Fluctuation-Dissipation Relation for Hard Partons in a Gluonic Plasma

TL;DR

This paper establishes a fluctuation-dissipation relation linking drag and diffusion coefficients for a high-energy quark moving through a thermal gluon plasma, using non-perturbative QCD techniques.

Contribution

It introduces a novel fluctuation-dissipation relation for hard partons in a gluonic plasma, connecting transport coefficients to local operators via complex analysis.

Findings

Derived a relation connecting drag and diffusion coefficients.

Expressed transport coefficients in terms of local operators.

Related local operators to physical coefficients near light-like dispersion.

Abstract

We derive a fluctuation dissipation relation connecting the drag and diffusion jet transport coefficients for an energetic light quark traversing a non-perturbative thermalized gluon plasma. The hard quark is taken to be close to on-shell, with an energy scale parametrically larger than the medium temperature. We introduce a general complex-valued function for each transport coefficient. Evaluating these in the deep Euclidean momentum region enables their expression in terms of local operators. Using contour-integration techniques, we relate these local operators, after vacuum subtraction, to the physical transport coefficients that arise along a branch cut, close to light-like dispersion. The derived relation relates the longitudinal drag coefficient to the longitudinal and transverse diffusion coefficients, and the thermal gluon condensate.