On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions

TL;DR

This paper investigates the low-momentum behavior of Yang-Mills propagators in the PT-BFM scheme, comparing numerical and analytical results, and clarifies the nature of decoupling and scaling solutions in Dyson-Schwinger equations.

Contribution

It provides a detailed comparison between numerical PT-BFM propagators and analytical low-momentum expressions, and clarifies the non-existence of scaling solutions as actual DSE solutions in this scheme.

Findings

Analytical ghost dressing function fits well with numerical results.

Approaching a critical coupling leads to scaling-like behavior.

Scaling solutions are shown to be unattainable in the PT-BFM scheme.

Abstract

We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex 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 ${\cal O}(q^2)$ is proven to fit pretty well the numerical PT-BFM results. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the numerical PT-BFM propagators tend to behave as the scaling ones. We also show that the scaling solution, implying a diverging ghost dressing function, cannot be a DSE solution in the PT-BFM scheme but an unattainable limiting case.