Quark running mass and vacuum energy density in truncated Coulomb gauge QCD for five orders of magnitude of current masses

We study in detail the effect of the finite current quark mass on chiral symmetry breaking, in the framework of truncated Coulomb gauge QCD with a linear confining quark–antiquark potential. In the chiral limit of massless current quarks, the breaking of chiral symmetry is spontaneous. But for a finite current quark mass, some dynamical symmetry breaking continues to add to the explicit breaking caused by the quark mass. Moreover, while in the chiral limit of a massless quark we have a chiral phase transition, with a finite quark mass we expect a crossover only. For the study of the QCD phase diagram it thus is relevant to determine how the current quark mass affects chiral symmetry breaking. Since the current quark masses of the six standard flavors u, d, s, c, b, t span over five orders of magnitude from 1.5 MeV to 171 GeV, we develop an accurate numerical method to study the running quark mass gap and the quark vacuum energy density from very small to very large current quark masses. We also consider two different order parameters, the quark mass at vanishing moment or the quark condensate.