Momentum Broadening of a Fast Parton in a Perturbative Quark-Gluon Plasma

TL;DR

This paper investigates how a fast parton gains transverse momentum in a quark-gluon plasma, showing that instabilities can cause exponential growth in momentum broadening, with implications for understanding jet quenching.

Contribution

It introduces a quantum definition of the momentum transfer coefficient  in a quark-gluon plasma and analyzes its behavior in both equilibrium and unstable off-equilibrium conditions.

Findings

 grows exponentially in unstable plasmas.

In equilibrium,  is related to classical Langevin dynamics.

Unstable modes significantly enhance momentum broadening.

Abstract

The average transverse momentum transfer per unit path length to a fast parton scattering elastically in a perturbative quark-gluon plasma is related to the radiative energy loss of the parton. We first calculate the momentum transfer coefficient $\hat q$ in terms of a classical Langevin problem and then define it quantum-mechanically through scattering matrix element. After treating the well known case of a quark-gluon plasma in equilibrium we consider an off-equilibrium unstable plasma. As a specific example, we treat the two-stream plasma with unstable modes of longitudinal chromoelectric field. In the presence of the instabilities, $\hat q$ is shown to exponentially grow in time.