Quark mass and the masses of Goldstone bosons

Abstract

Based on the Dyson-Schwinger Equations (DSEs) of QCD in the "rainbow" approximation, the fully dressed quark propagator S(f)(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes A(f) and B(f) which built up the fully dressed quark propagator, and the dynamical running masses M(f), which is defined by A(f) and B(f) for light quarks u, d and s, are calculated, respectively. Using the predicted current masses m(f), quark local vacuum condensates, and our predicted value of pion decay constant, the masses of Goldstone bosons K, pi and eta and their in-medium values are also evaluated. Our predictions fit to data and to many other different calculations quite well. The numerical results show that the mass of quark is dependent of its momentum p(2). The fully dressed quark amplitudes A(f) and B(f) have correct behaviors and can be used for many purposes in our future researches on non-perturbative QCD.