Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.

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 p^2-plane and has no Lehmann representation. The vector and scalar self-energy functions [1 - Af（p^2）] and [Bf（p^2） - mf], dynamlcally running effective mass of quark Mf（p^2） 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 axe compatible with other theoretical calculations,

Parametrization of Fully Dressed Quark Propagator

Based on an extensive study of the Dyson-Schwinger equations for a fullydressed quark propagator in the 'rainbow' approximation, a parametrized form of the quark propagatoris suggested. The corresponding quark self-energy Σ_f and tie structure of non-local quark vacuumcondensate 【 0 | : q(x)q(0) : | 0 】 are investigated. The algebraic form of the quark propagatorproposed in this work describes a confining quark propagation, and is quite convenient to be used inany numerical calculations.

Dependence of Quark Effective Mass on Gluon Propagators

Based on Dyson Schwinger Equations （DSEs） in the “rainbow” approximation, the dependence of quark effective mass on gluon propagator is investigated by use of three different phenomenological gluon propagators with two parameters, the strength parameter x and range parameter △. Our theoretical calculations for the quark effective mass Mf（p^2）, defined by the self-energy functions Af（p^2） and Bi（p%2） of the DSEs, show that the dynamically running quark effective mass is strongly dependent on gluon propagator. Therefore, because gluon propagator is completely unknown, the quark effective mass cannot be exactly determined theoretically.

Tensor Susceptibilities of QCD Vacuum and Parameterized Quark Propagator

Based on the parameterized fully dressed quark propagator proposed by us, the tensor susceptibilities of QCD vacuum and quark vacuum condensates are investigated. Our predicted values of the tensor susceptibilities are in agreement with those predicted by many other theoretical models with QCD feature. The results also show that the tensor susceptibility of QCD vacuum strongly depends on flavor of quark but not sensitive to variation of quark vacuum condensates. However, the quark vacuum condensate is very sensitive to the change of cut-off-parameter μ^2 of the integration, that is, it depends on the separation point of perturbative and non-perturbative QCD region. The successful predictions clearly indicate the extensive validity of our parameterized fully dressed quark propagator used here.

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.

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.

Dynamical Running Mass of Quark in the Dyson－Schwinger Equation Approach

Based on the Dyson–Schwinger equations of QCD in the 'rainbow' approximation, the fully dressed quark propagator is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes and built up the fully dressed quark propagator and the dynamical running masses defined by and for light quarks u, d and s are calculated, respectively. Using the predicted running masses , quark condensates for u, d quarks, and for s quark, and experimental pion decay constant , the masses of Goldstone bosons K, π, and η are also evaluated. The numerical results show that the masses of quarks are dependent on their momentum . The fully dressed quark amplitudes and have correct behaviors which can be used for many purposes in our future researches on nonperturbative QCD.

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（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.

Pion Decay Constant and Masses of Light Quarks and In-medium Goldstone Bosons

Based on the fully dressed confining quark propagator, the pion decay constant fπ, local quark vacuum condensate, and the masses of light quarks and in-medlum Goldstone bosons are investigated. The pion decay constant fπ is predicted and compared with its value of experimental measurement. A great agreement is obtained. With the predicted fπ and values of Goldstone boson masses measured by experiments in free configuration the current masses of light quarks and the masses of in-medium Goldstone bosons are obtained.

Ratio of a strange quark mass m_s to up or down quark mass m_(u,d) predicted by a quark propagator in the framework of the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass ms to up or down quark mass mu,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 （χPT） 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 ms/mu,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.

从流夸克质量到组分夸克质量的动力学过渡的研究

在彩虹近似下用Dyson Schwinger方程研究了禁闭夸克的传播子 ,得到了夸克动力学质量随动量变化的关系 ,即得到了从流夸克质量到组分夸克质量的动力学过渡 .

夸克的真空凝聚值和张量感应率及参数化的夸克传播子

利用以前提出的参数化的夸克传播子,计算了夸克的真空凝聚值和QCD真空的张量感应率。结果表明,张量感应率对不同味道的夸克的依赖是很明显的,而几乎不依赖于夸克的真空凝聚值的变化。但夸克凝聚值却明显地与积分的截断值有关,即依赖于微扰区与非微扰区的分界线,在常用的积分截断值1—2GeV2之间计算得到的夸克凝聚值与文献中常用的值及其他理论的预言值是一致的。理论预言的张量感应率也与其他理论结果相一致。

非定域夸克真空的结构和Kisslinger函数

夸克的真空凝聚是量子色动力学(QCD)研究中一个非常重要的问题。用完全穿衣服的夸克传播子研究了QCD真空性质和夸克的真空结构。计算了定域夸克的真空凝聚值,预言了夸克的真空结构。其结果与文献中的经验值相符合,也与Dyson-Schwinger方程解一致。说明参数化的夸克传播子是成功和可靠的。

QCD真空凝聚和参数化的夸克传播子

基于整体色对称模型,用完全穿衣服参数化的夸克传播子研究了量子色动力学(QCD)真空的性质,预言了各种表征QCD真空的凝聚值。其结果与其他唯象QCD理论模型的预言是一致的。结果清楚地表明了参数化的夸克传播子是成功和可靠的。讨论了计算QCD真空凝聚值时积分截断参数的问题,提出了一个避免计算的结果对截断参数强烈依赖的物理方法。

核介质中的夸克凝聚

在讨论了夸克真空凝聚的基础上 ,本文研究了核介质中夸克凝聚随介质密度变化的规律—即随着介质的密度的增加而减少。这对于研究相对论重离子碰撞及在核介质中介子动力学等问题是非常重要的。

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。

在QCD中核子的静态性质

基于参数化的完全穿衣服的夸克传播子,利用量子色动力学(QCD)研究了核子的磁矩和电荷半径平方的平均值与夸克动量的依赖关系。预言的核子磁矩和电荷半径的数值与文献中广泛应用的经验值和其他许多具有QCD特征的理论模型所预言的值一致。结果说明了核子的磁矩和电荷半径不是人们通常所理解的一个不变的常数,而是依赖于核子中夸克动量的一个跑动量,对于不同动量它们的值是不同的。计算结果也清楚地表明了所采用的参数化的夸克传播子的适用性和可靠性。

量子色动力学(QCD)求和定则在密物质的结果

讨论量子色动力学求和定则解决在真空及核物质中强子性质的方法。核物质情况下,关于谱函数的形式和确定的四夸克凝聚的值,初始的限制缺少可靠的唯象信息;这个方法给出了支持强吸引的Lorentz标量和推斥的Lorentz矢量光学势的Dirac唯象图像的适当证据。对介质中减少的矢量介子质量,这个方法提供了弱证据。

超越彩虹近似夸克传播子的DS方程研究

在QCD的DS方程方法框架下,文章研究了夸克-胶子顶点的着衣效应对夸克传播子的影响,也就是超越彩虹近似,利用BC顶点以及CP顶点对夸克传播子进行了系统的研究.结果发现,不论采用什么夸克-胶子顶点,夸克传播子在高动量区域趋于裸的夸克传播子,这个结论符合QCD的"渐近自由"特性.而在小动量区域,夸克传播子的着衣效应很大,出现了手征对称性自发破缺,夸克在低动量区域获得了很大的质量,并且不同的夸克-胶子顶点对夸克传播子的低动量区域的着衣效应差别很大.