Non-perturbative dynamics of hot non-Abelian gauge fields: beyond leading log approximation

TL;DR

This paper advances the understanding of hot non-Abelian gauge fields by extending Bodeker's effective theory to next-to-leading-log order, providing more precise calculations of color conductivity and related physical quantities.

Contribution

It systematically extends the effective theory for hot non-Abelian plasmas beyond leading-log order, including a new calculation of color conductivity at NLLO.

Findings

Derived the NLLO correction to color conductivity.

Extended the effective theory without introducing new operators.

Provided a more accurate estimate of electroweak baryon number violation rate.

Abstract

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to Bodeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by G. Moore to yield a NLLO result for the hot electroweak baryon number violation rate.