Effect of a Small Current Quark Mass on Bag Constant

A method for obtaining the small current quark mass effect on the dressed quark propagator within the Dyson Schwinger approach is developed. From this the small current quark mass dependence of the bag constant is evaluated. It is found that the bag constant decreases with the increasing current quark mass and the contribution of the current quark mass cannot be dropped.     

Probing Quark Loop Effects on Dressed Gluon Propagator

We study the quark loop effects on the dressed gluon propagator and also on the quark propagator itself. We find that the gluon propagators are different in two phases. The quark mass effects on the gluon propagator are small but not negligible. We also study the current quark mass dependence on the bag constant.     

Effect of a Small Current Quark Mass on Bag Constant

A method for obtaining the small current quark mass effect on the dressed quark propagator within the Dyson-Schwinger approach is developed. From this the small current quark mass dependence of the bag constant is evaluated. It is found that the bag constant decreases with the increasing current quark mass and the contribution of the current quark mass cannot be dropped.     

Applicability of Parametrized Form of Fully Dressed Quark Propagator

According to extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the "rainbow" approximation with an effective gluon propagator, a parametrized fully dressed confining quark propagator is suggested in this paper. The parametrized quark propagator describes a confined quark propagation in hadron, and is analytic everywhere in complex p2-plane and has no Lehmann representation. The vector and scalar self-energy functions [1 - Af(p2)] and [Bf(p2) - mf], dynamically running effective mass of quark Mf(p2) and the structure of non-local quark vacuum condensates as well as local quark vacuum condensates are predicted by use of the parametrized quark propagator. The results are compatible with other theoretical calculations.     

Validity of Parametrized Quark Propagator

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow”approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p2-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on selfenergy functions A/(p2), Bl(p2) and effective mass M$(p2) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.     

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.     

关于夸克质量问题

指出了研究夸克质量的重要性、 科学意义和夸克质量产生的机制。 用夸克传播子定义了夸克的质量, 进而讨论了夸克的有效质量。 最后指出了存在的问题和研究前景。 Importance, scientific significance of studying quark mass, and the production mechanisim of quark mass have been pointed out. The quark mass is defined by quark propagator and from this definition we calculate effective mass of quark. Finally we also point out some open problems and perspective of this research field.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A(p2) in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Scalar Susceptibility of QCD from Dyson-Schwinger Approach

In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Effect of a Small Current Quark Mass on Dressed Gluon and Quark Propagator

Based on the Dyson-Schwinger approach, a method for obtaining the small current quark mass effect on the dressed gluon and quark propagator is developed. A comparison with the results of the previous approach is given.     

Numerically Solving Quark-Loop Effects on Dressed Gluon Propagator in Chiral Limit

We do a numerical calculation on the quark-loop effects on the dressed gluon propagator in the chiral limit. It is found that the quark-loop effects on the dressed gluon propagator are significant in solving the quark propagator in the rainbow approximation of the Dyson-Schwinger equation. The approach we used here is quite general and can also be used to calculate both the chemical potential and current quark mass dependence of the dressed gluon propagator.     

Ratio of a strange quark mass ms to up or down quark mass mu,d predicted by a quark propagator in the frameworkof the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass m_s to up or down quark mass m_u,d. The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory (χ PT) with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p²-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio m_s/m_u,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.     

自能函数和夸克的动力学质量(英文)

研究夸克的质量是QCD研究中的一个非常重要问题。因为, 夸克质量是标准模型的基本输入参数, 准确地确定这些参数无论对于唯象的应用还是对于理论的应用都是极其重要的。基于参数化的完全穿衣服的夸克传播子, 研究了自能函数和夸克的动力学质量。理论预言了夸克质量和自能函数, 其结果与文献中的经验值相符合, 也与Dyson Schwinger方程解一致。反过来这也说明了参数化的夸克传播子是成功和可靠的。Study of mass of quark is one of the most important issues in the investigation of QCD. Because masses of quarks are fundamental QCD input parameters of standard Model, and an accurate determination of these parameters is extremely important for both phenomenological and theoretical applications. Based on the parameterized fully dressed quark propagator proposed by us, the theoretical predictions of the masses of quarks are predicted in this short note. The effective quark mass is defined by the scalar self energy function Bf(p2) and vector self energy function Af(p2). The results of our calculations are in agreement with the empirical values used widely in literature and also show that the parameterized form of quark propagator is an applicable and reliable approximation.     

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。     

Real-Time Thermal Schwinger-Dyson Equation for Quark Self-energy in Landau Gauge

By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A(p2)p - B(p2), we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A(p2) = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.     

Unquenched Effects and Quark Mass Dependence of Lattice Gluon Propagator in Infrared Region

In this paper, the gluon propagator in Landau gauge has been studied on a lattice, including the quenched and the unquenched one. The small geometry size of lattice we use is 16³×32, and the big one is 20³×64. For the quenched approximation, we fit the numerical results and give a little different fitting values. We also obtain unquenched effects by comparing the gluon propagator resulting from the quenched and unquenched configurations, for both the two-flavor and three-flavor cases. For the unquenched configurations, an obvious quark mass dependence has not been found in the small quark mass case, but is found in the three-flavor case when the quark mass is big.     

Massive Meson Fluctuation in NJL Model

Based on the self-consistent scheme beyond the mean-field approximation in the large N_c expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of N_c,an approximate internal meson propagator is deduced, which is in order of O(l/N_c). In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show that, different &om the mean-field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond the meanfield approximation.     

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.     

Parametrization of Fully Dressed Quark Propagator

Based on an extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow” approximation, a parametrized form of the quark propagator is suggested. The corresponding quark self-energy Σ_f and the structure of non-local quark vacuum condensate <0|:\bar{q}(x)q(0):|0> are investigated. The algebraic form of the quark propagator proposed in this work describes a confining quark propagation, and is quite convenient to be used in any numerical calculations.