The color gauge invariance and a possible origin of a mass gap in QCD

TL;DR

This paper explores how a dynamically generated mass scale in QCD affects the gluon propagator, proposing methods to preserve gauge invariance and transversality while accounting for a non-zero mass gap.

Contribution

It introduces a way to maintain gauge invariance and transversality in QCD with a non-zero mass gap, clarifying the structure of the gluon propagator.

Findings

Mass gap dominates at low gluon momentum.

Method to restore transversality in a gauge-invariant manner.

Mass gap contribution vanishes at high gluon momentum.

Abstract

The general scale parameter, having the dimensions of mass squared, is dynamically generated in the QCD gluon sector. It is introduced through the difference between the regularized full gluon self-energy and its value at some finite point. It violates transversality of the full gluon self-energy. The Slavnov-Taylor identity for the full gluon propagator, when it is given by the corresponding equation of motion, is also violated by it. So in order to maintain both transversality and the identity it should be disregarded from the very beginning, i.e., put formally zero everywhere. However, we have shown how to preserve the above-mentioned identity at non-zero mass squared parameter. This allows one to establish the structure of the full gluon propagator when it is explicitly present. Its contribution does not survive in the perturbation theory regime when the gluon momentum goes to infinity. At the same time, its contribution dominates the structure of the full gluon propagator when the gluon momentum goes to zero. We have also proposed a method how to restore transversality of the relevant gluon propagator in a gauge invariant way, while keeping the mass squared parameter "alive".