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, ? and ? 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 p². 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.

Keywords

DSEs, quark propagator, quark mass, Goldstone boson mass