Damping rate for transverse gluons with finite soft momentum in hot QCD

TL;DR

This paper calculates the damping rate of transverse gluons with finite soft momentum in hot QCD, revealing a convergent series expansion and contrasting it with previous logarithmic results, indicating potential critical phenomena.

Contribution

It provides a leading-order perturbative calculation of gluon damping rates with finite soft momentum using effective vertices and propagators, highlighting series convergence.

Findings

Series expansion of damping rate likely converges within a finite radius.

Contrasts with previous logarithmic behavior from different momentum limits.

Suggests possible interesting physics near a 'critical' region.

Abstract

We calculate the damping rate for transverse gluons with {\nineti finite} soft momentum to leading order in perturbative hot QCD. The internal momenta of the one-loop contributing diagrams are soft. This means we have to use effective vertices and propagators which incorporate the so-called hard thermal loops. We expand the damping rate in powers of the incoming momentum and argue that the series ought to converge within a finite radius of convergence. We contrast such a behavior with the one obtained from a previous calculation that produced a logarithmic behavior, a calculation based on letting the gluon momentum come from the hard limit down towards the interior of the soft region. This difference in behavior may point to interesting physics around some `critical' region.