Ghost propagator and ghost-gluon vertex from Schwinger-Dyson equations

TL;DR

This paper derives and solves coupled Schwinger-Dyson equations for the ghost propagator and ghost-gluon vertex in Landau gauge, showing results consistent with lattice data without artificially adjusting parameters.

Contribution

It introduces an approximate integral equation for the ghost-gluon vertex form factor in specific kinematic limits and demonstrates its role in accurately reproducing lattice results.

Findings

The coupled equations yield a ghost dressing function matching lattice data.

The form factor significantly influences the ghost propagator's behavior.

The approach avoids artificial parameter tuning.

Abstract

We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex, in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the "one-loop dressed" approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case, and the well-known Taylor limit. When coupled with the Schwinger-Dyson equation of the ghost dressing function, the contribution of this form factor provides considerable support to the relevant integral kernel. As a consequence, the solution of this coupled system of integral equations furnishes a ghost dressing function that reproduces the standard lattice results rather accurately, without the need to artificially increase the value of the gauge coupling.