Medium-induced gluon radiation and colour decoherence beyond the soft approximation

TL;DR

This paper derives a comprehensive in-medium gluon radiation spectrum for quarks at finite energies, incorporating all next-to-eikonal corrections and interference effects, providing a detailed physical picture relevant for parton shower modeling.

Contribution

It introduces a full finite-energy correction framework for medium-induced gluon radiation, extending previous soft and eikonal approximations with a factorized, physically intuitive approach.

Findings

Recovered known soft and eikonal results.

Presented a simple physical picture of radiation for any formation time.

Provided technical details for calculating relevant QCD path integrals.

Abstract

We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons. Results are computed for finite formation times, including interference with vacuum amplitudes. By rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation. This factorisation allows us to present a simple physical picture of the medium-induced radiation for any value of the formation time, that is of interest for a probabilistic implementation of the modified parton shower. Known results are recovered for the particular cases of soft radiation and eikonal quark and for the case of a very long medium, with length much larger than the average formation times for medium-induced radiation. Technical details of the computation of the relevant $n$-point functions in colour space and of the required path integrals in transverse space are provided. The final result completes the calculation of all finite energy corrections for the radiation off a quark in a QCD medium that exist in the small angle approximation and for a recoilless medium.