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.

Extending the Truncated Dyson-Schwinger Equation to Finite Temperatures

In view of the properties of mesons in hot strongly interacting matter, the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladder approximation are analysed in some detail. In Euclidean space within the Matsubara imaginary time formalism, the quark propagator is not longer a O(4) symmetric function and possesses a discrete spectrum of the fourth component of the momentum. This makes the treatment of the Dyson-Schwinger and Bethe-Salpeter equations conceptually different from the vacuum and technically much more involved. The question whether the interaction kernel known from vacuum calculations can be applied at finite temperatures remains still open. We find that, at low temperatures, the model interaction with vacuum parameters provides a reasonable description of the quark propagator, while at temperatures higher than a certain critical value Tc the interaction requires stringent modifications. The general properties of the quark propagator at finite temperatures can be inferred from lattice QCD (LQCD) calculations. We argue that, to achieve a reasonable agreement of the model calculations with that from LQCD, the kernel is to be modified in such a way as to screen the infra-red part of the interaction at temperatures larger than Tc . For this, we analyse the solutions of the truncated Dyson-Schwinger equation with existing interaction kernels in a large temperature range with particular attention on high temperatures in order to find hints to an adequate temperature dependence of the interaction kernel to be further implemented in the Bethe-Salpeter equation for mesons. This will allow investigating the possible in medium modifications of the meson properties as well as the conditions of quark deconfinement in hot matter.

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.