Effects of the ghost sector in gluon mass dynamics

TL;DR

This paper explores how the ghost sector influences gluon mass generation in Yang-Mills theory, revealing that ghost-gluon vertex poles have a suppressed effect compared to three-gluon vertex poles.

Contribution

It extends previous models by including ghost-gluon vertex poles in the Bethe-Salpeter equations for gluon mass dynamics, showing their relative suppression.

Findings

Ghost-gluon vertex poles are present but less influential.

The dominant contribution to gluon mass comes from three-gluon vertex poles.

The inclusion of ghost poles refines the understanding of mass generation mechanisms.

Abstract

In this work, we investigate the effects of the ghost sector on the dynamical mass generation for the gauge boson of a pure Yang-Mills theory. The generation of a dynamical mass for the gluon is realized by the Schwinger mechanism, which is triggered by the existence of longitudinally coupled massless poles in the fundamental vertices of the theory. The appearance of such poles occurs by purely dynamical reasons and is governed by a set of Bethe-Salpeter equations. In previous studies, only the presence of massless poles in the background-gauge three-gluon vertex was considered. Here, we include the possibility for such poles to appear also in the corresponding ghost-gluon vertex. Then, we solve the resulting Bethe-Salpeter system, which reveals that the contribution associated with the poles of the ghost-gluon vertex is suppressed with respect to those originating from the three-gluon vertex.