Effective Action for the Quark-Meson Model

Abstract

The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to 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 $f_{\pi }$ and $\text{VEV}\text{olpsi}\psi$ 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 $f_{\pi }$ around $100\text{MeV}$.

Comments: 56 pages (including 10 figures and 1 table), uses epsf.sty