Estimating $\hat{q}$ in Quenched Lattice SU(2) Gauge Theory

TL;DR

This paper non-perturbatively estimates the jet transport coefficient  in quenched SU(2) lattice gauge theory by relating a light-like correlator to local operators in Euclidean space, providing insights into jet quenching in a thermal medium.

Contribution

It introduces a method to estimate  in SU(2) gauge theory using lattice calculations and analytic relations, extending previous perturbative approaches.

Findings

 is estimated for temperatures 400-600 MeV and jet energies above 20 GeV.

The leading term in the series dominates, simplifying the estimate.

Numerical calculations support the dominance of the leading term.

Abstract

The propagation of a virtual quark in a thermal medium is considered. The non-perturbative jet transport coefficient $\hat{q}$ is estimated in quark less SU(2) lattice gauge theory. The light like correlator which defines $\hat{q}$, defined in the regime where the jet has small virtuality compared to its energy, is analytically related to a series of local operators in the deep Euclidean region, where the jet's virtuality is of the same order as its energy. It is demonstrated that in this region, for temperatures in the range of T=400-600 MeV, and for jet energies above 20 GeV, the leading term in the series is dominant over the next-to-leading term and thus yields an estimate of the value of $\hat{q}$. In these proceedings we discuss the details of the numerical calculation.