Screened perturbation theory for 3d Yang-Mills theory and the magnetic modes of hot QCD

TL;DR

This paper explores infrared divergences in finite-temperature non-abelian gauge theories, proposing a scheme based on the non-linear sigma model to estimate magnetic mode contributions to QCD pressure, indicating promising convergence.

Contribution

It introduces a gauge-invariant resummation scheme using the non-linear sigma model to estimate magnetic mode effects in hot QCD.

Findings

Magnetic soft modes contribute about 10% at NLO to the QCD pressure.

The series for magnetic contributions shows signs of reasonable convergence.

Infrared divergences can be regulated by a magnetic mass, with the gauge coupling dropping out of the expansion.

Abstract

Perturbation theory for non-abelian gauge theories at finite temperature is plagued by infrared divergences which are caused by magnetic soft modes ~g^2T, corresponding to gluon fields of a 3d Yang-Mills theory. While the divergences can be regulated by a dynamically generated magnetic mass on that scale, the gauge coupling drops out of the effective expansion parameter requiring summation of all loop orders for the calculation of observables. Some gauge invariant possibilities to implement such infrared-safe resummations are reviewed. We use a scheme based on the non-linear sigma model to estimate some of the contributions ~g^6 of the soft magnetic modes to the QCD pressure through two loops. The NLO contribution amounts to ~10% of the LO, suggestive of a reasonable convergence of the series.