Dynamical chiral symmetry breaking in SU(N_{c}) gauge theories with large number of fermion flavors

Abstract

In this paper we examine a phase transition in $SU(N_c)$ gauge theories governed by the existence of an infrared fixed point of the renormalization group $\beta$ function. The nonlinear integral Schwinger-Dyson equation for a mass function of massless fermions is solved numerically using the exact expression of the running coupling in two-loop approximation for an SU(3) gauge theory. Based on the obtained solution of the Schwinger-Dyson equation, the value of the chiral condensate, $<\bar{q}q>$, and the decay constant, $f_{\pi }$, of bound states (mesons) are calculated for several values of fermion flavors $N_f$. We show that this kind of phase transition is a transition of finite order.

5 pages,1 figure