Quark Propagator, QCD Vacuum Condensates And Quark Virtuality

Study of fully dressed quark propagator is one of the most important issue in the investigation of QCD, since it is related to the determination of quark masses, which are fundamental QCD input parameters of Standard Model, and an accurate determination of these parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the strong interaction theory - QCD, and then study fully dressed quark propagator in the framework of Dyson-Schwinger Equations (DSEs) in the "Rainbow" approximation with three different phenomenological gluon propagators. We solve the DSEs and use its solutions to study the structure of non-local quark vacuum condensate and calculate local quark vacuum condensates, quark-gluon mixed vacuum condensates, and quark virtuality in the QCD vacuum. Our predictions are consistent with other model predictions such as Lattice QCD, Instanton Model and empirical values used widely in the literature. At the same time, we also propose a parameterized quark propagator to approach to the DSEs which is very complicated to be solved. The parameterization form of the fully dressed quark propagatoris is analytic everywhere in the finite complex p~2-plane and has no Lehmann representation, and hence there are no quark production thresholds in theoretical calculations of observables. We re-calculate all of the physics quantities mentioned above by use of the parameterized quark propagator and compared its predictions with those given by the solutions of DSEs. The results show that the parametrized form of quark propagator is an applicable and reliable approximation since its predictions are consistent with DSEs predictions and reproduces all physical quantities in an acceptable way. Finally, the current masses of light quarks and the masses of Goldstone bosons are also obtained by using our theoretical results on local vacuum condensates. The resulting agreements of the Golsdtone beson masses with their experimental data are quite good. Evidently, it shows that the physics idea and the formulated theory presented in this paperare good for understanging non-perturbative feature of QCD.