Jet quenching parameter in an expanding QCD plasma

TL;DR

This paper develops a boost-invariant framework for understanding transverse momentum broadening of high-$p_T$ partons in an expanding quark-gluon plasma, including radiative corrections that modify the jet quenching parameter over time.

Contribution

It introduces a novel boost-invariant description of jet quenching in an expanding plasma and resums radiative corrections to the jet quenching parameter, accounting for local-in-time effects.

Findings

Radiative corrections to $\hat q$ are local in proper time.

Resummation slows down the decrease of $\hat q$ with time.

The framework applies to boost-invariant longitudinal expansion scenarios.

Abstract

We study the phenomenon of transverse momentum broadening for a high-$p_T$ parton propagating through a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant description for this phenomenon, in which the broadening refers to the angular variables $\eta$ (the pseudo-rapidity) and $\phi$ (the azimuthal angle). The jet quenching parameter $\hat{q}$ which enters this description depends upon the proper time alone. We furthermore consider radiative corrections to $\hat q$. As in the case of a static medium, we find potentially large corrections enhanced by a double logarithm. But unlike for the static medium, these corrections are now local in time: they depend upon the local (proper) time characterizing the expansion, and not upon the overall path length. We resum such corrections to all orders into a renormalized jet quenching parameter. The main effect of this resummation is to slow down the decrease of $\hat q$ with increasing proper time.