Thermalization of mini-jets in a quark-gluon plasma

TL;DR

This paper investigates how soft components of high-energy jets thermalize in a quark-gluon plasma, demonstrating that soft gluons relax quickly to equilibrium after quasi-democratic branchings, leading to jet quenching.

Contribution

It provides the first exact analytic solutions to the ultrarelativistic Fokker-Planck equation in one-dimensional phase-space, supporting the thermalization scenario.

Findings

Soft gluons thermalize rapidly via elastic collisions.

Jet quenching occurs through multiple branchings and thermalization.

Analytic solutions confirm the physical picture of jet evolution.

Abstract

We complete the physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma by investigating the thermalization of the soft components of the jet. We argue that the following scenario should hold: the leading particle emits a significant number of mini-jets which promptly evolve via quasi-democratic branchings and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature T. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equilibrium with the plasma over a time scale which is considerably shorter than the typical lifetime of the mini-jet. The thermalized gluons form a tail which lags behind the hard components of the jet. We support this scenario, first, via parametric arguments and, next, by studying a simplified kinetic equation, which describes the jet dynamics in longitudinal phase-space. We solve the kinetic equation using both (semi-)analytical and numerical methods. In particular, we obtain the first exact, analytic, solutions to the ultrarelativistic Fokker-Planck equation in one-dimensional phase-space. Our results confirm the physical picture aforementioned and demonstrate the quenching of the jet via multiple branching followed by the thermalization of the soft gluons in the cascades.