Static mass scales in hot gauge theories

TL;DR

This paper reviews non-perturbative results from lattice simulations on the static properties of hot gauge theories, highlighting the hierarchy of mass scales and screening phenomena in 3d SU(N) Higgs models relevant to the electroweak and QCD sectors.

Contribution

It provides a summary of recent lattice simulation results on the mass spectrum, string tension, and screening effects in 3d SU(N) Higgs models at finite temperature, emphasizing the hierarchy of scales.

Findings

Larger hierarchy observed in purely magnetic sector quantities.

Non-perturbative corrections to Debye mass quantified.

Electric and magnetic sectors are not well separated in finite T gauge theories.

Abstract

The static sectors of the electroweak Standard Model and QCD at finite temperatures are described by 3d SU(N) Higgs models with scalars in the fundamental and adjoint representation, respectively. I summarize the non-perturbative physics of these theories like mass spectrum, string tension, screening of the static potential and non-perturbative corrections to the Debye mass, as obtained from recent lattice simulations. It is observed that in the 3d theory corresponding to the purely magnetic sector there is a larger hierarchy between different quantities than between the electric ($\sim gT$) and magnetic ($\sim g^2T$) sectors of finite T gauge theories, which are not generally well separated.