Dynamical chiral symmetry breaking and a critical mass

Abstract

On a bounded, measurable domain of non-negative current-quark mass, realistic models of the QCD gap equation can simultaneously admit two nonequivalent dynamical chiral symmetry breaking (DCSB) solutions and a solution that is unambiguously connected with the realization of chiral symmetry in the Wigner mode. The Wigner solution and one of the DCSB solutions are destabilized by a current-quark mass, and both disappear when that mass exceeds a critical value. This critical value also bounds the domain on which the surviving DCSB solution possesses a chiral expansion. This value can therefore be viewed as an upper bound on the domain within which a perturbative expansion in the current-quark mass around the chiral limit is uniformly valid for physical quantities. For a pseudoscalar meson constituted of equal-mass current quarks, it corresponds to a mass ${m}_{{0}^{\ensuremath{-}}}~0.45$ GeV. In our discussion, we employ properties of the two DCSB solutions of the gap equation that enable a valid definition of $\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}$ in the presence of a nonzero current mass. The behavior of this condensate indicates that the essentially dynamical component of chiral symmetry breaking decreases with increasing current-quark mass.