Vertex Sensitivity in the Schwinger-Dyson Equations of QCD

TL;DR

This paper investigates how different vertex inputs affect the non-perturbative gluon and ghost propagators in Landau gauge QCD using Schwinger-Dyson equations, highlighting the importance of vertex structure in obtaining consistent solutions.

Contribution

It systematically analyzes the impact of various vertex functions on the Schwinger-Dyson equations for gluon and ghost propagators in Landau gauge QCD, emphasizing the necessity of non-trivial vertices for self-consistent solutions.

Findings

Self-consistent solutions show a mass-like gluon propagator consistent with Cornwall's proposal.

Finite ghost dressing is favored in the non-perturbative region.

Non-trivial vertices are essential for consistent gluon and ghost solutions.

Abstract

The non-perturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the non-perturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a masslike term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.