Diagrammatic approach to soft non-Abelian dynamics at high temperature

TL;DR

This paper develops a diagrammatic method to analyze the non-perturbative dynamics of soft non-Abelian gauge fields at high temperature, extending the effective theory beyond the hard thermal loop approximation.

Contribution

It introduces a gauge-invariant, transverse effective polarization tensor for soft non-Abelian gauge fields, including higher loop contributions beyond the hard thermal loop approximation.

Findings

The effective polarization tensor is gauge fixing independent.

The tensor is transverse at leading order in the coupling g.

Higher loop diagrams involving the scale gT are as important as hard thermal loops.

Abstract

The dynamics of soft ($|\vec{p}|\sim g^2 T$) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta $p_0\lsim g^2 T$, $|\vec{p}|\sim g^2 T$ and loop momenta larger than $g^2 T$. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order $T$. There are higher loop diagrams, involving also the scale $gT$, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories and their calculation is simplified by using the hard thermal loop effective theory. Remarkably, the effective one-loop polarization tensor is found to be gauge fixing independent and transverse at leading order in $g$. The transversality indicates that this approach leads to a gauge invariant effective theory.