The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that the mixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded as an additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from some ansatz for the gluon propagator are compared with those determined from QCD sum rules.     

Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in “rainbow” approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The values of various local quark vacuum condensates, quark-gluon mixed vacuum condensates, and the structure of non-local quark vacuum condensate are predicted by the solution of Dyson-Schwinger Equations in "rainbow" approximation with three sets of different parameters for effective gluon propagator. The light quark virtuality is also obtained in a consistent way. Our all theoretical results here are in good agreement with the empirical values used widely in literature and many other theoretical calculations.     

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

Propagators and Masses of Light Quarks

Based on Dyson-Schwinger equations in “rainbow“ approximation, fully dressed confining quark propagator is obtained, and then the masses of light quarks (mu, md, and ms) are derived from the fully dressed confining quark propagator. At the same time, the local and non-local quark vacuum condensates as well as the quark-gluon mixed condensate are also predicted. Furthermore, the quark masses are also deduced from the Gell-Mann-Oakes-Renner relation and chiral perturbative theory. The results from different methods are consistent with each other.     

Self-consistent treatment of one-gluon exchange in the soliton bag model

In the context of the soliton bag model, the quarks, soliton field and the gluon propagator are calculated self-consistently in the mean-field, one-gluon exchange approximation. The use of a confined propagator, as compared with a free propagator, is primarily to change the effective quark-gluon coupling constant by a factor of approximately two in the case of static, spherical bags. Self-consistency leads to only a small improvement in the fit to physical data, after readjustment of model parameters. Nevertheless, use of a confined propagator is expected to have an important effect on deformed bags and in dynamical calculations.     

Propagators and Masses of Light Quarks

Based on Dyson-Schwinger equations in “rainbow” approximation, fully dressed confining quark propagator is obtained, and then the masses of light quarks (mu, md, and ms) are derived from the fully dressed confining quark propagator. At the same time, the local and non-local quark vacuum condensates as well as the quark-gluon mixed condensate are also predicted. Furthermore, the quark masses are also deduced from the Gell-Mann-Oakes-Renner relation and chiral perturbative theory. The results from different methods are consistent with each other.     

非微扰QCD真空中夸克真空凝聚的结构(英文)

基于Dyson-Schwinger方程(DSEs)所确定的夸克传播子和算符成积展开(OPE),在彩虹近似下,预言了QCD真空中非定域夸克真空凝聚的结构。这种结构由夸克自能函数Af和Bf决定,通过数值求解DSEs就可以得到这些自能函数。但是,直接数值求解DSEs方程非常复杂,这里采用Roberts和Williams提出的参数化方法,用参数化的夸克传播函数σf v(p2)和σf s(p2)计算夸克自能函数。同时,也计算了定域的夸克真空凝聚值,夸克胶子混合的真空凝聚值,以及夸克的虚度。理论预言和计算结果均与标准QCD求和定则、格点QCD和瞬子模型的理论结果大致相符。和这些模型的结果相比,参数化方法得到的轻夸克(u,d,s)的定域真空凝聚偏大,这主要是由于模型依赖导致的。与u,d夸克相比,s夸克的真空凝聚比较大,这是因为s夸克自身质量较大的缘故。当然,Roberts-Williams参数化的夸克传播子只是一个经验公式,只能近似描述夸克的传播。     

Vacuum Condensates from the Modification of Global Color Symmetry Model

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate , the mixed quark gluon condensate g,μνσ^μνq) and the four-quark condensate at the mean-field level in the framework of global color symmetry model. The numerical calculation shows that our result is compatible with the range obtained within other nonperturbative approaches. In particular, we have found that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.     

Light 0- Meson Solution of Bethe-Salpeter Equation Involving the Vacuum Condensates in QCD

We dkcuss the Bethe-Salpeter equation involving the vacuum condensates in QCD in the backgrouud fields. The bound state equation for the light 0^- meson (π and K) is solved in the ladder approximation of single gluon exchange, where the gluon propagator is calculated in tree level of a gluon condensate and a quark condensate. The kernel is divided into two parts: perturbative and non-pert,urbative. The non-perturbative part is determined by the vacuum condensate. Pseudo-scalar meson spectrum and decay constants are in good agreement with data.     

高能重离子非对心碰撞中的整体夸克极化

There exists a large local relative orbital angular momentum between produced partons along the direction opposite to the reaction plane in the early stage of non-central heavy-ion collisions. This initial local orbital angular momentum can lead to quark polarization along the same direction due to spin-orbital coupling in QCD. We present the quark polarization by using hard thermal loop gluon propagator for quark-quark scattering in quark-gluon plasma and compare it with the result obtained from the static potential model.     

Low-Energy Scattering of Heavy-Light Mesons from Nucleons

We study the low-energy scattering of charmed (D) and strange (K) mesons by nucleons. The short-distance part of the interaction is due to quark-gluon interchanges derived from a model that realizes dynamical chiral symmetry breaking and confines color. The quark-gluon interaction incorporates a confining Coulomb-like potential extracted from lattice QCD simulations in Coulomb gauge and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The long-distance part of the interaction is due to single vector (??, ??) and scalar (??) meson exchanges. We show results for scattering cross-sections for isospin I?=?0 and I?=?1.     

Plane-wave,coordinate-space,and moment techniques in the operator-product expansion: Equivalence,improved methods,and the heavy quark expansion

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.     

UA(1) anomaly and $ \eta^{{\prime}}_{}$ -mass from an infrared singular quark-gluon vertex

The U _A(1) problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the -mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as ∼ 1/k ⁴ . We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass.     

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.     

Non-perturbative Quark Propagator and the Study of the Non-trivial Q2 Dependence in the Nucleon Structure Functions

In consideration of the lowest order non-perturbative effect due to the quark condensate <qq>and gluon condensate on the quark propagator,we calculate QCD non-pertubative quark propagator under the chain approximation.Using the obtained non-perturbative quark propagator,we analyse the non-perturbative effect in the nucleon structure functions and show the non-trivial Q²-dependence in the nucleon structure functions.     

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one should use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.     

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 Effective Gluon Propagator in the Global Color Symmetry Model

It is shown that the effective gluon propagator in the global color symmetry model can be calculated in the instanton dilute liquid approximation. The calculated effective gluon propagator is consistent with the general command on the qualitative features of the gluon propagator, i.e., (i) the gluon propagator is significantly enhanced at small space-like k², and (ii) for k² > 1.5 GeV² the perturbative results are quantitatively reliable.