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

TL;DR

This paper investigates how finite current quark masses influence chiral symmetry breaking in truncated Coulomb gauge QCD, analyzing the effects across five orders of magnitude of quark masses using a new numerical method.

Contribution

The study introduces an accurate numerical approach to analyze the running quark mass gap and vacuum energy density over a wide range of quark masses in QCD.

Findings

Finite quark mass turns chiral symmetry breaking from a phase transition into a crossover.

Chiral symmetry breaking is affected by explicit mass, modifying the order parameter behavior.

The method effectively covers quark masses from 1.5 MeV to 171 GeV.

Abstract

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, using as order parameter the mass gap, i. e. the quark mass at vanishing moment or the quark condensate, a finite quark mass transforms the chiral symmetry breaking from a phase transition into a crossover. 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 flavours 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.