Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories

TL;DR

This paper develops a gauge-invariant resummation scheme for 3d Yang-Mills theories at finite temperature, providing a two-loop magnetic mass calculation that improves convergence and generalizes previous SU(2) results to SU(N).

Contribution

It introduces a gauge-independent two-loop gap equation for magnetic mass in hot gauge theories, extending previous SU(2) work to SU(N) and correcting earlier errors.

Findings

Two-loop magnetic mass is about 15% higher than the one-loop estimate.

The resummation scheme shows reasonable convergence.

The method is generalized from SU(2) to SU(N).

Abstract

Perturbation theory for non-Abelian gauge theories at finite temperature is plagued by infrared divergences caused by magnetic soft modes $\sim g^2T$, which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge invariant resummation scheme to solve this problem by self-consistent mass generation using an auxiliary scalar field, improving over previous attempts in two respects. First, we generalise earlier SU(2) treatments to SU(N). Second, we obtain a gauge independent two-loop gap equation, correcting an error in the literature. The resulting two-loop approximation to the magnetic mass represents a $\sim 15%$ correction to the leading one-loop value, indicating a reasonable convergence of the resummation.