Gauge invariant definition of the jet quenching parameter

TL;DR

This paper generalizes the gauge-invariant definition of the jet quenching parameter $$ in the Soft-Collinear Effective Theory by incorporating transverse Wilson lines, enabling consistent calculations across different gauges.

Contribution

It introduces a gauge-invariant formulation of $$ using transverse Wilson lines, extending previous covariant gauge results to arbitrary gauges.

Findings

Derived explicit expressions for transverse Wilson lines in non-covariant gauges.

Showed how to incorporate Glauber gluon interactions in a gauge-invariant manner.

Discussed the impact of transverse momenta on $$ in a weakly-coupled quark-gluon plasma.

Abstract

In the framework of Soft-Collinear Effective Theory, the jet quenching parameter, $\hat{q}$, has been evaluated by adding the effect of Glauber gluon interactions to the propagation of a highly-energetic collinear parton in a medium. The result, which holds in covariant gauges, has been expressed in terms of the expectation value of two Wilson lines stretching along the direction of the four-momentum of the parton. In this paper, we show how that expression can be generalized to an arbitrary gauge by the addition of transverse Wilson lines. The transverse Wilson lines are explicitly computed by resumming interactions of the parton with Glauber gluons that appear only in non-covariant gauges. As an application of our result, we discuss the contribution to $\hat{q}$ coming from transverse momenta of order $g^2T$ in a medium that is a weakly-coupled quark-gluon plasma.