# Gluon bremsstrahlung in finite media beyond multiple soft scattering approximation

## TL;DR

This paper introduces a new method for calculating gluon radiation in finite media that surpasses the multiple soft scattering approximation, accurately capturing both single hard and multiple soft scattering regimes.

## Contribution

The authors develop an approach expanding around the harmonic oscillator to unify and extend existing analytic limits of gluon spectra in finite media.

## Key findings

- The method accurately reproduces known limits at high and low frequencies.
- The spectrum shows weak dependence on infrared medium scale for large media.
- The approach provides a more comprehensive understanding of gluon bremsstrahlung in finite media.

## Abstract

We revisit the calculation of the medium-induced gluon spectrum in a finite QCD and develop a new approach that goes beyond multiple soft scattering approximation. We show by expanding around the harmonic oscillator that the first two orders encompass the two known analytic limits: single hard and multiple soft scattering regimes, valid at high and low frequencies, respectively. Finally, we investigate the sensitivity of our results to the infrared and observe that for large media the spectrum is weakly dependent on the infrared medium scale.