Effective action for the chiral quark-meson model

Abstract

The scale dependence of an effective average action for mesons and quarks is described by an exact nonperturbative flow equation. The running of couplings follows from a truncation of this equation. For the dimensionless scalar and Yukawa couplings it proceeds according to renormalization-group-improved one-loop \ensuremath{\beta} functions including mass threshold functions. The running scalar mass term becomes negative for small scales and induces spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between quarks and mesons the low momentum physics is essentially determined by infrared fixed points. This allows us to establish relations between various parameters related to the meson potential. The results for ${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$ and 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\psi}〉 are not very sensitive to the poorly known details of the quark-meson effective action at scales where the mesonic bound states form. For realistic constituent quark masses we find ${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$ around 100 MeV. \textcopyright{} 1996 The American Physical Society.