Evidence of ghost suppression in gluon mass dynamics

TL;DR

This paper investigates how ghost sector dynamics influence gluon mass generation in Yang-Mills theories, revealing that ghost-related poles have a minimal impact, mainly slightly altering the gluon mass running at high momenta.

Contribution

It extends previous models by allowing ghost-gluon vertex poles to contribute to gluon mass dynamics, and analyzes their suppressed effect through Bethe-Salpeter equations.

Findings

Ghost-gluon vertex poles are highly suppressed.

Ghost sector contributions slightly modify gluon mass at high energies.

Derived a version of Taylor's theorem for ghost-gluon vertices.

Abstract

In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved.