Gauge invariant definition of the jet quenching parameter $\hat{q}$

TL;DR

This paper derives a gauge invariant expression for the jet quenching parameter $$ using Glauber extended Soft-Collinear Effective Theory, incorporating Wilson lines and gauge links for consistency across gauges.

Contribution

It introduces a systematic effective theory approach to define $$ gauge invariance, including transverse gauge links, improving theoretical consistency.

Findings

Derived a gauge invariant expression for $$ involving Wilson lines.

Showed the necessity of transverse gauge links in general gauges.

Provided a systematic power counting scheme within the effective theory.

Abstract

We use the framework of Glauber extended Soft-Collinear Effective Theory to explicitly derive a gauge invariant expression of the jet quenching parameter $\hat{q}$. The effective theory approach offers a systematic power counting scheme at the Lagrangian level and allows for a consistent treatment of the relevant scales in the problem. Employing this approach in a covariant gauge scenario lead to an expression for $\hat{q}$ containing the expectation value of two light-cone Wilson lines. We find that in a general gauge, additional interaction terms in the Lagrangian have to be considered, leading to the introduction of transverse gauge links.