Theoretical formalism of radiative jet energy loss in a finite size dynamical QCD medium

TL;DR

This paper develops a formalism to calculate radiative energy loss of quark jets in finite, dynamical QCD media, revealing non-linear path length effects and a simple relation to static media results.

Contribution

It introduces a first-order opacity formalism for dynamical media, addressing infrared divergences and linking static and dynamical QCD energy loss models.

Findings

Infrared divergences are regulated when all diagrams are included.

Finite size effects lead to non-linear path length dependence.

A simple mapping between static and dynamical medium energy loss expressions is proposed.

Abstract

The computation of radiative energy loss in a finite size QCD medium with dynamical constituents is a key ingredient for obtaining reliable predictions for jet quenching in ultra-relativistic heavy ion collisions. We here present a theoretical formalism for the calculation of the first order in opacity radiative energy loss of a quark jet traveling through a finite size dynamical QCD medium. We show that, while each individual contribution to the energy loss is infrared divergent, the divergence is naturally regulated once all diagrams are taken into account. Finite size effects are shown to induce a non-linear path length dependence of the energy loss, recovering both the incoherent Gunion-Bertsch limit, as well as destructive Landau-Pomeanchuk-Migdal limit. Finally, our results suggest a remarkably simple general mapping between energy loss expressions for static and dynamical QCD media.