The low-momentum ghost dressing function and the gluon mass

TL;DR

This paper analyzes low-momentum Yang-Mills propagators, showing how regular and critical solutions behave and how the decoupling solution approaches the scaling solution near a critical coupling.

Contribution

It provides an asymptotic expression for the ghost dressing function and explores the transition from decoupling to scaling solutions in Landau gauge Yang-Mills theory.

Findings

The asymptotic expression fits well with numerical solutions.

Approaching a critical coupling causes the decoupling solution to trend towards the scaling solution.

The analysis supports the connection between decoupling and scaling solutions in the low-momentum regime.

Abstract

We study both regular (the zero-momentum ghost dressing function not diverging), also named decoupling, and critical (diverging), also named scaling, Yang-Mills propagators solutions by analyzing the low-momentum behaviour of the 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. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ fits pretty well the low-momentum ghost propagator obtained through the numerical integration of the coupled gluon and ghost DSE in the PT-BFM scheme and, when the size of the coupling renormalized at some scale approaches some critical value, the PT-BFM results seems to trend to the the scaling solution as a limiting case