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.     

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(p2), defined by the self-energy functions Af(p2) and Bf(p2) 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.     

The Production of Pseudo Goldstone Boson in Top Quark Rare Decay

We calculate the flavor changing t → cπ0 decay in the framework of the topcolor assisted multiscaletechnicolor model. We find that (a) the branching ratio of t → cπ0 is insensitive to mπ, mπs and mπt, while it increasesquickly as ε increases; (b) for reasonable ranges of the parameters, the maximum of the branching ratio in this modelmay reach 7 × 10-6, seven orders larger compared to the one t → cH0 calculated in the standard model. This mightprovide an opportunity to detect the rare decay of the top quark in experiments.     

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.     

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.     

Top Quark Pair Production at e^＋e^— Colliders in the Topcolor—Assisted Technicolor Model

In the framework of topcolor-assisted technicolor model we calculate the contributions from the preudo Goldstone bosons and new gauge bosons to e^ e^-→ttk.We find that for reasonable ranges of the parameters,the preudo Goldstone bosons afford dominate contribution,the correction arising from new gauge bosons is negligibly small,the maximum of the relative corrections is-10% with the center-of-mass energy √s=500GeV;whereas in the case of √s=1500 GeV,the relative corrections could be up to 16%.Thus large new physics might be observable at the experiments of next-generation linear colliders.     

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.     

Dynamically Running Mass of Light Quark and QCD Vacuum Condensates

Based on Dyson-Schwinger equations (DSEs) in “rainbow“ approximation, the dynamically running mass of light quark and QCD vacuum condensate are investigated. The structure of non-local quark vacuum condensate, the values of local vacuum condensate of quarks and quark-gluon mixture, and dynamical transition of quark mass from current quark to constituent quark are illustrated. At the same time, according to the knowledge and experience learned from an extensive study of the solutions of DSEs, a parameterized form of confining quark propagator is suggested for a practical use. The new parameterized form of quark propagator is analytic everywhere in the finite complex p2-plane and has no Lehmann representation. The predictions for p2-dependence of effective quark masses, Mf(p2), defined by the self-energy functions Af(p2) and Bf(p2), both from the numerical solutions of DSEs and from its parameterized form, are shown dynamically. Our conclusion is that all numerical results are consistent with empirical values used in QCD sum rules and lattice QCD calculations. For a qualitative study, the parameterized form is a sufficiently good approximation to confining quark propagator.     

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—2 GeV2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。     

超新星核中的夸克相变及夸克质量效应

分别基于组夸克质量模型和流夸克质量模型, 讨论了超新星核心区两味夸克物质到更稳定的三味夸克物质的相变过程. 结果表明, 两种质量模型下相变的特征时标都短于10^-8s, 且质量越小的流夸克质量模型的相变速率越快;组分夸克质量模型下所得到的超新星核区的s夸克丰度, 中微子丰度及中微子总能量(除温度)相比前人的结果有轻微的增加, 而流夸克质量模型下所得到的这些参量的增加更为明显, 采用流夸克质量模型更有利于超新星的中微子延迟爆发机理的成功. 关键词： 夸克相变 组分夸克质量 流夸克质量 超新星     

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 Af(p2), Bf(p2) and effective mass Mf(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.     

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.     

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.     

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.     

Quark chiral condensate from the overlap quark propagator

From the overlap lattice quark propagator calculated in the Landau gauge,we determine the quark chiral condensate by fitting operator product expansion formulas to the lattice data.The quark propagators are computed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations with N_f = 2 + 1flavors.Three ensembles with different light sea quark masses are used at one lattice spacing 1/a = 1.75(4) Ge V.We obtain ψψ (2 GeV)MS =(-304(15)(20) MeV)~3in the SU(2) chiral limit.     

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.     

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.     

Quark mass dependence of masses and decay constants of the pseudo-Goldstone bosons in QCD

The dependence of the pseudo-scalar meson masses and decay constants on sea and valence quark masses is compared to next-to-leading order (NLO) chiral perturbation theory (ChPT). The numerical simulations with two light dynamical quark flavors are performed with the Wilson quark lattice action at gauge coupling and hopping parameters on a 16⁴ lattice. lattice artifacts are taken into account by applying chiral perturbation theory for the Wilson lattice action. The values of the relevant combinations of Gasser-Leutwyler constants L ₄, L ₅, L ₆ and L ₈ are estimated.Received: 7 July 2003, Published online: 2 October 2003     

TC2模型下底夸克对产生的研究

在顶色辅助的technicolor模型下, 计算了来自赝标哥得斯通玻色子和新规范玻色子对e⁺e^－→bb的截面贡献. 发现由technipions和新规范玻色子产生截面的修正足够小以至于可以忽略, 在合理的参数范围内, top pions起主要作用, 在质心能量√s=500GeV, 修正的最大值可以达到43%; 在√s=1500GeV, 最大的相对修正却只有3.1%. 这为我们在下一代直线对撞机实验中探测顶色辅助的technicolor模型下(TC2模型)提供了可行的方法.     

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.