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

TL;DR

This paper investigates the phase transition related to chiral symmetry breaking in SU(Nc) gauge theories with many fermion flavors, using numerical solutions of Schwinger-Dyson equations and two-loop running coupling, revealing a finite order phase transition.

Contribution

It provides a numerical analysis of chiral symmetry breaking in SU(Nc) gauge theories with many flavors, highlighting the nature of the phase transition and calculating related physical quantities.

Findings

Identifies a finite order phase transition in the theory.

Calculates chiral condensate and decay constant for various fermion flavors.

Shows the impact of the infrared fixed point on chiral symmetry breaking.

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.