Small systems and regulator dependence in relativistic hydrodynamics

TL;DR

This paper investigates how the choice of regulator in relativistic hydrodynamics affects small systems like those in pA or pp collisions, showing regulator dependence is significant only at very low multiplicities, thus supporting hydrodynamics' applicability.

Contribution

It demonstrates that regulator dependence in relativistic hydrodynamics becomes relevant only for very small multiplicities, clarifying the conditions under which hydrodynamics remains reliable in small systems.

Findings

Regulator dependence is negligible for high multiplicities.

Dependence becomes significant at multiplicities around a few.

Supports the validity of hydrodynamics in small systems.

Abstract

Consistent theories of hydrodynamics necessarily include nonhydrodynamic modes, which can be viewed as a regulator necessary to ensure causality. Under many circumstances the choice of regulator is not relevant, but this is not always the case. In particular, for sufficiently small systems (such as those arising in pA or pp collisions) such dependence may be inevitable. We address this issue in the context of the modern version of M\"uller-Israel-Stewart theory of relativistic hydrodynamics. In this case, by demanding that the nonhydrodynamic modes be subdominant, we find that regulator dependence becomes inevitable only for multiplicities $dN/dY$ of the order of a few. This conclusion supports earlier studies based on hydrodynamic simulations of small systems, at the same time providing a simple physical picture of how hydrodynamics can be reliable even in such seemingly extreme conditions.