Gasser-Leutwyler Coefficients of Chiral Lagrangian for Pseudoscalar Goldstone Bosons

Based on the Dyson-Schwinger equations in rainbow approximation for quark propagator with an effective gluon propagator, and on the parametrized fully dressed quark propagator proposed by us, the unknown Gasser-Leutwyler coefficients of the chiral Lagrangian for pseudoscalar Goldstone bosons, Li, are predicted respectively. The predicted values of Li in the two different ways are not only in reasonable agreement each other but also in agreement with empirical values used widely in literature and the values predicted by many other theoretical models with QCD characteristics. The compatible results of Gasser-Leutwyler coefficients predicted by our parameterized quark propagator,in turn, clearly verify its extensive validity.     

Gasser-Leutwyler Coefficients of Chiral Lagrangian for Pseudoscalar Goldstone Bosons

Based on the Dyson-Schwinger equations in raAnbow approximation for quark propagator with an effective gluon propagator, and on the parametrized fully dressed quark propagator proposed by us, the unknown GasserLeutwyler coeiticients of the chiral Lagrangian for pseudoscalar Goldstone bosons, Li, are predicted respectively. The predicted values of Li in the two different ways are not only in reasonable agreement each other but also in agreement with empirical values used widely in literature and the values predicted by many other theoretical models with QCD characteristics. The compatible results of Gasser-Leutwyler coefficients predicted by our parameterized quark propagator, in turn, clearly verify its extensive validity.     

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。     

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.     

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 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 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.     

Vacuum condensates of QCD

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

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.     

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 f_π, local quark vacuum condensate, and the masses of light quarks and in-medium Goldstone bosons are investigated. The pion decay constant f_π is predicted and compared with its value of experimental measurement. A great agreement is obtained. With the predicted f_π 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.     

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.     

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.     

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

［1］R.T. Cahill and C.D. Roberts, Phys. Rev. D32 (1985)2419. ［2］P.C. Tandy, Prog. Part. Nucl. Phys. 39 (1997) 117; C.D.Roberts, R.T. Chill, and J. Praschiflca, Ann. Phys. (N.Y.)188 (1988) 20; M.R. Frank, P.C. Tandy, and G. Fai, Phys.Rev. C43 (1991) 2808; M.R. Frank and P.C. Tandy, Phys.Rev. C49 (1994) 478; M.R. Frank and C.D. Roberts,Phys. Rev. C53 (1996) 390; P. Maris and C.D. Roberts,Phys. Rev. C56 (1997) 3369; C.W. Johnson and G. Fai,Phys. Rev C56 (1997) 3353; P. Maris, C.D. Roberts,and P.C. Tandy, Phys. Lett B420 (1998) 267; XiaoFu LU, Yu-Xin LIU, Hong-Shi ZONG and En-Guang ZHAO, Phys. Rev. C58 (1998) 1195; Hong-Shi ZONG,Xiao-Fu LU, Jian-Zhong GU, Chao-Hsi CHANG, and EnGuang ZHAO, Phys. Rev. C60 (.1999) 055208; Hong-Shi ZONG, Yu-Xin LIU, Xiao-Fu LU, Fan WANG, and EnGuang ZHAO, Commun. Theor. Phys. (Beijing, China)36 (2001) 187. ［3］M.R. Frank and T. Meissner, Phys. Rev. C53 (1996)2410. ［4］T. Meissner, Phys. Lett. B405 (1997) 8. ［5］C.D. Roberts and A.G. Williams, Prog. Part. Nucl. Phys.33 (1994) 477, and the references therein. ［6］H.B. Tang and R. J. Furnstahl, hep-ph/9502326. ［7］M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys.B147 (1979) 385. ［8］L. Reinders, H. Rubinstein, and S. Yazaki, Phys. Rep.127 (1985) 1; S. Narison, QCD Spectral Sum Rules, World Scientific, Singapore (1989), and the rererences therein. ［9］Hong-Shi ZONG, Jia-Lun PING, Hong-Ting YANG,Xiao-Fu LU, and Fan WANG, nuth-th/0201001. ［10］C.D. Roberts, A.G. Williams, and G. Krein, Int. J. Mod.Phys. A7 (1992) 5607.     

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.     

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.     

Infrared effects on the axial gauge quark propagator

The axial gauge quark propagator is studied when only the most singular infrared part of the gluon propagator is retained in the Dyson-Schwinger equation. With a new representation for the quark-gluon vertex a simple configuration space propagator and a momentum space form valid for all values of the gauge variable n · p are obtained. The propagator has no poles. The effective potential is minimized when there is no chiral symmetry breaking.     

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.     

Square-Root Operator Quantization and Nonlocality: A Review

A square-root-operator formalism is developed for quantum systems described with nonrelativistic and relativistic equations of motion. Spectral representation for Green's functions are designed for particles with spin 0, with the implication of its generalization to other spin values. Nonlocal operators suggest that a duality exists between physical particles and dual partners, which are tachyonic mathematical particles. It is shown that nonlocal operators result naturally from square-root operators, with the implication that microcausality holds only asymptotically. Applications help enlighten the formalism in order to envisage realistic situations with Schrödinger equations, Higgs fields, vacuum fluctuations, extra-dimensional methods in the potential theory, and electromagnetic interactions of extended charges and their consequences. It turns out that the innermost structure of these extended charges is associated with nonlocal photon propagators. It is shown that the propagator arisen from the charged torus potential consists of two different parts: a nonlocal photon propagator and a propagator of neutrino-like particles, which is described by square-root-operator equation. We examine the potential of the torus and its propagator as the appearance of superfields in terms of the photon and the massless fermion (photino).     

Polarization propagator for x-ray spectra

A polarization propagator for x-ray spectra is outlined and implemented in density functional theory. It rests on a formulation of a resonant-convergent first-order polarization propagator approach which makes it possible to directly calculate the x-ray absorption cross section at a particular frequency without explicitly addressing the excited states. The quality of the predicted x-ray spectrum relates only to the type of density functional applied without any separate treatment of dynamical relaxation effects.     

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。