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.

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.

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 ofvarious local quark and gluon vacuum condensates,quark-gluon mixed vacuum condensate,quark and gluon virtualityin QCD vacuum state,quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted byuse of the solutions of Dyson Schwinger equations in'rainbow'approximation with a modeling gluon propagator andthree different sets of quark-quark interaction parameters.Our theoretical predictions are in good agreement with thecorrespondent empirical values used widely in literature,and many other theoretical calculations.The quark propagatorand self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations.This work iscentrally important for studying non-perturbative QCD,and has many important applications both in particle andnuclear physics.

Dynamical Model of QCD Vacuum and Quark Confinement

The phase transition of a simple local gauge model is investigated in terms of the Nambu–Jona-Lasinio mechanism and it is pointed out that the physical vacuum of QCD is bound state of quark-antiquark pairs which can be viewed, generally, as a nearly perfect color dia-electric medium. An important relation between the vacuum expectation value of gauge fields and scalar fields is also derived by solving the Euler equation for the gauge fields. Based on this relation the gauge potential is given which can be used to explain the asymptotic behavior and confinement of quarks in a hadron, and at the same time the Yukawa potential of strong interaction can be given too.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

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,

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.

Prediction of Cosmological Constant Λ in Veneziano Ghost Theory of QCD

Based on the Veneziano ghost theory of QCD, we estimate the cosmological constant Λ, which is related to the vacuum energy density, , by =8πG . In the recent Veneziano ghost theory is given by the absolute value of the product of the local quark condensate and quark current mass: =(2NfH/m)*c|mq<0|:qq:|0>|.By solving Dyson-Schwinger Equations for a dressed quark propagator, we found the local quark condensate;-(235 MeV)3, the generally accepted value. The quark current mass is mq 4.0 Mev. This gives the same result for as found by previous authors, which is somewhat larger than the observed value. However, when we make use of the nonlocal quark condensate, =g(x), with g(x) estimated from our previous work, we find Λ is in a good agreement with the observations.

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.

Virtualities of quark and gluon in QCD vacuum

The non-local vacuum condensates of quantum chromodynamics (QCD) describe the distributions of quarks and gluons in the non-perturbative QCD vacuum state. Physically, this means that vacuum quarks and gluons have a nonzero mean-squared momentum in the vacuum, called virtuality. The quark virtuality is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The gluon virtuality is expressed by gluon vacuum condensates and four-quark vacuum condensates. We study the two virtualities by solving Dyson-Schwinger Equations and calculating quark and gluon vacuum condensates. Our theoretical results for quark virtuality are in good agreement with many other theoretical model predictions such as QCD sum rules and lattice QCD calculations. Our calculation on gluon virtuality is initial and the results are quite interesting.

A comparison of condensate mass of QCD vacuum between Wilson line approach and Schwinger effect

We studied the condensate mass of QCD vacuum through the duality approach via dilaton wall back-ground in the presence of the parameter c,which represents the condensation in a holographic set up.First,fromWilson line calculation,we found m_(0)^(2)(i.e.,the condensate parameter in mixed non-local condensation),whose beha-vior mimics that of QCD.The value of m_(0)^(2)that we found by this approach is in agreement with QCD data.Second we considered the produced mass m via the Schwinger effect mechanism in the presence of the parameter c.We show that vacuum condensation generally contributes the mass dominantly and that the produced mass via Schwing.er effect is suppressed by m_(0).

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.

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。

重夸克偶素中的非微扰QCD效应(英文)

在势模型的框架下，通过粲夸克偶素及底夸克偶素能谱的计算，研究了由高维夸克胶子凝聚描述的非微扰ＱＣＤ效应结果表明：六维算符真空凝聚仍有明显的贡献；单圈微扰修正在散射和湮灭过程中的贡献几乎相同。

Theoretical prediction of cosmological constant ∧ in Veneziano ghost theory of QCD

Based on the Veneziano ghost theory of QCD, we predict the cosmological constant A, which is related to energy density of cosmological vacuum by A = 3-8tG/pA. In the Veneziano ghost theory, the vacuum energy density PA is expressed by absolute value of the product of quark vacuum condensate and quark current mass： PA = 2g/Hclmq（OI ： qq ： 10）l- We calculate the quark local vacuum condensates （01 ： qq ： 10） by solving Dyson Schwinger Equations for a fully dressed confining quark propagator S/（p） with an effective gluon propagator G^b（q）. The quark current mass mq is predicted by use of chiral perturbation theory. Our theoretical result of A, with the resulting （01 ： qq ： ]0} = -（235 MeV）3 and light quark current mass rnq = 3.29 6.15 MeV, is in a good agreement with the observable of the A =10-52 m-2 used widely in a great amount of literatures. Keywords cosmological constant A, Veneziano sate, quantum chromodynamics （QCD） ghost theory of QCD, local quark vacuum conden-

QCD求和规则与强子物理

量子色动力学(QCD)求和规则是强子物理研究中的一种重要的非微扰方法,已经成为强子物理与核物理研究中有力的工具。简单介绍了QCD求和规则的基本概念、方法与应用,特别讨论了QCD求和规则近年来的发展和与之相关的一些前沿问题。

非微扰QCD和核遮蔽效应对K因子的影响

考虑非微扰量子色动力学物理真空夸克凝聚效应,计算了碳核与碳核在质心系能量分别为630和200 GeV时碰撞Drell-Yan过程的K因子,以及加入核遮蔽因子后非微扰效应对K因子的影响,并把计算结果与没有考虑夸克凝聚非微扰效应的K值进行了对比。结果表明,非微扰效应和核遮蔽效应对K因子影响很小。

Modified Approach for Calculating Four-Quark Condensates

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background tield as an illustration, we extract a general formula for the four-quark condensate （0： q（0）γμq（0）q（0）γμq（0） ： ｜0）. This formula contains the corresponding fully dressed vector vertex. We use this formula to analyze the factorization problem of the four-quark condensate and show that in the bare vertex approximation factorization holds exactly.

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.

金核与金核碰撞Drell-Yan过程QCD非微扰效应对K因子的影响

在考虑QCD物理真空夸克凝聚非微扰效应下,详细计算了金核与金核碰撞Drell-Yan过程的K因子,并把计算结果与没有考虑夸克凝聚非微扰效应的K值进行了对比.结果表明,非微扰效应对K因子影响很小.