Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium

TL;DR

This paper derives a simple formula for high-energy gluon bremsstrahlung in a finite, expanding QCD medium, analyzing medium effects, pair production, and the convergence of the opacity expansion.

Contribution

It presents a simplified, leading-logarithmic expression for gluon bremsstrahlung in dynamic media and discusses the convergence limits of the opacity expansion.

Findings

The gluon spectrum formula is remarkably simple in the general case.

Opacity expansion diverges when plasma thickness exceeds the formation time.

Provides translation between different notations used in related research groups.

Abstract

Previous authors have considered the problem of the medium effects on single gluon bremsstrahlung associated with producing a high-energy particle in a finite, time-dependent QCD plasma. Working to leading logarithmic order, I show that the result for the bremsstrahlung gluon spectrum can be cast into a remarkably simple form in the general case. I similarly analyze the process of pair production. Also, I comment on the radius of convergence of the opacity expansion in cases where the leading-log approximation holds, showing that the opacity expansion does not converge when the thickness of the plasma is greater than roughly the bremsstrahlung formation time. Additionally, as a special bonus -- available for a limited time only while supplies last! -- I summarize translations between the notation used by a few of the groups who have worked on this and related problems.