The color gauge invariance and a possible origin of the Jaffe-Witten mass gap in QCD

TL;DR

This paper explores the origin of the QCD mass gap by proposing a self-consistent violation of gauge invariance, leading to two types of solutions for the gluon propagator, including one with an effective gluon mass.

Contribution

It introduces a novel approach to understanding the QCD mass gap by relaxing gauge invariance constraints and analyzing resulting gluon propagator solutions.

Findings

Existence of a mass gap related to nonlinear gluon interactions

Two types of gluon propagator solutions identified

Demonstration of an effective gluon mass solution

Abstract

The physical meaning of a mass gap introduced by Jaffe and Witten is to be responsible for the large-scale (low-energy/momentum), i.e., the non-perturbative structure of the true QCD vacuum. In order to make the existence of a mass gap pefrectly clear it is defined as the difference between the regularized full gluon self-energy and its subtracted (also regularized) counterpart. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. A self-consistent violation of SU(3) color gauge invariance/symmetry is duscussed in order to realize a mass gap in QCD. For this purpose, we propose not to impose the transversality condition on the full gluon self-energy, while restoring the transversality of the full gluon propagtor relevant for the non-perturbative QCD at the final stage. At the same time, the Slavnov-Taylor identity for the full gluon propagator is always preserved. All this allows one to establish the general structure of the full gluon propagator in the presence of a mass gap. In this case, two independent types of formal solutions for the full gluon propagator have been established. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.