Covariant diffusion tensor for jet momentum broadening out of equilibrium

TL;DR

This paper introduces a Lorentz-covariant diffusion tensor to describe jet momentum broadening in out-of-equilibrium media, revealing additional effects beyond the standard scalar coefficient, and studies its evolution towards equilibrium.

Contribution

It generalizes the jet transport coefficient to a tensor form, capturing frame-covariant medium effects and correlations, and applies the formalism to out-of-equilibrium scalar field theory.

Findings

Out-of-equilibrium corrections can enhance or reduce jet broadening.

The tensor formalism captures energy diffusion and correlations.

The evolution of the tensor towards equilibrium is characterized.

Abstract

Jets are produced in the earliest stages of heavy-ion collisions, where they can interact with a medium that is not yet close to local equilibrium. Motivated by this, we generalize the usual jet transport coefficient $\hat q$ to a Lorentz-covariant diffusion tensor $\hat q^{\mu\nu}$ within a leading-order elastic (Boltzmann/Fokker--Planck) description of jet--medium interactions. The tensor formulation organizes medium effects in a frame-covariant way and reveals additional information beyond the standard scalar definition, including energy diffusion and off-diagonal components that encode correlations between energy and momentum exchange which are absent (or redundant) in equilibrium. We illustrate the formalism in (tree-level) massless $\lambda\varphi^4$ theory for isotropic but out-of-equilibrium states. For sufficiently large jet momentum, quantum statistical effects become subleading, so that the non-equilibrium evolution can be studied reliably in the classical (Boltzmann) limit. This allows us to solve the corresponding Boltzmann equation for the medium and determine the time dependence of $\hat q^{\mu\nu}$ as the system approaches equilibrium. We find that out-of-equilibrium corrections can either enhance or reduce jet momentum broadening, depending on the initial distribution function.