Gauge invariant definition of the jet quenching parameter

TL;DR

The paper derives a gauge-invariant definition of the jet quenching parameter $\hat{q}$ within Soft-Collinear Effective Theory extended to include Glauber gluons. By performing explicit calculations in both covariant and light-cone gauges and introducing transverse Wilson lines, the authors show how $\hat{q}$ can be expressed through a gauge-invariant correlator that combines longitudinal and transverse Wilson lines. The formalism unifies gauge choices and enables connections to lattice methods via a gauge-invariant observable related to the medium's static energy at the magnetic scale $g^2T$, with implications for nonperturbative contributions to transverse momentum broadening. The approach provides a clear path to incorporating nonperturbative effects and lattice data (via EQCD/MQCD) into quantitative estimates of $\hat{q}$ in a weakly coupled quark-gluon plasma, and sets the stage for potential NNLO refinements. Overall, the work delivers a rigorous, gauge-consistent framework for jet quenching that can leverage lattice gauge theory inputs and improve phenomenological interpretations of jet quenching in heavy-ion collisions.

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.

Figures (7)

• Figure 1: Cutting diagram contributing to ${\cal A}_{mn}$. The dashed line is the cut. The continuous line across the cut in the initial state and in the final state represents a collinear parton.
• Figure 2: The Wilson lines in the right-hand side of eq. (\ref{['eq:eramo']}): the upper line corresponds to the operator $W^\dagger[0,x_\perp]$, the lower line to the operator $W[0,0]$, both taken in the limit $L\to\infty$.
• Figure 3: Leading-order diagram in the opacity expansion.
• Figure 4: Arbitrary order diagram in the opacity expansion in light-cone gauge. Any number of 1- or 2-gluon vertices can appear on both sides of the cut.
• Figure 5: Transverse Wilson lines contributing to the right-hand side of eq. (\ref{['eq:Plc']}). For convenience, in the picture, we have chosen $l_\perp \parallel x_\perp$.