaction cross section, {sigma}{sub eff} = 16.4 {+-} 2.3 mb, and limit existing MPI models.
Andersen, Jens O.; Leganger, Lars E.; Strickland, Michael; Su, Nan
2011-10-15
In this brief report we compare the predictions of a recent next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt) calculation of the QCD trace anomaly to available lattice data. We focus on the trace anomaly scaled by T{sup 2} in two cases: N{sub f}=0 and N{sub f}=3. When using the canonical value of {mu}=2{pi}T for the renormalization scale, we find that for Yang-Mills theory (N{sub f}=0) agreement between HTLpt and lattice data for the T{sup 2}-scaled trace anomaly begins at temperatures on the order of 8T{sub c}, while treating the subtracted piece as an interaction term when including quarks (N{sub f}=3) agreement begins already at temperatures above 2T{sub c}. In both cases we find that at very high temperatures the T{sup 2}-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.
LATTICE QCD AT FINITE TEMPERATURE AND DENSITY.
BLUM,T.; CREUTZ,M.; PETRECZKY,P.
2004-02-24
With the operation of the RHIC heavy ion program, the theoretical understanding of QCD at finite temperature and density has become increasingly important. Though QCD at finite temperature has been extensively studied using lattice Monte-Carlo simulations over the past twenty years, most physical questions relevant for RHIC (and future) heavy ion experiments remain open. In lattice QCD at finite temperature and density there have been at least two major advances in recent years. First, for the first time calculations of real time quantities, like meson spectral functions have become available. Second, the lattice study of the QCD phase diagram and equation of state have been extended to finite baryon density by several groups. Both issues were extensively discussed in the course of the workshop. A real highlight was the study of the QCD phase diagram in (T, {mu})-plane by Z. Fodor and S. Katz and the determination of the critical end-point for the physical value of the pion mass. This was the first time such lattice calculations at, the physical pion mass have been performed. Results by Z Fodor and S. Katz were obtained using a multi-parameter re-weighting method. Other determinations of the critical end point were also presented, in particular using a Taylor expansion around {mu} = 0 (Bielefeld group, Ejiri et al.) and using analytic continuation from imaginary chemical potential (Ph. de Forcrand and O. Philipsen). The result based on Taylor expansion agrees within errors with the new prediction of Z. Fodor and S. Katz, while methods based on analytic continuation still predict a higher value for the critical baryon density. Most of the thermodynamics studies in full QCD (including those presented at this workshop) have been performed using quite coarse lattices, a = 0.2-0.3 fm. Therefore one may worry about cutoff effects in different thermodynamic quantities, like the transition temperature T{sub tr}. At the workshop U. Heller presented a study of the transition
Recent QCD results from the Tevatron
Pickarz, Henryk; CDF and DO collaboration
1997-02-01
Recent QCD results from the CDF and D0 detectors at the Tevatron proton-antiproton collider are presented. An outlook for future QCD tests at the Tevatron collider is also breifly discussed. 27 refs., 11 figs.
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.
Light-Front Holography and Novel Effects in QCD
Brodsky, Stanley J.; Teramond, Guy F. de
2009-04-20
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. 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, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate z with an invariant light-front coordinate {zeta} which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The mapping of electromagnetic and gravitational form factors in AdS space to their corresponding expressions in light-front theory confirms this correspondence. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. The distinction between static structure functions such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical structure functions which include the effects of rescattering is emphasized. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.
Light-Front Holography and Novel Effects in QCD
Brodsky, Stanley J.; de Teramond, Guy F.
2008-12-18
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. 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, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate z with an invariant light-front coordinate {zeta} which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The mapping of electromagnetic and gravitational form factors in AdS space to their corresponding expressions in light-front theory confirms this correspondence. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. The distinction between static structure functions such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical structure functions which include the effects of rescattering is emphasized. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.
Small-x Evolution in the Next-to-Leading Order
Ian Balitsky
2009-10-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear BK equation. The NLO corrections define the scale of the running-coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N=4 SYM theory, then we define the 'composite dipole operator' with the rapidity cutoff preserving conformal invariance, and the resulting Möbius invariant kernel for this operator agrees with the forward NLO BFKL calculation.
General QED/QCD aspects of simple systems
Telegdi, V.L.; Brodsky, S.J.
1989-09-01
This paper discusses the following topics: renormalization theory; the Kinoshita-Lee-Nauenberg theorem; the Yennie-Frautschi-Suura relation; scale invariance at large momentum transfer; scaling and scaling violation at large momentum transfers; low-energy theorem in Compton scattering; does the perturbation series in QED converge; renormalization of the weak angle /Theta//sub w/; the Nambu-Bethe-Salpeter (NBS) equation; the decay rate of /sup 3/S, positronium; radiative corrections to QCD Born cross section; and progress on the relativistic 2-body equation.
J.J. Sakurai Prize for Theoretical Particle Physics: 40 Years of Lattice QCD
NASA Astrophysics Data System (ADS)
Lepage, Peter
2016-03-01
Lattice QCD was invented in 1973-74 by Ken Wilson, who passed away in 2013. This talk will describe the evolution of lattice QCD through the past 40 years with particular emphasis on its first years, and on the past decade, when lattice QCD simulations finally came of age. Thanks to theoretical breakthroughs in the late 1990s and early 2000s, lattice QCD simulations now produce the most accurate theoretical calculations in the history of strong-interaction physics. They play an essential role in high-precision experimental studies of physics within and beyond the Standard Model of Particle Physics. The talk will include a non-technical review of the conceptual ideas behind this revolutionary development in (highly) nonlinear quantum physics, together with a survey of its current impact on theoretical and experimental particle physics, and prospects for the future. Work supported by the National Science Foundation.
Vacuum Energy, EoS, and the Gluon Condensate at Finite Baryon Density in QCD
Zhitnitsky, Ariel R.
2007-02-27
The Equation of States (EoS) plays the crucial role in all studies of neutron star properties. Still, a microscopical understanding of EoS remains largely an unresolved problem. We use 2-color QCD as a model to study the dependence of vacuum energy (gluon condensate in QCD) as function of chemical potential {mu} << {lambda}QCD where we find very strong and unexpected dependence on {mu}. We present the arguments suggesting that similar behavior may occur in 3-color QCD in the color superconducting phases. Such a study may be of importance for analysis of EoS when phenomenologically relevant parameters (within such models as MIT Bag model or NJL model) are fixed at zero density while the region of study lies at much higher densities not available for terrestrial tests.
The supercritical pomeron in QCD.
White, A. R.
1998-06-29
Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This talk outlines a derivation of a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ''wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a super-critical phase of Reggeon Field Theory.
QCD inequalities for hadron interactions.
Detmold, William
2015-06-01
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}. PMID:26196617
Yun, J.C.
1990-10-10
In this paper we report recent QCD analysis with the new data taken from CDF detector. CDF recorded an integrated luminosity of 4.4 nb{sup {minus}1} during the 1988--1989 run at center of mass system (CMS) energy of 1.8 TeV. The major topics of this report are inclusive jet, dijet, trijet and direct photon analysis. These measurements are compared of QCD predictions. For the inclusive jet an dijet analysis, tests of quark compositeness are emphasized. 11 refs., 6 figs.
QCD corrections to triboson production
NASA Astrophysics Data System (ADS)
Lazopoulos, Achilleas; Melnikov, Kirill; Petriello, Frank
2007-07-01
We present a computation of the next-to-leading order QCD corrections to the production of three Z bosons at the Large Hadron Collider. We calculate these corrections using a completely numerical method that combines sector decomposition to extract infrared singularities with contour deformation of the Feynman parameter integrals to avoid internal loop thresholds. The NLO QCD corrections to pp→ZZZ are approximately 50% and are badly underestimated by the leading order scale dependence. However, the kinematic dependence of the corrections is minimal in phase space regions accessible at leading order.
Lattice QCD clusters at Fermilab
Holmgren, D.; Mackenzie, Paul B.; Singh, Anitoj; Simone, Jim; /Fermilab
2004-12-01
As part of the DOE SciDAC ''National Infrastructure for Lattice Gauge Computing'' project, Fermilab builds and operates production clusters for lattice QCD simulations. This paper will describe these clusters. The design of lattice QCD clusters requires careful attention to balancing memory bandwidth, floating point throughput, and network performance. We will discuss our investigations of various commodity processors, including Pentium 4E, Xeon, Opteron, and PPC970. We will also discuss our early experiences with the emerging Infiniband and PCI Express architectures. Finally, we will present our predictions and plans for future clusters.
Glueball decay in holographic QCD
Hashimoto, Koji; Tan, C.-I; Terashima, Seiji
2008-04-15
Using holographic QCD based on D4-branes and D8-anti-D8-branes, we have computed couplings of glueballs to light mesons. We describe glueball decay by explicitly calculating its decay widths and branching ratios. Interestingly, while glueballs remain less well understood both theoretically and experimentally, our results are found to be consistent with the experimental data for the scalar glueball candidate f{sub 0}(1500). More generally, holographic QCD predicts that decay of any glueball to 4{pi}{sup 0} is suppressed, and that mixing of the lightest glueball with qq mesons is small.
QCD: Challenges for the future
Burrows, P.; Dawson, S.; Orr, L.; Smith, W.H.
1997-01-13
Despite many experimental verifications of the correctness of our basic understanding of QCD, there remain numerous open questions in strong interaction physics and we focus on the role of future colliders in addressing these questions. We discuss possible advances in the measurement of {alpha}{sub s}, in the study of parton distribution functions, and in the understanding of low x physics at present colliders and potential new facilities. We also touch briefly on the role of spin physics in advancing our understanding of QCD.
Nucleon Structure from Lattice QCD
David Richards
2007-09-05
Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distributions (GPDs). In particular, I show how lattice studies of GPDs contribute to building a three-dimensional picture of the proton, I conclude by describing the prospects for studying the structure of resonances from lattice QCD.
Michael Pennington
2011-05-01
The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.
Pennington, M. R.
2011-05-23
The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.
NASA Astrophysics Data System (ADS)
Boz, Tamer; Giudice, Pietro; Hands, Simon; Skullerud, Jon-Ivar; Williams, Anthony G.
2016-01-01
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.
Color Glass Condensate in Schwinger–Keldysh QCD
Jeon, Sangyong
2014-01-15
Within the Schwinger–Keldysh representation of many-body QCD, it is shown that the leading quantum corrections to the strong classical color field are “classical” in the sense that the fluctuation field still obeys the classical Jacobi-field equation, while the quantum effects solely reside in the fluctuations of the initial field configurations. Within this context, a systematic derivation of the JIMWLK renormalization group equation is presented. A clear identification of the correct form of gauge transformation rules and the correct form of the matter-field Lagrangian in the Schwinger–Keldysh QCD is also presented. -- Highlights: •Application of the Schwinger–Keldysh formalism to many-body QCD. •Clean separation of classical and quantum degrees of freedom. •Identification of the correct coupling between the gluon field and the color source. •Identification of the correct gauge transformation rules. •Sources of the classicality and quantum corrections to JIMWLK clarified.
Renormalization in Coulomb gauge QCD
NASA Astrophysics Data System (ADS)
Andraši, A.; Taylor, John C.
2011-04-01
In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.
QCD Phase Transitions, Volume 15
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 theorists 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.
Lattice QCD in Background Fields
William Detmold, Brian Tiburzi, Andre Walker-Loud
2009-06-01
Electromagnetic properties of hadrons can be computed by lattice simulations of QCD in background fields. We demonstrate new techniques for the investigation of charged hadron properties in electric fields. Our current calculations employ large electric fields, motivating us to analyze chiral dynamics in strong QED backgrounds, and subsequently uncover surprising non-perturbative effects present at finite volume.
Basics of QCD perturbation theory
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.
Experimenting with Langevin lattice QCD
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.
Seven topics in perturbative QCD
Buras, A.J.
1980-09-01
The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e/sup +/e/sup -/ annihilation, to photon structure functions and to quarkonia decays; (3) higher order corrections to fragmentation functions and to various semi-inclusive processes; (4) higher twist contributions; (5) exclusive processes; (6) transverse momentum effects; (7) jet and photon physics.
Axion cosmology, lattice QCD and the dilute instanton gas
NASA Astrophysics Data System (ADS)
Borsanyi, Sz.; Dierigl, M.; Fodor, Z.; Katz, S. D.; Mages, S. W.; Nogradi, D.; Redondo, J.; Ringwald, A.; Szabo, K. K.
2016-01-01
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ (T) of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ (T) in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Towards a Theoretical Understanding of the XYZ Mesons from QCD
NASA Astrophysics Data System (ADS)
Braaten, Eric
2016-03-01
The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark and antiquark. The list of XYZ mesons has grown to about two dozen over the last decade. A promising approach to understanding these mesons within QCD is the Born-Oppenheimer approximation, which reduces the problem to the solution of the Schrödinger equation in potentials that can be calculated using lattice QCD. The Born-Oppenheimer approximation has not yet revealed the pattern of the XYZ mesons, but it provides a compelling framework for understanding them from the fundamental theory.
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
QCD on the Light-Front. A Systematic Approach to Hadron Physics
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter
2014-06-01
Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable , which is conjugate to the invariant mass squared . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD
Geiger, K.; Longacre, R.; Srivastava, D.K.
1999-02-01
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme, as well as the development of hadron cascades after hadronization. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons, in position-space, momentum-space and color-space. The parton-evolution is described in terms of a space-time generalization of the familiar momentum-space description of multiple (semi)hard interactions in QCD, involving 2 {r_arrow} 2 parton collisions, 2 {r_arrow} 1 parton fusion processes, and 1 {r_arrow} 2 radiation processes. The formation of color-singlet pre-hadronic clusters and their decays into hadrons, on the other hand, is treated by using a spatial criterion motivated by confinement and a non-perturbative model for hadronization. Finally, the cascading of produced prehadronic clusters and of hadrons includes a multitude of 2 {r_arrow} n processes, and is modeled in parallel to the parton cascade description. This paper gives a brief review of the physics underlying VNI, as well as a detailed description of the program itself. The latter program description emphasizes easy-to-use pragmatism and explains how to use the program (including simple examples), annotates input and control parameters, and discusses output data provided by it.
anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models
NASA Astrophysics Data System (ADS)
Ayala, César; Cvetič, Gorazd
2016-02-01
We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2) ≡αs(Q2) / π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 δanQCD), and Massive Perturbation Theory (MPT). The index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran.
Dru Renner
2012-04-01
Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen precent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
Quark eigenmodes and lattice QCD
NASA Astrophysics Data System (ADS)
Liu, Guofeng
In this thesis, we study a number of topics in lattice QCD through the low-lying quark eigenmodes in the domain wall fermion (DWF) formulation in the quenched approximation. Specifically, we present results for the chiral condensate measured from these eigenmodes; we investigate the QCD vacuum structure by looking at the correlation between the magnitude of the chirality density, |psi†(x)gamma5psi( x)|, and the normal density, psi†( x)psi(x), for these states; we study the behavior of DWF formulation at large quark masses by investigating the mass dependence of the eigenvalues of the physical four dimensional-states as well as the bulk, five-dimensional states.
LATTICE QCD AT FINITE DENSITY.
SCHMIDT, C.
2006-07-23
I discuss different approaches to finite density lattice QCD. In particular, I focus on the structure of the phase diagram and discuss attempts to determine the location of the critical end-point. Recent results on the transition line as function of the chemical potential (T{sub c}({mu}{sub q})) are reviewed. Along the transition line, hadronic fluctuations have been calculated; which can be used to characterize properties of the Quark Gluon plasma and eventually can also help to identify the location of the critical end-point in the QCD phase diagram on the lattice and in heavy ion experiments. Furthermore, I comment on the structure of the phase diagram at large {mu}{sub q}.
Innovations in Lattice QCD Algorithms
Konstantinos Orginos
2006-06-25
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today.
Sudakov safety in perturbative QCD
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Marzani, Simone; Thaler, Jesse
2015-06-01
Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling αs. Observables that are calculable in this way are known as "safe." Recently, a class of unsafe observables was discovered that do not have a valid αs expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each αs order are regulated by an all-orders Sudakov form factor. In this paper, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of αs.
Heavy quarkonium production at collider energies: Factorization and evolution
NASA Astrophysics Data System (ADS)
Kang, Zhong-Bo; Ma, Yan-Qing; Qiu, Jian-Wei; Sterman, George
2014-08-01
We present a perturbative QCD factorization formalism for inclusive production of heavy quarkonia of large transverse momentum, pT at collider energies, including both leading power (LP) and next-to-leading power (NLP) behavior in pT. We demonstrate that both LP and NLP contributions can be factorized in terms of perturbatively calculable short-distance partonic coefficient functions and universal nonperturbative fragmentation functions, and derive the evolution equations that are implied by the factorization. We identify projection operators for all channels of the factorized LP and NLP infrared safe short-distance partonic hard parts, and corresponding operator definitions of fragmentation functions. For the NLP, we focus on the contributions involving the production of a heavy quark pair, a necessary condition for producing a heavy quarkonium. We evaluate the first nontrivial order of evolution kernels for all relevant fragmentation functions, and discuss the role of NLP contributions.
Huston, J. |; CDF Collaboration
1994-01-01
CDF has recently concluded a very successful 1992--93 data run in which an integrated luminosity of 21.3 pb {sup {minus}1} was written to tape. The large data sample allows for a greater discovery potential for new phenomena and for better statistical and systematic precision in analysis of conventional physics. This paper summarizes some of the new results from QCD analyses for this run.
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. PMID:27517766
DeGrand, T.
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
Effects of LatticeQCD EoS and Continuous Emission on Some Observables
Hama, Y.; Andrade, R.; Grassi, F.; Socolowski, O.; Kodama, T.; Tavares, B.; Padula, S. S.
2006-04-11
Effects of lattice-QCD-inspired equations of state and continuous emission on some observables are discussed, by solving a 3D hydrodynamics. The particle multiplicity as well {nu} 2 are found to increase in the mid-rapidity. We also discuss the effects of the initial-condition fluctuations.
NASA Astrophysics Data System (ADS)
Pelinovsky, Efim; Chaikovskaia, Natalya; Rodin, Artem
2015-04-01
The paper presents the analysis of the formation and evolution of shock wave in shallow water with no restrictions on its amplitude in the framework of the nonlinear shallow water equations. It is shown that in the case of large-amplitude waves appears a new nonlinear effect of reflection from the shock front of incident wave. These results are important for the assessment of coastal flooding by tsunami waves and storm surges. Very often the largest number of victims was observed on the coastline where the wave moved breaking. Many people, instead of running away, were just looking at the movement of the "raging wall" and lost time. This fact highlights the importance of researching the problem of security and optimal behavior of people in situations with increased risk. Usually there is uncertainty about the exact time, when rogue waves will impact. This fact limits the ability of people to adjust their behavior psychologically to the stressful situations. It concerns specialists, who are busy both in the field of flying activity and marine service as well as adults, young people and children, who live on the coastal zone. The rogue wave research is very important and it demands cooperation of different scientists - mathematicians and physicists, as well as sociologists and psychologists, because the final goal of efforts of all scientists is minimization of the harm, brought by rogue waves to humanity.
Thermal relaxation, electrical conductivity, and charge diffusion in a hot QCD medium
NASA Astrophysics Data System (ADS)
Mitra, Sukanya; Chandra, Vinod
2016-08-01
The response of electromagnetic (EM) fields that are produced in noncentral heavy-ion collisions to electromagnetically charged quark gluon plasma can be understood in terms of charge transport and charge diffusion in the hot QCD medium. This article presents a perspective on these processes by investigating the temperature behavior of the related transport coefficients, viz. electrical conductivity and the charge diffusion coefficients along with charge susceptibility. In the process of estimating them, thermal relaxation times for quarks and gluons have been determined first. These transport coefficients have been studied by solving the relativistic transport equation in the Chapman-Enskog method. For the analysis, 2 →2 , quark-quark, quark-gluon and gluon-gluon scattering processes are taken into account along with an effective description of hot QCD equations of state (EOSs) in terms of temperature dependent effective fugacities of quasiquarks (antiquarks) and quasigluons. Both improved perturbative hot QCD EOSs at high temperature and a lattice QCD EOS are included for the analysis. The hot QCD medium effects entering through the quasiparticle momentum distributions along with an effective coupling, are seen to have significant impact on the temperature behavior of these transport parameters along with the thermal relaxation times for the quasigluons and quasiquarks.
FermiQCD: A tool kit for parallel lattice QCD applications
Di Pierro, M.
2002-03-01
We present here the most recent version of FermiQCD, a collection of C++ classes, functions and parallel algorithms for lattice QCD, based on Matrix Distributed Processing. FermiQCD allows fast development of parallel lattice applications and includes some SSE2 optimizations for clusters of Pentium 4 PCs.
NASA Astrophysics Data System (ADS)
Niemi, H.; Eskola, K. J.; Paatelainen, R.
2016-02-01
We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading-order perturbative QCD using a saturation conjecture to control soft-particle production and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries against the LHC and RHIC measurements. We compare also the computed event-by-event probability distributions of relative fluctuations of elliptic flow and event-plane angle correlations with the experimental data from Pb +Pb collisions at the LHC. We show how such a systematic multienergy and multiobservable analysis tests the initial-state calculation and the applicability region of hydrodynamics and, in particular, how it constrains the temperature dependence of the shear viscosity-to-entropy ratio of QCD matter in its different phases in a remarkably consistent manner.
None
2011-10-06
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.
Transport Processes in High Temperature QCD Plasmas
NASA Astrophysics Data System (ADS)
Hong, Juhee
The transport properties of high temperature QCD plasmas can be described by kinetic theory based on the Boltzmann equation. At a leading-log approximation, the Boltzmann equation is reformulated as a Fokker-Planck equation. First, we compute the spectral densities of
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.
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.
Bulk viscosity of anisotropically expanding hot QCD plasma
Chandra, Vinod
2011-11-01
The bulk viscosity, {zeta} and its ratio with the shear viscosity, {zeta}/{eta} have been studied in an anisotropically expanding pure glue plasma in the presence of turbulent color fields. It has been shown that the anisotropy in the momentum distribution function of gluons, which has been determined from a linearized transport equation eventually leads to the bulk viscosity. For the isotropic (equilibrium) state, a recently proposed quasiparticle model of pure SU(3) lattice QCD equation of state has been employed where the interactions are encoded in the effective fugacity. It has been argued that the interactions present in the equation of state, significantly contribute to the bulk viscosity. Its ratio with the shear viscosity is significant even at 1.5T{sub c}. Thus, one needs to take in account the effects of the bulk viscosity while studying the hydrodynamic expansion of quark-gluon plasma in the Relativistic Heavy Ion Collider and the Large Hadron Collider.
Lattice QCD study of the Boer-Mulders effect in a pion
NASA Astrophysics Data System (ADS)
Engelhardt, M.; Hägler, P.; Musch, B.; Negele, J.; Schäfer, A.
2016-03-01
The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentum-dependent parton distribution functions (TMDs). This work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. The primary goal is to gain insight into the behavior of TMDs as a function of a Collins-Soper evolution parameter, ζ ^, which quantifies the rapidity difference between the hadron momentum and a vector describing the trajectory of the struck quark, e.g., in a semi-inclusive deep-inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass mπ=518 MeV , utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. Aided by the lower mass of the pion, compared to the nucleon studied previously, the present investigation of pion TMD observables constitutes an important step towards the quantitative study of the physically important regime of large relative rapidity where the dependence on ζ ^ appears to approach a limit. Although matching to perturbative evolution equations in ζ ^ is not yet available, extrapolations based on Ansätze containing inverse powers of ζ ^ yield stable results with an uncertainty as low as 20%, and both upper and lower bounds for the asymptotics are obtained. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is noted.
Transverse Momentum-Dependent Parton Distributions From Lattice QCD
Michael Engelhardt, Bernhard Musch, Philipp Haegler, Andreas Schaefer
2012-12-01
Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evolution parameter.
Quark-gluon vertex model and lattice-QCD data
Bhagwat, M.S.; Tandy, P.C.
2004-11-01
A model for the dressed-quark-gluon vertex, at zero gluon momentum, is formed from a nonperturbative extension of the two Feynman diagrams that contribute at one loop in perturbation theory. The required input is an existing ladder-rainbow model Bethe-Salpeter kernel from an approach based on the Dyson-Schwinger equations; no new parameters are introduced. The model includes an Ansatz for the triple-gluon vertex. Two of the three vertex amplitudes from the model provide a pointwise description of the recent quenched-lattice-QCD data. An estimate of the effects of quenching is made.
Indication of divergent baryon-number susceptibility in QCD matter
Antoniou, N. G.; Diakonos, F. K.; Kapoyannis, A. S.
2010-01-15
The baryon-number density formed in relativistic nuclear collisions versus the chemical potential of the freeze-out states is systematically studied on the basis of existing measurements. A remarkable power-law behavior of the baryon-number susceptibility is found at the CERN Super Proton Synchrotron, consistent with the existence of a QCD critical point at mu{sub B,c}approx =222 MeV, T{sub c}approx =155 MeV. The equation of state in different asymptotic regimes of the critical region is also examined and confronted with freeze-out states in these experiments.
Viscous quark-gluon plasma model through fluid QCD approach
Djun, T. P.; Soegijono, B.; Mart, T.; Handoko, L. T. E-mail: Laksana.tri.handoko@lipi.go.id
2014-09-25
A Lagrangian density for viscous quark-gluon plasma has been constructed within the fluid-like QCD framework. Gauge symmetry is preserved for all terms inside the Lagrangian, except for the viscous term. The transition mechanism from point particle field to fluid field, and vice versa, are discussed. The energy momentum tensor that is relevant to the gluonic plasma having the nature of fluid bulk of gluon sea is derived within the model. By imposing conservation law in the energy momentum tensor, shear viscosity appears as extractable from the equation.
Kurbel, Sven
2014-01-01
Based on avian and mammalian fossils found in the northeastern Chinese province of Liaoning and physiological traits linked to homeothermy, a hypothesis of evolution of homeothermic animals is proposed. It is based on the importance of muscle function in cold environment, as a strong selection pressure that favors endothermic metabolism during periods of cold climates. The presented hypothesis postulates that in progressively cooling environment, animals will develop thermal insulation, increased basal metabolism if food is available, and torpor when food is scarce. Since late Permian, Triassic and Cretaceous global temperatures were high, an exceptional place that gradually became cold was needed for the homeothermy evolution. South China Craton is here proposed as a plausible candidate for that role since it drifted across the Paleo-Tethys ocean, from equator to high northern latitudes in a journey that lasted from 250 to 200Myr ago. After this small continent collided with North China Craton some 200Myr ago, the already cold-adapted animals had spread to large, mostly empty spaces on the North China Craton, due to their evolutionary advantage of making active living in the cold environment. The most advantageous early homeothermic animals went further north to the cold Liaoning to start an oasis that delivered modern birds during next 50Myr. Modern mammals possibly evolved somewhere in the cold vicinity. This made Liaoning and similarly cold places the cradles of early birds and early mammals since for the following millions of years these places remained too cold for poikilotherms to enter and warm enough for homeotherms to dwell, until the Cretaceous-Paleogene extinction event and subsequent global cooling that diminished poikilotherms. Homeothermy was probably even more important as a survival advantage in cooler climates of Paleogene, when mammals and birds became dominant animals. This interpretation is probably supported by a recent report that a small
Charm quark energy loss in infinite QCD matter using a parton cascade model
NASA Astrophysics Data System (ADS)
Younus, Mohammed; Coleman-Smith, Christopher E.; Bass, Steffen A.; Srivastava, Dinesh K.
2015-02-01
We utilize the parton cascade model to study the evolution of charm quarks propagating through a thermal brick of QCD matter. We determine the energy loss and the transport coefficient q ̂ for charm quarks. The calculations are done at a constant temperature of 350 MeV and the results are compared to analytical calculations of heavy-quark energy loss in order to validate the applicability of using a parton cascade model for the study of heavy-quark dynamics in hot and dense QCD matter.
QCD tests in electron-positron scattering
Maruyama, T.
1995-11-01
Recent results on QCD tests at the Z{sup o} resonance are described. Measurements of Color factor ratios, and studies of final state photon radiation are performed by the LEP experiments. QCD tests using a longitudinally polarized beam are reported by the SLD experiment.
Lattice QCD and High Baryon Density State
Nagata, Keitaro; Nakamura, Atsushi; Motoki, Shinji; Nakagawa, Yoshiyuki; Saito, Takuya
2011-10-21
We report our recent studies on the finite density QCD obtained from lattice QCD simulation with clover-improved Wilson fermions of two flavor and RG-improved gauge action. We approach the subject from two paths, i.e., the imaginary and chemical potentials.
Quantum properties of QCD string fragmentation
NASA Astrophysics Data System (ADS)
Todorova-Nová, Šárka
2016-07-01
A simple quantization concept for a 3-dim QCD string is used to derive properties of QCD flux tube from the mass spectrum of light mesons and to predict observable quantum effects in correlations between adjacent hadrons. The quantized fragmentation model is presented and compared with experimental observations.
Solvable models and hidden symmetries in QCD
Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.; Lerma H., S.
2010-12-23
We show that QCD Hamiltonians at low energy exhibit an SU(2) structure, when only few orbital levels are considered. In case many orbital levels are taken into account we also find a semi-analytic solution for the energy levels of the dominant part of the QCD Hamiltonian. The findings are important to propose the structure of phenomenological models.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Ryttov, Thomas A.
2016-08-01
We suggest how to consistently calculate the anomalous dimension γ* of the ψ ¯ ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n +1 loop beta function and n loop anomalous dimension are known, then γ* can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O (Δfn) , where Δf=N¯ f-Nf , Nf is the number of flavors, and N¯f is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δf. We then compute γ* through O (Δf2) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ* is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ* through O (Δf3) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ* are observed for a large range of flavors.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors. PMID:27563948
QCD Collisional Energy Loss Reexamined
NASA Astrophysics Data System (ADS)
Peshier, A.
2006-11-01
It is shown that at a large temperature and E→∞ the QCD collisional energy loss reads dE/dx˜α(mD2)T2. Compared to previous approaches, which led to dEB/dx˜α2T2ln(ET/mD2) similar to the Bethe-Bloch formula in QED, we take into account the running of the strong coupling. As one significant consequence, due to asymptotic freedom, dE/dx becomes E independent for large parton energies. Some implications with regard to heavy ion collisions are pointed out.
QCD collisional energy loss reexamined.
Peshier, A
2006-11-24
It is shown that at a large temperature and E --> infinity the QCD collisional energy loss reads dE/dx approximately alpha(m(D)2)T2. Compared to previous approaches, which led to dE(B)/dx approximately alpha2 T2 ln(ET/m(D)2) similar to the Bethe-Bloch formula in QED, we take into account the running of the strong coupling. As one significant consequence, due to asymptotic freedom, dE/dx becomes E independent for large parton energies. Some implications with regard to heavy ion collisions are pointed out. PMID:17155739
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Nucleon Structure from Lattice QCD
Haegler, Philipp
2011-10-24
Hadron structure calculations in lattice QCD have seen substantial progress during recent years. We illustrate the achievements that have been made by discussing latest lattice results for a limited number of important observables related to nucleon form factors and generalized parton distributions. A particular focus is placed on the decomposition of the nucleon spin 1/2 in terms of quark spin and orbital angular momentum contributions. Results and limitations of the necessary chiral extrapolations based on ChPT will be briefly discussed.
Spectral continuity in dense QCD
Hatsuda, Tetsuo; Yamamoto, Naoki; Tachibana, Motoi
2008-07-01
The vector mesons in three-flavor quark matter with chiral and diquark condensates are studied using the in-medium QCD sum rules. The diquark condensate leads to a mass splitting between the flavor-octet and flavor-singlet channels. At high density, the singlet vector meson disappears from the low-energy spectrum, while the octet vector mesons survive as light excitations with a mass comparable to the fermion gap. A possible connection between the light gluonic modes and the flavor-octet vector mesons at high density is also discussed.
Nuclear Physics from Lattice QCD
William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage
2011-01-01
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
Single transverse-spin asymmetry in QCD
NASA Astrophysics Data System (ADS)
Koike, Yuji
2014-09-01
So far large single transverse-spin asymmetries (SSA) have been observed in many high-energy processes such as semi-inclusive deep inelastic scattering and proton-proton collisions. Since the conventional parton model and perturbative QCD can not accomodate such large SSAs, the framework for QCD hard processes had to be extended to understand the mechanism of SSA. In this extended frameworks of QCD, intrinsic transverse momentum of partons and the multi-parton (quark-gluon and pure-gluonic) correlations in the hadrons, which were absent in the conventional framework, play a crucial role to cause SSAs, and well-defined formulation of these effects has been a big challenge for QCD theorists. Study on these effects has greatly promoted our understanding on QCD dynamics and hadron structure. In this talk, I will present an overview on these theoretical activity, emphasizing the important role of the Drell-Yan process.
Unconstrained Hamiltonian formulation of low energy QCD
NASA Astrophysics Data System (ADS)
Pavel, Hans-Peter
2014-04-01
Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g-2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case). The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the "constant Abelian fields" corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons), and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate that there is a finite
Applications of AdS/QCD and Light-Front Holography to Baryon Physics
Brodsky, Stanley J.; Teramond, Guy F. de
2011-10-21
The correspondence between theories in anti--de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. 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, thus providing a relativistic description of hadrons at the amplitude level. The meson and baryon wave-functions derived from light-front holography and AdS/QCD also have remarkable phenomenological features, including predictions for the electromagnetic form factors and decay constants. The approach can be systematically improved using light-front Hamiltonian methods. Some novel features of QCD for baryon physics are also discussed.
Light-Front Holography and QCD Hadronization at the Amplitude Level
Brodsky, Stanley J.; de Teramond, Guy F.; ,
2009-01-09
Light-front holography allows hadronic amplitudes in the AdS/QCD fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The AdS coordinate z is identified with an invariant light-front coordinate {zeta} which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. A new method for computing the hadronization of quark and gluon jets at the amplitude level using AdS/QCD light-front wavefunctions is outlined.
Effect of bulk viscosity on elliptic flow near the QCD phase transition
Denicol, G. S.; Kodama, T.; Mota, Ph.; Koide, T.
2009-12-15
In this work, we examine the effect of bulk viscosity on elliptic flow, taking into account the critical behavior of the equation of state and transport coefficients near the QCD phase transition. We found that the p{sub T} dependence of v{sub 2} is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v{sub 2} decreases by a factor of 15% at small p{sub T} values (<1 GeV). However, for larger values of p{sub T} (>2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v{sub 2}. We point out that Grad's 14-moment approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.
Applications of AdS/QCD and Light-Front Holography to Baryon Physics
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2011-08-22
The correspondence between theories in anti-de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. 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, thus providing a relativistic description of hadrons at the amplitude level. The meson and baryon wavefunctions derived from light-front holography and AdS/QCD also have remarkable phenomenological features, including predictions for the electromagnetic form factors and decay constants. The approach can be systematically improved using light-front Hamiltonian methods. Some novel features of QCD for baryon physics are also discussed.
The QCD/SM working group: Summary report
W. Giele et al.
2004-01-12
Quantum Chromo-Dynamics (QCD), and more generally the physics of the Standard Model (SM), enter in many ways in high energy processes at TeV Colliders, and especially in hadron colliders (the Tevatron at Fermilab and the forthcoming LHC at CERN), First of all, at hadron colliders, QCD controls the parton luminosity, which rules the production rates of any particle or system with large invariant mass and/or large transverse momentum. Accurate predictions for any signal of possible ''New Physics'' sought at hadron colliders, as well as the corresponding backgrounds, require an improvement in the control of uncertainties on the determination of PDF and of the propagation of these uncertainties in the predictions. Furthermore, to fully exploit these new types of PDF with uncertainties, uniform tools (computer interfaces, standardization of the PDF evolution codes used by the various groups fitting PDF's) need to be proposed and developed. The dynamics of colour also affects, both in normalization and shape, various observables of the signals of any possible ''New Physics'' sought at the TeV scale, such as, e.g. the production rate, or the distributions in transverse momentum of the Higgs boson. Last, but not least, QCD governs many backgrounds to the searches for this ''New Physics''. Large and important QCD corrections may come from extra hard parton emission (and the corresponding virtual corrections), involving multi-leg and/or multi-loop amplitudes. This requires complex higher order calculations, and new methods have to be designed to compute the required multi-legs and/or multi-loop corrections in a tractable form. In the case of semi-inclusive observables, logarithmically enhanced contributions coming from multiple soft and collinear gluon emission require sophisticated QCD resummation techniques. Resummation is a catch-all name for efforts to extend the predictive power of QCD by summing the large logarithmic corrections to all orders in perturbation theory. In
Khodadi, M. Sepangi, H.R.
2014-07-15
We study the phase transition from quark–gluon plasma to hadrons in the early universe in the context of non-equilibrium thermodynamics. According to the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electro-weak transition has occurred when the universe was about 1–10 μs old. We focus attention on such a phase transition in the presence of a viscous relativistic cosmological background fluid in the framework of non-detailed balance Hořava–Lifshitz cosmology within an effective model of QCD. We consider a flat Friedmann–Robertson–Walker universe filled with a non-causal and a causal bulk viscous cosmological fluid respectively and investigate the effects of the running coupling constants of Hořava–Lifshitz gravity, λ, on the evolution of the physical quantities relevant to a description of the early universe, namely, the temperature T, scale factor a, deceleration parameter q and dimensionless ratio of the bulk viscosity coefficient to entropy density (ξ)/s . We assume that the bulk viscosity cosmological background fluid obeys the evolution equation of the steady truncated (Eckart) and full version of the Israel–Stewart fluid, respectively. -- Highlights: •In this paper we have studied quark–hadron phase transition in the early universe in the context of the Hořava–Lifshitz model. •We use a flat FRW universe with the bulk viscosity cosmological background fluid obeying the evolution equation of the steady truncated (Eckart) and full version of the Israel–Stewart fluid, respectively.
Nuclear Physics and Lattice QCD
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 j 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
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 and 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.
NASA Astrophysics Data System (ADS)
Khodadi, M.; Sepangi, H. R.
2014-07-01
We study the phase transition from quark-gluon plasma to hadrons in the early universe in the context of non-equilibrium thermodynamics. According to the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electro-weak transition has occurred when the universe was about 1-10 μs old. We focus attention on such a phase transition in the presence of a viscous relativistic cosmological background fluid in the framework of non-detailed balance Hořava-Lifshitz cosmology within an effective model of QCD. We consider a flat Friedmann-Robertson-Walker universe filled with a non-causal and a causal bulk viscous cosmological fluid respectively and investigate the effects of the running coupling constants of Hořava-Lifshitz gravity, λ, on the evolution of the physical quantities relevant to a description of the early universe, namely, the temperature T, scale factor a, deceleration parameter q and dimensionless ratio of the bulk viscosity coefficient to entropy density ξ/s. We assume that the bulk viscosity cosmological background fluid obeys the evolution equation of the steady truncated (Eckart) and full version of the Israel-Stewart fluid, respectively.
Dark Energy from graviton-mediated interactions in the QCD vacuum
Pasechnik, Roman; Beylin, Vitaly; Vereshkov, Grigory E-mail: vbey@rambler.ru
2013-06-01
Adopting the hypothesis about the exact cancellation of vacuum condensates contributions to the ground state energy in particle physics to the leading order in graviton-mediated interactions, we argue that the observable cosmological constant can be dynamically induced by an uncompensated quantum gravity correction to them after the QCD phase transition epoch. To start with, we demonstrate a possible cancellation of the quark-gluon condensate contribution to the total vacuum energy density of the Universe at temperatures T < 100 MeV without taking into account the graviton-mediated effects. In order to incorporate the latter, we then calculate the leading-order quantum correction to the classical Einstein equations due to metric fluctuations induced by the non-perturbative vacuum fluctuations of the gluon and quark fields in the quasiclassical approximation. It has been demonstrated that such a correction to the vacuum energy density has a form ε{sub Λ} ∼ GΛ{sub QCD}{sup 6}, where G is the gravitational constant, and Λ{sub QCD} is the QCD scale parameter. We analyze capabilities of this approach based on the synthesis between quantum gravity in quasiclassical approximation and theory of non-perturbative QCD vacuum for quantitative explanation of the observed Dark Energy density.
Brodsky, Stanley J.; Cao, Fu-Guang; de Teramond, Guy F.; /Costa Rica U.
2011-11-04
The QCD evolution of the pion distribution amplitude (DA) {phi}{sub {pi}} (x, Q{sup 2}) is computed for several commonly used models. Our analysis includes the nonperturbative form predicted by lightfront holographic QCD, thus combining the nonperturbative bound state dynamics of the pion with the perturbative ERBL evolution of the pion distribution amplitude. We calculate the meson-photon transition form factors for the {pi}{sup 0}, {eta} and {eta}' using the hard-scattering formalism. We point out that a widely-used approximation of replacing {phi} (x; (1 - x)Q) with {phi} (x;Q) in the calculations will unjustifiably reduce the predictions for the meson-photon transition form factors. It is found that the four models of the pion DA discussed give very different predictions for the Q{sup 2} dependence of the meson-photon transition form factors in the region of Q{sup 2} > 30 GeV{sup 2}. More accurate measurements of these transition form factors at the large Q{sup 2} region will be able to distinguish the four models of the pion DA. The rapid growth of the large Q{sup 2} data for the pion-photon transition form factor reported by the BABAR Collaboration is difficult to explain within the current framework of QCD. If the BABAR data for the meson-photon transition form factor for the {pi}{sup 0} is confirmed, it could indicate physics beyond-the-standard model, such as a weakly-coupled elementary C = + axial vector or pseudoscalar z{sup 0} in the few GeV domain, an elementary field which would provide the coupling {gamma}{sup *}{gamma} {yields} z{sup 0} {yields} {pi}{sup 0} at leading twist. Our analysis thus indicates the importance of additional measurements of the pion-photon transition form factor at large Q{sup 2}.
Vranas, P
2007-06-18
Quantum Chromodynamics is the theory of nuclear and sub-nuclear physics. It is a celebrated theory and one of its inventors, F. Wilczek, has termed it as '... our most perfect physical theory'. Part of this is related to the fact that QCD can be numerically simulated from first principles using the methods of lattice gauge theory. The computational demands of QCD are enormous and have not only played a role in the history of supercomputers but are also helping define their future. Here I will discuss the intimate relation of QCD and massively parallel supercomputers with focus on the Blue Gene supercomputer and QCD thermodynamics. I will present results on the performance of QCD on the Blue Gene as well as physics simulation results of QCD at temperatures high enough that sub-nuclear matter transitions to a plasma state of elementary particles, the quark gluon plasma. This state of matter is thought to have existed at around 10 microseconds after the big bang. Current heavy ion experiments are in the quest of reproducing it for the first time since then. And numerical simulations of QCD on the Blue Gene systems are calculating the theoretical values of fundamental parameters so that comparisons of experiment and theory can be made.
The QCD vacuum, hadrons and superdense matter
Shuryak, E.
1986-01-01
This is probably the only textbook available that gathers QCD, many-body theory and phase transitions in one volume. The presentation is pedagogical and readable. Contents: The QCD Vacuum: Introduction; QCD on the Lattice Topological Effects in Gauges Theories. Correlation Functions and Microscopic Excitations: Introduction; Operator Product Expansion; The Sum Rules beyond OPE; Nonpower Contributions to Correlators and Instantons; Hadronic Spectroscopy on the Lattice. Dense Matter: Hadronic Matter; Asymptotically Dense Quark-Gluon Plasma; Instantons in Matter; Lattice Calculations at Finite Temperature; Phase Transitions; Macroscopic Excitations and Experiments: General Properties of High Energy Collisions; ''Barometers'', ''Thermometers'', Interferometric ''Microscope''; Experimental Perspectives.
Excited light isoscalar mesons from lattice QCD
Christopher Thomas
2011-07-01
I report a recent lattice QCD calculation of an excited spectrum of light isoscalar mesons, something that has up to now proved challenging for lattice QCD. With novel techniques we extract an extensive spectrum with high statistical precision, including spin-four states and, for the first time, light isoscalars with exotic quantum numbers. In addition, the hidden flavour content of these mesons is determined, providing a window on annihilation dynamics in QCD. I comment on future prospects including applications to the study of resonances.
Death to perturbative QCD in exclusive processes?
Eckardt, R.; Hansper, J.; Gari, M.F.
1994-04-01
The authors discuss the question of whether perturbative QCD is applicable in calculations of exclusive processes at available momentum transfers. They show that the currently used method of determining hadronic quark distribution amplitudes from QCD sum rules yields wave functions which are completely undetermined because the polynomial expansion diverges. Because of the indeterminacy of the wave functions no statement can be made at present as to whether perturbative QCD is valid. The authors emphasize the necessity of a rigorous discussion of the subject and the importance of experimental data in the range of interest.
Shape of mesons in holographic QCD
Torabian, Mahdi; Yee, Ho-Ung
2009-10-15
Based on the expectation that the constituent quark model may capture the right physics in the large N limit, we point out that the orbital angular momentum of the quark-antiquark pair inside light mesons of low spins in the constituent quark model may provide a clue for the holographic dual string model of large N QCD. Our discussion, relying on a few suggestive assumptions, leads to a necessity of world-sheet fermions in the bulk of dual strings that can incorporate intrinsic spins of fundamental QCD degrees of freedom. We also comment on the interesting issue of the size of mesons in holographic QCD.
Towards the chiral limit in QCD
Shailesh Chandrasekharan
2006-02-28
Computing hadronic observables by solving QCD from first principles with realistic quark masses is an important challenge in fundamental nuclear and particle physics research. Although lattice QCD provides a rigorous framework for such calculations many difficulties arise. Firstly, there are no good algorithms to solve lattice QCD with realistically light quark masses. Secondly, due to critical slowing down, Monte Carlo algorithms are able to access only small lattice sizes on coarse lattices. Finally, due to sign problems it is almost impossible to study the physics of finite baryon density. Lattice QCD contains roughly three mass scales: the cutoff (or inverse lattice spacing) a{sup -1}, the confinement scale {Lambda}{sub QCD}, and the pion mass m{sub {pi}}. Most conventional Monte Carlo algorithms for QCD become inefficient in two regimes: when {Lambda}{sub QCD} becomes small compared to a{sup -1} and when m{sub {pi}} becomes small compared to {Lambda}{sub QCD}. The former can be largely controlled by perturbation theory thanks to asymptotic freedom. The latter is more difficult since chiral extrapolations are typically non-analytic and can be unreliable if the calculations are not done at sufficiently small quark masses. For this reason it has been difficult to compute quantities close to the chiral limit. The essential goal behind this proposal was to develop a new approach towards understanding QCD and QCD-like theories with sufficiently light quarks. The proposal was based on a novel cluster algorithm discovered in the strong coupling limit with staggered fermions [1]. This algorithm allowed us to explore the physics of exactly massless quarks and as well as light quarks. Thus, the hope was that this discovery would lead to the complete solution of at least a few strongly coupled QCD-like theories. The solution would be far better than those achievable through conventional methods and thus would be able to shed light on the chiral physics from a new
NASA Astrophysics Data System (ADS)
Wu, Lian-Ao
1994-12-01
It is shown that the cyclic evolution posed by Aharonov and Anandan [Phys. Rev. Lett. 58, 1593 (1987)] universally exists in any quantum system: cyclic evolution occurs for special initial wave functions, whatever the concrete form of the Hamiltonian. The above results are illustrated and some specific geometric phases are given.
From QCD to physical resonances
NASA Astrophysics Data System (ADS)
Bolton, Daniel R.; Briceño, Raúl A.; Wilson, David J.
2016-05-01
In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at mπ = 236 MeV [1], for the isotriplet ππ channel are analyzed using the Lüscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to the complex plane to obtain the ρ-pole at [ 755 (2 )(1 )(02 20 ) -i/2 129 (3 )(1 )(1 7 ) ] MeV.
QCD tests with polarized beams
Maruyama, Takashi; SLD Collaboration
1996-09-01
The authors present three QCD studies performed by the SLD experiment at SLAC, utilizing the highly polarized SLC electron beam. They examined particle production differences in light quark and antiquark hemispheres, and observed more high momentum baryons and K{sup {minus}}`s than antibaryons and K{sup +}`s in quark hemispheres, consistent with the leading particle hypothesis. They performed a search for jet handedness in light q- and {anti q}-jets. Assuming Standard Model values of quark polarization in Z{sup 0} decays, they have set an improved upper limit on the analyzing power of the handedness method. They studied the correlation between the Z{sup 0} spin and the event-plane orientation in polarized Z{sup 0} decays into three jets.
Gluonic transversity from lattice QCD
NASA Astrophysics Data System (ADS)
Detmold, W.; Shanahan, P. E.
2016-07-01
We present an exploratory study of the gluonic structure of the ϕ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-2 double-helicity-flip gluonic structure function Δ (x ,Q2). This structure function only exists for targets of spin J ≥1 and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and nonflip gluonic distributions, finding it to be saturated at the level of 80%. This work sets the stage for more complex LQCD studies of gluonic structure in the nucleon and in light nuclei where Δ (x ,Q2) is an "exotic glue" observable probing gluons in a nucleus not associated with individual nucleons.
Lattice QCD Beyond Ground States
Huey-Wen Lin; Saul D. Cohen
2007-09-11
In this work, we apply black box methods (methods not requiring input) to find excited-state energies. A variety of such methods for lattice QCD were introduced at the 3rd iteration of the numerical workshop series. We first review a selection of approaches that have been used in lattice calculations to determine multiple energy states: multiple correlator fits, the variational method and Bayesian fitting. In the second half, we will focus on a black box method, the multi-effective mass. We demonstrate the approach on a toy model, as well as on real lattice data, extracting multiple states from single correlators. Without complicated operator construction or specialized fitting programs, the black box method shows good consistency with the traditional approaches.
Nuclear Force from Lattice QCD
Ishii, N.; Aoki, S.; Hatsuda, T.
2007-07-13
The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32{sup 4} [{approx_equal}(4.4 fm){sup 4}] lattice. A NN potential V{sub NN}(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the {sup 1}S{sub 0} and {sup 3}S{sub 1} channels, we show that the central part of V{sub NN}(r) has a strong repulsive core of a few hundred MeV at short distances (r < or approx. 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.
Nuclear force from lattice QCD.
Ishii, N; Aoki, S; Hatsuda, T
2007-07-13
The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32(4) [approximately (4.4 fm)(4)] lattice. A NN potential V(NN)(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the (1)S(0) and (3)S(1) channels, we show that the central part of V(NN)(r) has a strong repulsive core of a few hundred MeV at short distances (r approximately < 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force. PMID:17678213
SAITO,N.
1999-12-09
In this lecture I give a pedagogical introduction to the Perturbative QCD to understand the short-distance dynamics of the strong interaction. Starting with fundamental concepts such as the color degree of freedom of QCD, non-abelian gauge field theory, renormalization group equation etc., I explain a basic idea of the perturbative QCD and apply this idea to the e{sup +}e{sup {minus}} processes and the structure functions. The notion of mass singularity and the necessity of its factorization is discussed in some detail.
Parton distributions from lattice QCD: an update
Detmold, W; Melnitchouk, W; Thomas, A W
2004-04-01
We review the extraction of parton distributions from their moments calculated in lattice QCD, focusing in particular on their extrapolation to the physical region. As examples, we consider both the unpolarized and polarized isovector parton distributions of the nucleon.
Opportunities, challenges, and fantasies in lattice QCD
NASA Astrophysics Data System (ADS)
Wilczek, Frank
2003-05-01
Some important problems in quantitative QCD will certainly yield to hard work and adequate investment of resources, others appear difficult but may be accessible, and still others will require essentially new ideas. Here I identify several examples in each class.
None
2011-10-06
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.
Strange Baryon Physics in Full Lattice QCD
Huey-Wen Lin
2007-11-01
Strange baryon spectra and form factors are key probes to study excited nuclear matter. The use of lattice QCD allows us to test the strength of the Standard Model by calculating strange baryon quantities from first principles.
Excited light meson spectroscopy from lattice QCD
Christopher Thomas, Hadron Spectrum Collaboration
2012-04-01
I report on recent progress in calculating excited meson spectra using lattice QCD, emphasizing results and phenomenology. With novel techniques we can now extract extensive spectra of excited mesons with high statistical precision, including spin-four states and those with exotic quantum numbers. As well as isovector meson spectra, I will present new calculations of the spectrum of excited light isoscalar mesons, something that has up to now been a challenge for lattice QCD. I show determinations of the flavor content of these mesons, including the eta-eta' mixing angle, providing a window on annihilation dynamics in QCD. I will also discuss recent work on using lattice QCD to map out the energy-dependent phase shift in pi-pi scattering and future applications of the methodology to the study of resonances and decays.
Simplifying Multi-Jet QCD Computation
Peskin, Michael E.; /SLAC
2011-11-04
These lectures give a pedagogical discussion of the computation of QCD tree amplitudes for collider physics. The tools reviewed are spinor products, color ordering, MHV amplitudes, and the Britto-Cachazo-Feng-Witten recursion formula.
QCD mechanisms for heavy particle production
Brodsky, S.J.
1985-09-01
For very large pair mass, the production of heavy quarks and supersymmetric particles is expected to be governed by ACD fusion subprocesses. At lower mass scales other QCD mechanisms such as prebinding distortion and intrinsic heavy particle Fock states can become important, possibly accounting for the anomalies observed for charm hadroproduction. We emphasize the importance of final-state Coulomb interactions at low relative velocity in QCD and predict the existence of heavy narrow four quark resonances (c c-bar u u-bar) and (cc c-bar c-bar) in ..gamma gamma.. reactions. Coherent QCD contributions are discussed as a contribution to the non-additivity of nuclear structure functions and heavy particle production cross sections. We also predict a new type of amplitude zero for exclusive heavy meson pair production which follows from the tree-graph structure of QCD. 35 refs., 8 figs., 1 tab.
Difference equation for superradiance
NASA Technical Reports Server (NTRS)
Lee, C. T.
1974-01-01
The evolution of a completely excited system of N two-level atoms, distributed over a large region and interacting with all modes of radiation field, is studied. The distinction between r-conserving (RC) and r-nonconserving (RNC) processes is emphasized. Considering the number of photons emitted as the discrete independent variable, the evolution is described by a partial difference equation. Numerical solution of this equation shows the transition from RNC dominance at the beginning to RC dominance later. This is also a transition from incoherent to coherent emission of radiation.
Recent QCD Studies at the Tevatron
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.
QCD and hard diffraction at the LHC
Albrow, Michael G.; /Fermilab
2005-09-01
As an introduction to QCD at the LHC the author gives an overview of QCD at the Tevatron, emphasizing the high Q{sup 2} frontier which will be taken over by the LHC. After describing briefly the LHC detectors the author discusses high mass diffraction, in particular central exclusive production of Higgs and vector boson pairs. The author introduces the FP420 project to measure the scattered protons 420m downstream of ATLAS and CMS.
Novel QCD effects in nuclear collisions
Brodsky, S.J.
1991-12-01
Heavy ion collisions can provide a novel environment for testing fundamental dynamical processes in QCD, including minijet formation and interactions, formation zone phenomena, color filtering, coherent co-mover interactions, and new higher twist mechanisms which could account for the observed excess production and anomalous nuclear target dependence of heavy flavor production. The possibility of using light-cone thermodynamics and a corresponding covariant temperature to describe the QCD phases of the nuclear fragmentation region is also briefly discussed.
Lattice and Phase Diagram in QCD
Lombardo, Maria Paola
2008-10-13
Model calculations have produced a number of very interesting expectations for the QCD Phase Diagram, and the task of a lattice calculations is to put these studies on a quantitative grounds. I will give an overview of the current status of the lattice analysis of the QCD phase diagram, from the quantitative results of mature calculations at zero and small baryochemical potential, to the exploratory studies of the colder, denser phase.
Precision lattice QCD: challenges and prospects
NASA Astrophysics Data System (ADS)
Hashimoto, Shoji
2013-04-01
With Peta-flops scale computational resources, lattice QCD simulation has recently reached one of its primary goals, i.e. reproducing the low-lying hadron spectrum starting from the QCD Lagrangian. Applications to various other phenomenological quantities, for which no other way of precise theoretical calculation is available, would become the next milestone. In this talk I will provide a brief overview of the field and summarize the remaining problems to be solved before achieving the precision calculations.
Soft and hard contributions to QCD processes
Slavnov, D.A.; Bakulina, E.N.
1995-06-01
QCD corrections of order {alpha}{sub s} for deep inelastic lepton scattering and the Drell-Yan process are considered. The common soft part of these corrections is found. This result makes it possible to determine the modified parton distribution functions unambiguously beyond the leading logarithmic approximation. These distribution functions are used to obtain QCD corrections that are free of infrared and collinear ambiguities. 6 refs., 2 figs.
Some new/old approaches to QCD
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.
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.
Lattice QCD and the Jefferson Laboratory Program
Jozef Dudek, Robert Edwards, David Richards, Konstantinos Orginos
2011-06-01
Lattice gauge theory provides our only means of performing \\textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.
Windows on the axion. [quantum chromodynamics (QCD)
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1989-01-01
Peccei-Quinn symmetry with attendant axion is a most compelling, and perhaps the most minimal, extension of the standard model, as it provides a very elegant solution to the nagging strong CP-problem associated with the theta vacuum structure of QCD. However, particle physics gives little guidance as to the axion mass; a priori, the plausible values span the range: 10(-12)eV is approx. less than m(a) which is approx. less than 10(6)eV, some 18 orders-of-magnitude. Laboratory experiments have excluded masses greater than 10(4)eV, leaving unprobed some 16 orders-of-magnitude. Axions have a host of interesting astrophysical and cosmological effects, including, modifying the evolution of stars of all types (our sun, red giants, white dwarfs, and neutron stars), contributing significantly to the mass density of the Universe today, and producting detectable line radiation through the decays of relic axions. Consideration of these effects has probed 14 orders-of-magnitude in axion mass, and has left open only two windows for further exploration: 10(-6)eV is approx. less than m(a) is approx. less than 10(-3)eV and 1eV is approx. less than m(a) is approx. less than 5eV (hadronic axions only). Both these windows are accessible to experiment, and a variety of very interesting experiments, all of which involve heavenly axions, are being planned or are underway.
QCD: results from lattice quantum chromodynamics
Kronfeld, Andreas S.; /Fermilab
2006-10-01
Quantum chromodynamics (QCD) is the modern theory of the strong force. In this theory, the main objects are quarks and gluons, which are bound by the strong force into protons, neutrons, and other particles called hadrons. In the framework of QCD, the strong nuclear force binding protons and neutrons together into nuclei is actually only a residue of the much stronger forces acting between quarks and gluons. In fact, inside the proton, even the concept of force is not very useful. Within all hadrons they have a swirl of gluons being exchanged back and forth as a manifestation of the strong force. To make matters worse, gluons can split into two, and then rejoin, or they can split into a quark-antiquark pair. Even the simplest hadron is a complex system hosting constantly interacting components. Despite this complexity, QCD is well established experimentally. This is because at short distances (or high energies), the coupling between the particles is effectively small and particles move around with relative freedom. This is called asymptotic freedom and QCD is amenable to the traditional methods of quantum field theory in this regime. High-energy experiments have tested and confirmed QCD in this realm, which led to the 2004 Nobel Prize in Physics for Drs. David Gross, David Politzer, and Frank Wilczek, the theorists who provided the theory for short-range QCD and asymptotic freedom.
Behavior of single-scale hard small-x processes in QCD near the black disk limit
NASA Astrophysics Data System (ADS)
Blok, B.; Frankfurt, L.
2006-03-01
We argue that at sufficiently small Bjorken x where pQCD amplitudes rapidly increase with energy and violate probability conservation the shadowing effects in the single-scale small x hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles—perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within the physical vacuum and, in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small x. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of αs. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the “massless” particles—phonons. It is explained that phonons are relevant for the black disk behavior of cross sections of small x processes. The Bose-Einstein condensation of the ladders produces a color network occupying a “macroscopic” longitudinal volume. We discuss briefly the possible detection of new QCD effects. We outline albeit briefly the relationship between the small x hard QCD processes and the coherent critical phenomena.
QCD structure of nuclear interactions
NASA Astrophysics Data System (ADS)
Granados, Carlos G.
The research presented in this dissertation investigated selected processes involving baryons and nuclei in hard scattering reactions. These processes are characterized by the production of particles with large energies and transverse momenta. Through these processes, this work explored both, the constituent (quark) structure of baryons (specifically nucleons and Delta-Isobars), and the mechanisms through which the interactions between these constituents ultimately control the selected reactions. The first of such reactions is the hard nucleon-nucleon elastic scattering, which was studied here considering the quark exchange between the nucleons to be the dominant mechanism of interaction in the constituent picture. In particular, it was found that an angular asymmetry exhibited by proton-neutron elastic scattering data is explained within this framework if a quark-diquark picture dominates the nucleon's structure instead of a more traditional SU(6) three quarks picture. The latter yields an asymmetry around 90o center of mass scattering with a sign opposite to what is experimentally observed. The second process is the hard breakup by a photon of a nucleon-nucleon system in light nuclei. Proton-proton (pp) and proton-neutron (pn) breakup in 3He, and DeltaDelta-isobars production in deuteron breakup were analyzed in the hard rescattering model (HRM), which in conjunction with the quark interchange mechanism provides a Quantum Chromodynamics (QCD) description of the reaction. Through the HRM, cross sections for both channels in 3He photodisintegration were computed without the need of a fitting parameter. The results presented here for pp breakup show excellent agreement with recent experimental data. In DeltaDelta-isobars production in deuteron breakup, HRM angular distributions for the two DeltaDelta channels were compared to the pn channel and to each other. An important prediction fromthis study is that the Delta++Delta- channel consistently dominates Delta+Delta0
Simple analytic QCD model with perturbative QCD behavior at high momenta
Contreras, Carlos; Espinosa, Olivier; Cvetic, Gorazd; Martinez, Hector E.
2010-10-01
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of the running coupling at high momentum scales is the same as in perturbative QCD (just like in the analytic QCD model of Shirkov and Solovtsov), but at low scales it is replaced by a delta function which parametrizes the unknown behavior there. We require that the running coupling agree to a high degree with the perturbative coupling at high energies, which reduces the number of free parameters of the model from four to one. The remaining parameter is fixed by requiring the reproduction of the correct value of the semihadronic tau decay ratio.
Nucleon spin structure and perturbative QCD frontier on the move
NASA Astrophysics Data System (ADS)
Pasechnik, Roman S.; Shirkov, Dmitry V.; Teryaev, Oleg V.; Solovtsova, Olga P.; Khandramai, Vyacheslav L.
2010-01-01
We discuss the interplay between higher orders of the perturbative QCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab data on the lowest moments of spin-dependent proton and neutron structure functions Γ1p,n(Q2) and Bjorken sum rule function Γ1p-n(Q2) at 0.05
The Excited-state Spectrum of QCD through Lattice Gauge Theory Calculations
David Richards
2012-12-01
I describe recent progress at understanding the excited state spectrum of QCD through lattice gauge calculations. I begin by outlining the evolution of the lattice effort at JLab. I detail the impact of recent lattice calculations on the present and upcoming experimental programs, and in particular that of the 12 GeV upgrade of Jefferson Laboratory. I conclude with the prospect for future calculations.
QCD bound states and their response to extremes of temperature and density.
Maris, P.
1998-06-09
We describe the application of Dyson-Schwinger equations to the calculation of hadron observable. The studies at zero temperature (T) and quark chemical potential ({mu}) provide a springboard for the extension to finite-(T, {mu}). Our exemplars highlight that much of hadronic physics can be understood as simply a manifestation of the nonperturbative, momentum-dependent dressing of the elementary Schwinger functions in QCD.
NASA Astrophysics Data System (ADS)
Drozd-Rzoska, Aleksandra; Rzoska, Sylwester J.
A consistent set of temperature- (T), pressure- (P), volume- (V) and density- (ρ) related VFT-type equations for portraying the evolution of the structural relaxation time or viscosity is presented, namely: andτ (V) = τ 0 exp[D T (V SL — V)(V 0 V SL )/(V — V 0)], where T 0,P 0,V 0 and ρ0 are VFT estimates of the ideal glass loci and T SL , P SL , V SL and ρ SL are estimates of the location of the absolute stability limit, partially hidden in the negative pressures domain (P<0). For these equations prefactors are well defined via ρ 0 = ρ (T SL ,P SL , V SL ,ρ SL ), ie. they are linked to the absolute stability limit loci (gas-liquid spinodal). Noteworthy is their smooth transformation into VFT-type equations, used so far, on approaching the glass transition, and into Arrhenius-type equations remote from the glass transition, on approaching the absolute stability limit. The latter may suggest the re-examination of experimental data suggesting the VFT-to-Arrhenius crossover far away from the glass transition. Novel VFT counterparts also lead to the consistent set of fragility strength coefficients (D T ,D P ,D V ,D ρ) and fragilities associated with the slope (steepness index) at appropriate "Angell plot" counterparts.
QCD as a topologically ordered system
Zhitnitsky, Ariel R.
2013-09-15
We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1){sub A} problem where the would be η{sup ′} Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1){sub A} problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations. -- Highlights: •QCD may belong to a topologically ordered phase similar to condensed matter (CM) systems. •We identify the non-propagating topological field in deformed QCD with the Veneziano ghost. •Relation between “string-net” condensates in CM systems and the “skeletons” in QCD lattice simulations is studied.
Hadronic and nuclear interactions in QCD
Not Available
1982-01-01
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 the 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.
Two flavor QCD and confinement
D'Elia, Massimo; Di Giacomo, Adriano; Pica, Claudio
2005-12-01
We argue that the order of the chiral transition for N{sub f}=2 is a sensitive probe of the QCD vacuum, in particular, of the mechanism of color confinement. A strategy is developed to investigate the order of the transition by use of finite size scaling analysis. An in-depth numerical investigation is performed with staggered fermions on lattices with L{sub t}=4 and L{sub s}=12, 16, 20, 24, 32 and quark masses am{sub q} ranging from 0.01335 to 0.307036. The specific heat and a number of susceptibilities are measured and compared with the expectations of an O(4) second order and of a first order phase transition. A detailed comparison with previous works, which all use similar techniques as ours, is performed. A second order transition in the O(4) and O(2) universality classes are incompatible with our data, which seem to prefer a first order transition. However we have L{sub t}=4 and unimproved action, so that a check with improved techniques (algorithm and action) and possibly larger L{sub t} will be needed to assess this issue on a firm basis.
Antiangular Ordering of Gluon Radiation in QCD Media
Mehtar-Tani, Yacine; Salgado, Carlos A.; Tywoniuk, Konrad
2011-03-25
We investigate angular and energy distributions of medium-induced gluon emission off a quark-antiquark antenna in the framework of perturbative QCD as an attempt toward understanding, from first principles, jet evolution inside the quark-gluon plasma. In-medium color coherence between emitters, neglected in all previous calculations, leads to a novel mechanism of soft-gluon radiation. The structure of the corresponding spectrum, in contrast with known medium-induced radiation, i.e., off a single emitter, retains some properties of the vacuum case; in particular, it exhibits a soft divergence. However, as opposed to the vacuum, the collinear singularity is regulated by the pair opening angle, leading to a strict angular separation between vacuum and medium-induced radiation, denoted as antiangular ordering. We comment on the possible consequences of this new contribution for jet observables in heavy-ion collisions.
Transverse momentum-dependent parton distribution functions from lattice QCD
Michael Engelhardt, Philipp Haegler, Bernhard Musch, John Negele, Andreas Schaefer
2012-12-01
Transverse momentum-dependent parton distributions (TMDs) relevant for semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process can be defined in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection. Starting from such a definition, a scheme to determine TMDs in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are obtained using ensembles at the pion masses 369MeV and 518MeV, focusing in particular on the dependence of these shifts on the staple extent and a Collins-Soper-type evolution parameter quantifying proximity of the staples to the light cone.
Transient anomalous charge production in strong-field QCD
NASA Astrophysics Data System (ADS)
Tanji, Naoto; Mueller, Niklas; Berges, Jürgen
2016-04-01
We investigate axial charge production in two-color QCD out of equilibrium. We compute the real-time evolution starting with spatially homogeneous strong gauge fields, while the fermions are in vacuum. The idealized class of initial conditions is motivated by glasma flux tubes in the context of heavy-ion collisions. We focus on axial charge production at early times, where important aspects of the anomalous dynamics can be derived analytically. This is compared to real-time lattice simulations. Quark production at early times leading to anomalous charge generation is investigated using Wilson fermions. Our results indicate that coherent gauge fields can transiently produce significant amounts of axial charge density, while part of the induced charges persist to be present even well beyond characteristic decoherence times. The comparisons to analytic results provide stringent tests of real-time representations of the axial anomaly on the lattice.
Deuteron Electromagnetic Form Factors in AdS/QCD
NASA Astrophysics Data System (ADS)
Lyubovitskij, Valery E.; Gutsche, Thomas; Schmidt, Ivan; Vega, Alfredo
2016-03-01
We extend a soft-wall AdS/QCD approach to a description of deuteron properties. Our framework is based an effective action formulated in terms of AdS fields, which are holographically equivalent to the deuteron and photon fields. This action produces the equation of motion for the deuteron wave function and the Q^2 -dependent electromagnetic current, which are then used to calculate the deuteron electromagnetic form factors and structure functions in the Euclidean region. We show that the predicted deuteron quantities are expressed through a universal function, which is defined by a single scale parameter κ and which has the correct 1/Q^{10} power scaling at large Q^2.
Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
Brodsky, Stanley J.; de Teramond, Guy F.
2006-03-03
We show how the string amplitude {Phi}(z) defined on the fifth dimension in AdS{sub 5} space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable z and an impact variable {zeta}, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schroedinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for spacelike Q{sup 2}. Only one parameter which sets the mass scale, {Lambda}{sub QCD}, is introduced.
Deuteron Electromagnetic Form Factors in AdS/QCD
NASA Astrophysics Data System (ADS)
Lyubovitskij, Valery E.; Gutsche, Thomas; Schmidt, Ivan; Vega, Alfredo
2016-07-01
We extend a soft-wall AdS/QCD approach to a description of deuteron properties. Our framework is based an effective action formulated in terms of AdS fields, which are holographically equivalent to the deuteron and photon fields. This action produces the equation of motion for the deuteron wave function and the Q^2-dependent electromagnetic current, which are then used to calculate the deuteron electromagnetic form factors and structure functions in the Euclidean region. We show that the predicted deuteron quantities are expressed through a universal function, which is defined by a single scale parameter κ and which has the correct 1/Q^{10} power scaling at large Q^2.
Simple Derivation of the Lindblad Equation
ERIC Educational Resources Information Center
Pearle, Philip
2012-01-01
The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…
Light-front holographic QCD and emerging confinement
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; Erlich, Joshua
2015-07-01
In this report 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. The 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 space-time. 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 q2 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 q2 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.
Light-front holographic QCD and emerging confinement
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; Erlich, Joshua
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. The 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.
Ads/cft and Exclusive Processes in QCD
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.
2008-03-01
The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. One can use holography to map the amplitude describing the hadronic state in the fifth dimension of Anti-de Sitter space AdS5 to the light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons in QCD at the amplitude level. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. New relativistic light-front equations in ordinary space-time can then be derived which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess elegant algebraic structures and integrability properties. This connection between the AdS and the light-front representations allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, deeply virtual Compton scattering, exclusive heavy hadron decays and other exclusive scattering amplitudes. As specific examples we compute the pion coupling constant fπ and study the behavior of the pion form factor Fπ(q2) in the space and time-like regions. We also determine the Dirac nucleon form factors Fp1(q^2) and Fn1(q^2) in the space-like region.
QCD ghost reconstruction of f(G) gravity and its thermodynamic consequences
NASA Astrophysics Data System (ADS)
Chattopadhyay, Surajit
2016-07-01
In the present study we have presented a reconstruction scheme for f(G) gravity, where G represents Gauss-Bonnet invariant and we have chosen the scale factor in power-law form. It should be mentioned that f(G) gravity is not ``ad hoc" but comes out from the problem of non-local gravity theories. The works of Capozziello et al. (2013, 2014) need to be mentioned in this context. Capozziello et al. (2013) studied the Gauss-Bonnet gravity with Lagrange multiplier constraints in view to recover realistic dark energy behaviors and could recover the so-called Little Rip cosmology. Capozziello et al. (2014) built several solutions for F(R) + F(G) gravity with matter, but without Lagrange multipliers. In the present work, considering a flat FRW universe, we have considered a correspondence between f(G) gravity and QCD ghost dark energy. After getting a reconstructed solution for f(G) we have plotted f(G) against G, where it is apparent that f(G)→ 0 as G→ 0, which is one of the sufficient conditions for a realistic model. We have plotted the effective equation of state parameter for n>1 and observed that w_{eff}≥ -1 i.e. it behaves like quintessence. For n≈ 2, w_{eff} is reaching -1 at late stage of the universe. However, it is not crossing the phantom boundary. Subsequently, considering dynamical apparent horizon as the enveloping horizon of the universe we have derived expression for the time derivative of total entropy dot{S}_{total} and we have observed that dot{S}_{total}>0 throughout the evolution of the universe. This indicated validity of the generalized second law of thermodynamics under this reconstruction of f(G) gravity. References: Capozziello, S., Francaviglia, M., Makarenko, A. N.: Astrophys. Space Sci., 603 (2014) Capozziello, S., Makarenko, A. N., Odintsov, S. D.: Phys. Rev. D, 87 084037 (2013)
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
QCD sign problem for small chemical potential
Splittorff, K.; Verbaarschot, J. J. M.
2007-06-01
The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the p-expansion of the chiral Lagrangian is calculated as well.
Exploring hyperons and hypernuclei with lattice QCD
Beane, S.R.; Bedaque, P.F.; Parreno, A.; Savage, M.J.
2003-01-01
In this work we outline a program for lattice QCD that wouldprovide a first step toward understanding the strong and weakinteractions of strange baryons. The study of hypernuclear physics hasprovided a significant amount of information regarding the structure andweak decays of light nuclei containing one or two Lambda's, and Sigma's.From a theoretical standpoint, little is known about the hyperon-nucleoninteraction, which is required input for systematic calculations ofhypernuclear structure. Furthermore, the long-standing discrepancies inthe P-wave amplitudes for nonleptonic hyperon decays remain to beunderstood, and their resolution is central to a better understanding ofthe weak decays of hypernuclei. We present a framework that utilizesLuscher's finite-volume techniques in lattice QCD to extract thescattering length and effective range for Lambda-N scattering in both QCDand partially-quenched QCD. The effective theory describing thenonleptonic decays of hyperons using isospin symmetry alone, appropriatefor lattice calculations, is constructed.
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.
QCD subgroup on diffractive and forward physics
Albrow, M.G.; Baker, W.; Bhatti, A.
1997-09-01
Over the last few years, there has been a resurgence of interest in small-x or diffractive physics. This has been due to the realization that perturbative QCD techniques may be applicable to what was previously thought of as a non-perturbative problem and to the opening up of new energy regimes at HERA and the Tevatron collider. The goal is to understand the pomeron, and hence the behavior of total cross sections, elastic scattering and diffractive excitation, in terms of the underlying theory, QCD. This paper is divided into experiments of hadron-hadron colliders and electron-proton colliders.
Experimental Study of Nucleon Structure and QCD
Jian-Ping Chen
2012-03-01
Overview of Experimental Study of Nucleon Structure and QCD, with focus on the spin structure. Nucleon (spin) Structure provides valuable information on QCD dynamics. A decade of experiments from JLab yields these exciting results: (1) valence spin structure, duality; (2) spin sum rules and polarizabilities; (3) precision measurements of g{sub 2} - high-twist; and (4) first neutron transverse spin results - Collins/Sivers/A{sub LT}. There is a bright future as the 12 GeV Upgrade will greatly enhance our capability: (1) Precision determination of the valence quark spin structure flavor separation; and (2) Precision extraction of transversity/tensor charge/TMDs.
Chiral symmetry restoration in holographic noncommutative QCD
NASA Astrophysics Data System (ADS)
Nakajima, Tadahito; Ohtake, Yukiko; Suzuki, Kenji
2011-09-01
We consider the noncommutative deformation of the Sakai-Sugimoto model at finite temperature and finite baryon chemical potential. The space noncommutativity is possible to have an influence on the flavor dynamics of the QCD. The critical temperature and critical value of the chemical potential are modified by the space noncommutativity. The influence of the space noncommutativity on the flavor dynamics of the QCD is caused by the Wess-Zumino term in the effective action of the D8-branes. The intermediate temperature phase, in which the gluons deconfine but the chiral symmetry remains broken, is easy to be realized in some region of the noncommutativity parameter.
Hadron scattering and resonances in QCD
NASA Astrophysics Data System (ADS)
Dudek, Jozef J.
2016-05-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study ππ elastic scattering, including the ρ resonance, as well as coupled-channel π >K, ηK scattering. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Exclusive hadronic and nuclear processes in QCD
Brodsky, S.J.
1985-12-01
Hadronic and nuclear processes are covered, in which all final particles are measured at large invariant masses compared with each other, i.e., large momentum transfer exclusive reactions. Hadronic wave functions in QCD and QCD sum rule constraints on hadron wave functions are discussed. The question of the range of applicability of the factorization formula and perturbation theory for exclusive processes is considered. Some consequences of quark and gluon degrees of freedom in nuclei are discussed which are outside the usual domain of traditional nuclear physics. 44 refs., 7 figs. (LEW)
QCD resummation for hadronic final states
NASA Astrophysics Data System (ADS)
Luisoni, Gionata; Marzani, Simone
2015-10-01
We review the basic concepts of all-order calculations in quantum chromodynamics (QCD) and their application to collider phenomenology. We start by discussing the factorization properties of QCD amplitudes and cross-sections in the soft and collinear limits and their resulting all-order exponentiation. We then discuss several applications of this formalism to observables which are of great interest at particle colliders. In this context, we describe the all-order resummation of event-shape distributions, as well as observables that probe the internal structure of hadronic jets.
String breaking in four dimensional lattice QCD
Duncan, A.; Eichten, E.; Thacker, H.
2001-06-01
Virtual quark pair screening leads to breaking of the string between fundamental representation quarks in QCD. For unquenched four dimensional lattice QCD, this (so far elusive) phenomenon is studied using the recently developed truncated determinant algorithm (TDA). The dynamical configurations were generated on a 650 MHz PC. Quark eigenmodes up to 420 MeV are included exactly in these TDA studies performed at low quark mass on large coarse [but O(a{sup 2}) improved] lattices. A study of Wilson line correlators in Coulomb gauge extracted from an ensemble of 1000 two-flavor dynamical configurations reveals evidence for flattening of the string tension at distances R{approx}>1 fm.
Topological Charge Evolution in the Markov-Chain of QCD
Derek Leinweber; Anthony Williams; Jian-bo Zhang; Frank Lee
2004-04-01
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
Light-like Wilson line in QCD without path ordering
NASA Astrophysics Data System (ADS)
Nayak, Gouranga C.
2016-07-01
Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of noncommuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of soft and collinear divergences at all order in coupling constant in QCD processes at high energy colliders.
Matching excluded-volume hadron-resonance gas models and perturbative QCD to lattice calculations
NASA Astrophysics Data System (ADS)
Albright, M.; Kapusta, J.; Young, C.
2014-08-01
We match three hadronic equations of state at low energy densities to a perturbatively computed equation of state of quarks and gluons at high energy densities. One of them includes all known hadrons treated as point particles, which approximates attractive interactions among hadrons. The other two include, in addition, repulsive interactions in the form of excluded volumes occupied by the hadrons. A switching function is employed to make the crossover transition from one phase to another without introducing a thermodynamic phase transition. A χ2 fit to accurate lattice calculations with temperature 100
Chiral logarithms in quenched QCD
Y. Chen; S. J. Dong; T. Draper; I. Horvath; F. X. Lee; K. F. Liu; N. Mathur; and J. B. Zhang
2004-08-01
The quenched chiral logarithms are examined on a 163x28 lattice with Iwasaki gauge action and overlap fermions. The pion decay constant fpi is used to set the lattice spacing, a = 0.200(3) fm. With pion mass as low as {approx}180 MeV, we see the quenched chiral logarithms clearly in mpi2/m and fP, the pseudoscalar decay constant. The authors analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory (chiPT) to apply. With the constrained curve-fitting method, they are able to extract the quenched chiral logarithmic parameter delta together with other low-energy parameters. Only for mpi<=300 MeV do we obtain a consistent and stable fit with a constant delta which they determine to be 0.24(3)(4) (at the chiral scale Lambdachi = 0.8 GeV). By comparing to the 123x28 lattice, they estimate the finite volume effect to be about 2.7% for the smallest pion mass. They also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to mpi {approx}500-600 MeV. The scale independent delta is determined to be 0.20(3) in this case. The authors study the quenched non-analytic terms in the nucleon mass and find that the coefficient C1/2 in the nucleon mass is consistent with the prediction of one-loop chiPT. They also obtain the low energy constant L5 from fpi. They conclude from this study that it is imperative to cover only the range of data with the pion mass less than {approx}300 MeV in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop chiPT.
AdS/QCD, Light-Front Holography, and Sublimated Gluons
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
The gauge/gravity duality leads to a simple analytical and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian - 'Light-Front Holography', which provides a Lorentz-invariant first-approximation to QCD, and successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schroedinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holography connects the fifth-dimensional coordinate of AdS space z to an invariant impact separation variable {zeta} in 3+1 space at fixed light-front time. A key feature is the determination of the frame-independent light-front wavefunctions of hadrons - the relativistic analogs of the Schroedinger wavefunctions of atomic physics which allow one to compute form factors, transversity distributions, spin properties of the valence quarks, jet hadronization, and other hadronic observables. One thus obtains a one-parameter color-confining model for hadron physics at the amplitude level. AdS/QCD also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function with an infrared fixed point which agrees with the effective coupling a{sub g1} (Q{sup 2}) extracted from measurements of the Bjorken sum rule below Q{sup 2} < 1 GeV{sup 2}. This is consistent with a flux-tube interpretation of QCD where soft gluons with virtualities Q{sup 2} < 1 GeV{sup 2} are sublimated into a color-confining potential for quarks. We discuss a number of phenomenological hadronic properties which support this picture.
QCD Physics at the Tevatron Collider
Messina, Andrea
2005-10-12
In this contribution some of the prominent QCD physics results from CDF and D0 experiments in Run II are presented. The cross sections and the properties of jets are discussed for both the inclusive and the b-jet production. Results on the associate production of light and heavy flavour jets together with vector bosons are also reported.
Large Scale Commodity Clusters for Lattice QCD
A. Pochinsky; W. Akers; R. Brower; J. Chen; P. Dreher; R. Edwards; S. Gottlieb; D. Holmgren; P. Mackenzie; J. Negele; D. Richards; J. Simone; W. Watson
2002-06-01
We describe the construction of large scale clusters for lattice QCD computing being developed under the umbrella of the U.S. DoE SciDAC initiative. We discuss the study of floating point and network performance that drove the design of the cluster, and present our plans for future multi-Terascale facilities.
BRST invariance in Coulomb gauge QCD
NASA Astrophysics Data System (ADS)
Andraši, A.; Taylor, J. C.
2015-12-01
In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ħ2, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g4) , example.
Toward lattice QCD simulation on AP1000
NASA Astrophysics Data System (ADS)
Ohta, Shigemi
AP1000 is Fujitsu Laboratory's experimental parallel computer consisting of up to 1024 microcomputers called cells. It is found that each AP1000 cell can sustain two to three megaflops computational speed for full QCD lattice numerical simulations in IEEE 64-bit floating point format
Phase structure of QCD for heavy quarks
NASA Astrophysics Data System (ADS)
Fischer, Christian S.; Luecker, Jan; Pawlowski, Jan M.
2015-01-01
We investigate the nature of the deconfinement and Roberge-Weiss transition in the heavy quark regime for finite real and imaginary chemical potential within the functional approach to continuum QCD. We extract the critical phase boundary between the first-order and crossover regions and also explore tricritical scaling. Our results confirm previous ones from finite volume lattice studies.
QCD PHASE TRANSITIONS-VOLUME 15.
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 theorists 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.
Nonperturbative QCD corrections to electroweak observables
Dru B Renner, Xu Feng, Karl Jansen, Marcus Petschlies
2011-12-01
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important hadronic corrections may be feasibly calculated using lattice QCD methods. To illustrate this, we will examine the lattice computation of the leading-order QCD corrections to the muon magnetic moment, paying particular attention to a recently developed method but also reviewing the results from other calculations. We will then continue with several examples that demonstrate the potential impact of the new approach: the leading-order corrections to the electron and tau magnetic moments, the running of the electromagnetic coupling, and a class of the next-to-leading-order corrections for the muon magnetic moment. Along the way, we will mention applications to the Adler function, the determination of the strong coupling constant and QCD corrections to muonic-hydrogen.
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.
Quark screening lengths in finite temperature QCD
Gocksch, A. California Univ., Santa Barbara, CA . Inst. for Theoretical Physics)
1990-11-01
We have computed Landau gauge quark propagators in both the confined and deconfined phase of QCD. I discuss the magnitude of the resulting screening lengths as well as aspects of chiral symmetry relevant to the quark propagator. 12 refs., 1 fig., 1 tab.
The CKM Matrix from Lattice QCD
Mackenzie, Paul B.; /Fermilab
2009-07-01
Lattice QCD plays an essential role in testing and determining the parameters of the CKM theory of flavor mixing and CP violation. Very high precisions are required for lattice calculations analyzing CKM data; I discuss the prospects for achieving them. Lattice calculations will also play a role in investigating flavor mixing and CP violation beyond the Standard Model.
Exact Adler Function in Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Shifman, M.; Stepanyantz, K.
2015-02-01
The Adler function D is found exactly in supersymmetric QCD. Our exact formula relates D (Q2) to the anomalous dimension of the matter superfields γ (αs(Q2)) . En route we prove another theorem: the absence of the so-called singlet contribution to D . While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Marking up lattice QCD configurations and ensembles
P.Coddington; B.Joo; C.M.Maynard; D.Pleiter; T.Yoshie
2007-10-01
QCDml is an XML-based markup language designed for sharing QCD configurations and ensembles world-wide via the International Lattice Data Grid (ILDG). Based on the latest release, we present key ingredients of the QCDml in order to provide some starting points for colleagues in this community to markup valuable configurations and submit them to the ILDG.
THE TOP QUARK, QCD, AND NEW PHYSICS.
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.
On-Shell Methods in Perturbative QCD
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-04-25
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.
Exploring Hyperons and Hypernuclei with Lattice QCD
S.R. Beane; P.F. Bedaque; A. Parreno; M.J. Savage
2005-01-01
In this work we outline a program for lattice QCD that would provide a first step toward understanding the strong and weak interactions of strange baryons. The study of hypernuclear physics has provided a significant amount of information regarding the structure and weak decays of light nuclei containing one or two Lambda's, and Sigma's. From a theoretical standpoint, little is known about the hyperon-nucleon interaction, which is required input for systematic calculations of hypernuclear structure. Furthermore, the long-standing discrepancies in the P-wave amplitudes for nonleptonic hyperon decays remain to be understood, and their resolution is central to a better understanding of the weak decays of hypernuclei. We present a framework that utilizes Luscher's finite-volume techniques in lattice QCD to extract the scattering length and effective range for Lambda-N scattering in both QCD and partially-quenched QCD. The effective theory describing the nonleptonic decays of hyperons using isospin symmetry alone, appropriate for lattice calculations, is constructed.
Effective charges and expansion parameters in QCD
Braaten, E.; Leveille, J.P.
1981-10-01
The momentum subtraction scheme MOM has been empirically successful in producing small QCD corrections to physical quantities at one loop order. By explicit calculations, we show that with a suitable shift in the renormalization scale, the minimal subtraction scheme coupling constant ..cap alpha../sub MS/ coincides with typical momentum scheme coupling constants at both one and two loop order.
Pluto collaboration
1981-02-01
Results obtained with the PLUTO detector at PETRA are presented. Multihadron final states have been analysed with respect to clustering, energy-energy correlations and transverse momenta in jets. QCD predictions for hard gluon emission and soft gluon-quark cascades are discussed. Results on ..cap alpha../sub s/ and the gluon spin are given.
Schvellinger, Martin
2008-07-28
We briefly review one of the current applications of the AdS/CFT correspondence known as AdS/QCD and discuss about the calculation of four-point quark-flavour current correlation functions and their applications to the calculation of observables related to neutral kaon decays and neutral kaon mixing processes.
The Chroma Software System for Lattice QCD
Robert Edwards; Balint Joo
2004-06-01
We describe aspects of the Chroma software system for lattice QCD calculations. Chroma is an open source C++ based software system developed using the software infrastructure of the US SciDAC initiative. Chroma interfaces with output from the BAGEL assembly generator for optimized lattice fermion kernels on some architectures. It can be run on workstations, clusters and the QCDOC supercomputer.
Varelas, N.; D0 Collaboration
1997-10-01
We present recent results on jet production, dijet angular distributions, W+ Jets, and color coherence from p{anti p} collisions at {radical}s = 1.8 TeV at the Fermilab Tevatron Collider using the D0 detector. The data are compared to perturbative QCD calculations or to predictions of parton shower based Monte Carlo models.
QCD in hadron-hadron collisions
Albrow, M.
1997-03-01
Quantum Chromodynamics provides a good description of many aspects of high energy hadron-hadron collisions, and this will be described, along with some aspects that are not yet understood in QCD. Topics include high E{sub T} jet production, direct photon, W, Z and heavy flavor production, rapidity gaps and hard diffraction.
Factorization and other novel effects in QCD
Brodsky, S.J.
1983-09-01
Recent progress in proving the validity of factorization for inclusive reactions in QCD is reviewed. A new necessary condition involving the target length is emphasized. We also discuss a number of novel effects in gauge theory including null zone phenomena, color transparency, formation zone conditions, and possible heavy quark Fock states components in ordinary hadrons. 36 references.
Dual condensate and QCD phase transition
Zhang Bo; Bruckmann, Falk; Fodor, Zoltan; Szabo, Kalman K.; Gattringer, Christof
2011-05-23
The dual condensate is a new QCD phase transition order parameter, which connnects confinement and chiral symmetry breaking as different mass limits. We discuss the relation between the fermion spectrum at general boundary conditions and the dual condensate and show numerical results for the latter from unquenched SU(3) lattice configurations.
Visualization Tools for Lattice QCD - Final Report
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, 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.
Heavy quark masses from lattice QCD
NASA Astrophysics Data System (ADS)
Lytle, Andrew T.
2016-07-01
Progress in quark mass determinations from lattice QCD is reviewed, focusing on results for charm and bottom mass. These are of particular interest for precision Higgs studies. Recent determinations have achieved percent-level uncertainties with controlled systematics. Future prospects for these calculations are also discussed.
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N_{C} → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower