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

TL;DR

This paper compares two mechanisms for fixed point emergence in QCD—Banks-Zaks and dynamical gluon mass generation—analyzing their beta functions and fixed points, and exploring their implications near the conformal window.

Contribution

It provides a comparative analysis of BZ and DGM fixed points in QCD, highlighting their similarities and potential physical implications near the conformal window.

Findings

Both mechanisms exhibit fixed points at similar coupling values near the conformal window.

States of minimum vacuum energy are linked to dynamical gluon mass generation.

The analysis relies on extrapolations of dynamical gluon masses at large N_f.

Abstract

Fixed points in QCD can appear when the number of quark flavors ($N_f$) 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 generation (DGM) does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $\beta$ functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large $N_f$, we verify that near the so called QCD conformal window both cases exhibit fixed points at similar coupling constant values ($g^*$). We argue that the states of minimum vacuum energy, as a function of the coupling constant up to $g^*$ and for several $N_f$ values, are related to the dynamical gluon mass generation mechanism.