Energy loss and (de)coherence effects beyond eikonal approximation

TL;DR

This paper develops a comprehensive calculation of gluon radiation energy loss in a QCD medium, incorporating finite energy corrections and decoherence effects beyond the eikonal approximation, using a path integral approach.

Contribution

It introduces a general expression for gluon radiation that includes finite energy corrections and accounts for both coherence and decoherence effects in a medium.

Findings

Provides a unified framework for coherence and decoherence regimes.

Allows particles to undergo Brownian motion in the transverse plane.

Includes arbitrary energy fractions for emitted partons.

Abstract

The parton branching process is known to be modified in the presence of a medium. Colour decoherence processes are known to determine the process of energy loss when the density of the medium is large enough to break the correlations between partons emitted from the same parent. In order to improve existing calculations that consider eikonal trajectories for both the emitter and the hardest emitted parton, we provide in this work, the calculation of all finite energy corrections for the gluon radiation off a quark in a QCD medium that exist in the small angle approximation and for static scattering centres. Using the path integral formalism, all particles are allowed to undergo Brownian motion in the transverse plane and the offspring allowed to carry an arbitrary fraction of the initial energy. The result is a general expression that contains both coherence and decoherence regimes that are controlled by the density of the medium and by the amount of broadening that each parton acquires independently.