Ultrasoft Amplitudes in Hot QCD

TL;DR

This paper derives effective amplitudes for ultrasoft color fields in hot QCD by solving the Boltzmann equation, extending the hard thermal loop framework to include collision effects among hard particles.

Contribution

It introduces ultrasoft amplitudes in hot QCD that incorporate collision effects, generalizing the HTL framework with a non-perturbative resummation approach.

Findings

Ultrasoft amplitudes are gauge invariant and obey Ward identities.

They reduce to the Debye mass in the static limit.

A formula for color conductivity including hard and soft modes is obtained.

Abstract

By using the Boltzmann equation describing the relaxation of colour excitations in the QCD plasma, we obtain effective amplitudes for the ultrasoft colour fields carrying momenta of order $g^2 T$. These amplitudes are of the same order in $g$ as the hard thermal loops (HTL), which they generalize by including the effects of the collisions among the hard particles. The ultrasoft amplitudes share many of the remarkable properties of the HTL's: they are gauge invariant, obey simple Ward identities, and, in the static limit, reduce to the usual Debye mass for the electric fields. However, unlike the HTL's, which correspond effectively to one-loop diagrams, the ultrasoft amplitudes resum an infinite number of diagrams of the bare perturbation theory. By solving the linearized Boltzmann equation, we obtain a formula for the colour conductivity which accounts for the contributions of the hard and soft modes beyond the leading logarithmic approximation.