Small systems and regulator dependence in relativistic hydrodynamics

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 Müller-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.

v2: many small improvements in the text; additional references; the missing term in Eq. (4) restored

References in corpus (9)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• The QCD equation of state with dynamical quarks
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Entropy production in collisions of gravitational shock waves and of heavy ions
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• From strong to weak coupling in holographic models of thermalization
• How big are the smallest drops of quark-gluon plasma?
• Quasinormal modes and the phase structure of strongly coupled matter
• Statistics of thermalization in Bjorken Flow

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