QCD fixed points: Banks–Zaks scenario or dynamical gluon mass generation?

Abstract

Fixed points in QCD can appear when the number of quark flavors [Formula: see text] is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass (DGM) generation does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their [Formula: see text] functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large [Formula: see text], we verify that between [Formula: see text] and [Formula: see text] both cases exhibit fixed points at similar coupling constant values [Formula: see text]. We argue that the states of minimum vacuum energy, as a function of the coupling constant up to [Formula: see text] and for several [Formula: see text] values, are related to the dynamical gluon mass generation mechanism.