Relativistic diffusion and heavy-ion collisions

TL;DR

This paper compares first and second order relativistic diffusion theories in heavy-ion collisions, highlighting their different predictions for observable quantities and implications for understanding transient dynamics and diffusion constants.

Contribution

It introduces a detailed comparison between first and second order relativistic diffusion theories in the context of heavy-ion collisions, emphasizing their distinct evolution predictions.

Findings

First order theory washes out initial state memory.

Second order theory allows transient dynamics during freezeout.

Potential to bound diffusion constant from observations.

Abstract

We study first and second order theories of relativistic diffusion coupled to hydrodynamics under the approximation, valid at mid-rapidity in the RHIC and LHC, that conserved number densities are much smaller than the entropy density. We identify experimentally accessible quantities of interest, and show that the first and second order theories may lead to radically different evolutions of these quantities. In the first order theory the memory of the initial state is almost completely washed out, whereas in the second order theory it is possible that freezeout occurs at a time when transient dynamics is still on, and the memory of the initial state remains. There are observational consequences which we touch upon. In the first order theory, and for initial conditions when the second order theory mimics the first order, one may be able to put a bound on the diffusion constant.