# First 4D lattice calculation of transport coefficient $\hat{q}$ for pure gluon plasma

## TL;DR

This paper introduces a first-principles lattice QCD method to calculate the jet quenching parameter $t$ in a gluon plasma, combining perturbative techniques with non-perturbative lattice computations.

## Contribution

It develops an ab initio formulation of $t$ using lattice gauge theory and perturbative QCD, enabling non-perturbative estimates of this transport coefficient.

## Key findings

- Computed $t$ on quenched SU(3) lattice.
- Expressed $t$ in terms of local field operators.
- Provided estimates for $t$ in gluon plasma.

## Abstract

The transport coefficient $\hat{q}$ plays a pivotal role in describing the phenomenon of jet quenching in the quark-gluon plasma (QGP) produced in ultra-relativistic nucleus-nucleus collisions. It is challenging to compute this coefficient from first principles due to its non-perturbative nature. In this article, we present an $ab$-$initio$ formulation of $\hat{q}$ based on the standard techniques of perturbative quantum chromodynamics (pQCD) and lattice gauge theory. We construct $\hat{q}$ by considering a leading order (LO) process where a hard parton produced from the hard scattering undergoes transverse broadening due to scatterings with the thermal medium. We do an analytic continuation to the Euclidean region and use the dispersion relation to express $\hat{q}$ in terms of series of local Field-Strength-Field-Strength (FF) operators. Each term in the series is suppressed by the hard scale $q^{-}$. Finally, we compute the local operators on the quenched SU(3) lattice and present our estimates for $\hat{q}$.