The low-momentum ghost dressing function and the gluon mass

TL;DR

This paper analyzes the low-momentum ghost propagator in Landau gauge using Dyson-Schwinger equations, demonstrating that a massive gluon propagator model accurately describes lattice simulation results.

Contribution

It introduces a simple model with a massive gluon propagator and shows it effectively describes the low-momentum ghost propagator, aligning DSE solutions with lattice data.

Findings

Regular DSE solutions with finite zero-momentum ghost dressing function.

Asymptotic expression fits lattice data well up to order q^2.

Dependence of the ghost propagator on gluon mass and effective charge.

Abstract

We study the low-momentum ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular DSE solutions (the zero-momentum ghost dressing function not diverging) appear to emerge and we show the ghost propagator to be described by an asymptotic expression reliable up to the order ${\cal O}(q^2)$. That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well the low-momentum ghost propagator obtained through big-volume lattice simulations.