Infrared finite ghost propagator in the Feynman gauge

TL;DR

This paper shows how to derive an infrared finite ghost propagator in QCD's Feynman gauge using Schwinger-Dyson equations, highlighting the role of the gluon-ghost vertex's longitudinal form factor.

Contribution

It introduces a method to obtain an infrared finite ghost propagator in Feynman gauge without assuming massless poles, emphasizing the non-trivial contribution of the vertex's longitudinal form factor.

Findings

The ghost propagator remains finite in the infrared in Feynman gauge.

The longitudinal form factor of the gluon-ghost vertex is crucial for finiteness.

Infrared cutoff ensures the form factor stays finite as ghost momentum vanishes.

Abstract

We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the non-perturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes non-trivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined.