Lattice QCD

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.     

Supersymmetry on the lattice

Supersymmetric gauge theories are fascinating for a number of reasons. However, unlike QCD, it was not known until recently how to devise a nonperturbative lattice construction for these theories. This has changed dramatically in recent years, and in these lectures I outline some of the recent progress, which expands our understanding of what is possible in lattice field theories in general.     

核子(强子)结构和性质的QCD研究

核子 (强子 )是夸克、胶子的束缚态 ,由量子色动力学 QCD描述。由于 QCD的基本特性(高能标度下的渐近自由、低能标度下色禁闭及动力学手征对称性破缺 ) ,对核子 (强子 )结构和性质的 QCD图象是标度相关的 .在高能标度下描述强子的是与探测强子结构的硬过程相联系的QCD部分子模型 .强子的夸克、胶子结构信息通过 QCD部分子求和规则得到 .QCD微扰论是适用的理论 .在低能标度时 ,必须发展 QCD非微扰途径来描述核子 (强子 )物理 .这里简要地讨论各种非微扰途径 (格点 QCD、Dyson- Schwinger方程、有效场论、QCD求和规则 )的某些结果和进展 ,并指出 QCD真空结构在描述低能标度下强子物理中担任重要角色 . The nucleon (hadron) is the bound state of guarks and gluons, which is described by the quantum chromodynamics (QCD). Due to the basic properties of QCD (the asymptotic freedom at the high energy scale, the color confinement and the dynamical chiral symmetry breaking at the low energy scale), the QCD picture for the nucleon’s (hadron’s) structure and property is scale dependent. At high energy scale, the QCD parton model, which is relative to the hard process for testing the...     

Evidence for instanton-induced dynamics from lattice QCD

We perform a study of the nonperturbative dynamics of the light-quark sector of QCD, based on some recent results of lattice simulations with chiral fermions. We analyze some correlators that are designed to probe the Dirac structure of the quark-quark interaction at different scales. We show that, in the nonperturbative regime, such an interaction contains very large scalar and pseudoscalar components. We observe quantitative agreement between lattice QCD results and the predictions of the instanton liquid model. Moreover, we study how the quark-quark interaction is modified, when quark loops are suppressed. We observe a dramatic effect related to the loss of unitarity, which is naturally explained in the instanton picture. Such an effect cannot be explained in a Dyson-Schwinger equations (DSE) approach, if one assumes a vector quark-gluon coupling.     

What lattice calculations can tell us about the gluon gas

Higher order perturbative and nonperturbative corrections to the grand potential of hot QCD are considered qualitatively Comparing with lattice results, it is argued that the nonperturbative parts are small but that the O(g⁴) term in $\text{Ω}$ is large and positive.     

Nonperturbative phenomena in QCD at finite temperature

The main objective of the present study is to analyze various nonperturbative phenomena in QCD both at low, T < T _c , and at high, T > T _c , temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCD on a lattice and, on the other hand, to study new physical phenomena in QCD at finite temperature.     

Two-flavor QCD correction to lepton magnetic moments at leading order in the electromagnetic coupling

We present a reliable nonperturbative calculation of the QCD correction, at leading order in the electromagnetic coupling, to the anomalous magnetic moment of the electron, muon, and tau leptons using two-flavor lattice QCD. We use multiple lattice spacings, multiple volumes, and a broad range of quark masses to control the continuum, infinite-volume, and chiral limits. We examine the impact of the commonly ignored disconnected diagrams and introduce a modification to the previously used method that results in a well-controlled lattice calculation. We obtain 1.513(43)×10(-12), 5.72(16)×10(-8), and 2.650(54)×10(-6) for the leading-order two-flavor QCD correction to the anomalous magnetic moment of the electron, muon, and tau, respectively, each accurate to better than 3%.     

Instantons in the nonperturbative QCD vacuum

The effect of nonperturbative fields on instantons in QCD is investigated. The nonperturbative vacuum is described in terms of nonlocal gauge-invariant vacuum expectation values of gluon fields. An effective action for instantons is obtained in the bilocal approximation, and it is shown that a stochastic background gluon field leads to an infrared stabilization of instantons. The dependence of a characteristic instanton size on the magnitude of the gluon condensate and on the correlation length in the nonperturbative vacuum is found. The size distribution of instantons that is obtained here is compared with the results of lattice calculations.     

Analytic methods in nonperturbative QCD

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quarkgluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations.     

夸克胶子等离子体中的次带头阶得拜屏蔽质量

采用实时有限温度下的QCD,考虑到胶子的衰减率计算了QGP中次领头阶得拜屏蔽质量的贡献,克服了通常计算中的红外发散的困难,且不必引入非微扰的磁屏蔽质量作红外截断.指出了所得结果的正定性和规范无关性并与格点模拟的结果进行了比较.     

On the next-to-leading order Debye screening mass in QGP

The next-to-leading order Debye screening mass in QGP is calculated by taking into account the damping rate of gluons in the formalism of real time finite temperature QCD, and the infrared singularity of the naive calculation is cured without adding a nonperturbative magnetic screening mass as a cutoff. In addition, the result is shown to be postive and gauge-independent, and is compared with the results from lattice simulations.     

On the next-to-leading order Debye screening mass in QGP

The next-to-leading order Debye screening mass in QGP is calculated by taking into account the damping rate of gluons in the formalism of real time finite temperature QCD, and the infrared singularity of the naive calculation is cured without adding a nonperturbative magnetic screening mass as a cutoff. In addition, the result is shown to be postive and gauge-independent, and is compared with the results from lattice simulations.     

Intermediate Range Force Contributions to Dynamical Chiral Symmetry Breaking in QCD

We propoee the intermediate range QCD force singular like δ(q) by analysing the gluon propagator in the nonperturbative region from QCD sum rules. With the help of the Slavnov- Taylor-Ward identity we derive the equations for the nonperturbative quark propagator from the Schwinger-Dyson (SD) equation. Solutione for the quark propagator in two special cases are given. We find that the intermediate range force L also responsible for the chiral symmetry breaking in QCD.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

The QCD spectrum: Mixing,strong decays,and the role of sea quarks

The light hadron spectrum as computed in nonperturbative QCD is reviewed and compared to lattice data and experiment. The mixing of mesons, hybrids, and glueballs is calculated in the field correlator method. The strong decay mechanisms are found in the method and compared to the known phenomenological models. The role of sea quarks (unquenched approximation) is studied analytically, using radially excited mesons as an example, and compared to experiment.     

Testing static quark-antiquark potentials with bottomonium

We investigate the question of whether experimental data on the energy levels of bottomonium can discriminate between quark-antiquark potentials which are motivated by what we know about QCD and potentials which are purely phenomenological. We restrict ourselves to bottomonium because, of all the quarkonia observed thus far, bottomonium is the least relativistic and therefore the best testing ground for the static quarkonium potential. We consider two potentials whose functional form is motivated from perturbative QCD at short quark-antiquark separations and from nonperturbative lattice QCD at large separations. We also consider three strictly phenomenological potentials. We find that the best of the three phenomenological potentials, which has never been previously used, fits the spin-averaged data at least as well as the best of the QCD-motivated potentials. We propose further measurements on bottomonium energy levels to provide additional tests.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

Anti-de sitter/conformal-field-theory calculation of screening in a hot wind

One of the challenges in relating experimental measurements of the suppression in the number of J/psi mesons produced in heavy ion collisions to lattice QCD calculations is that whereas the lattice calculations treat J/psi mesons at rest, in a heavy ion collision a cc[over ] pair can have a significant velocity with respect to the hot fluid produced in the collision. The putative J/psi finds itself in a hot wind. We present the first rigorous nonperturbative calculation of the consequences of a wind velocity v on the screening length L(s) for a heavy quark-antiquark pair in hot N=4 supersymmetric QCD. We find L(s)(v,T)=f(v)[1-v(2)](1/4)/piT with f(v) only mildly dependent on v and the wind direction. This L(s)(v,T) approximately L(s)(0,T)/sqrt[gamma] velocity scaling, if realized in QCD, provides a significant additional source of J/psi suppression at transverse momenta which are high but within experimental reach.     

Single spin asymmetries in high energy reactions and nonperturbative QCD effects

We discuss some experimental and theoretical results on single spin asymmetries (SSA) in high energy lepton-hadron and hadron-hadron reactions. In particular, recent results on meson SSA obtained by HERMES are considered in detail. We also discuss the SSA results obtained recently by COMPASS, as well as those from BRAHMS, PHENIX and STAR. Special attention is paid to a possible nonperturbative QCD mechanism that might be responsible for the observed meson SSA. This mechanism originates from the spin-flip quark-gluon chromomagnetic interaction induced by the complex topological structure of the QCD vacuum. We argue that in semi-inclusive deep-inelastic scattering a large SSA is expected not only for mesons but also for baryons due to strong nonperturbative final state interactions between ud-diquark and u-quark in the fragmenting proton.     

对单胶子交换势的非微扰修正研究

对单胶子交换势的非微扰修正进行了系统研究,结果表明,要获得规范不变的修正形式,QCD真空胶子场必须取为协变规范.在协变规范下,给出了单胶子交换势的非微扰修正的新形式.