Collisional energy loss distribution of a fast parton in a hot or dense QCD medium

TL;DR

This paper calculates the full probability distribution of collisional energy loss for a high-energy parton in a quark-gluon plasma, improving jet-quenching models by including stochastic effects and energy gain.

Contribution

It introduces a kinetic equation approach to determine the complete energy loss distribution, extending previous average loss calculations to finite path lengths and stochastic effects.

Findings

Derived the collisional quenching weight from a kinetic equation.

Included energy gain from thermal fluctuations in the distribution.

Extended the model to finite path lengths relevant for various collision types.

Abstract

We compute the probability distribution for collisional energy loss of an ultrarelativistic parton crossing a quark-gluon plasma. This collisional quenching weight has not been determined previously, unlike the average collisional loss per unit distance, although it should be a more accurate quantity to use in jet-quenching phenomenology. The quenching weight is obtained from a well-known kinetic equation which resums an arbitrary number of elastic scatterings of the energetic parton with the medium, providing a complete description of the stochastic energy exchange, including the possibility of energy gain from thermal fluctuations. The formulation also naturally extends the standard treatment of collisional energy loss to finite path lengths, which could be relevant not only for heavy-ion collisions, but also for light-ion, and possibly proton-nucleus and proton-proton collisions. We predict the quenching weight in a setup where individual elastic scatterings are described using the hard thermal loop approximation for soft exchanges, with a smooth matching to the hard domain.