Dissipative corrections to particle spectra and anisotropic flow from a saddle-point approximation to kinetic freeze out

Christian Lang,Nicolas Borghini

doi:10.1140/epjc/s10052-014-2955-7

Abstract

A significant fraction of the changes in momentum distributions induced by dissipative phenomena in the description of the fluid fireball created in ultrarelativistic heavy-ion collisions actually take place when the fluid turns into individual particles. We study these corrections in the limit of a low freeze-out temperature of the flowing medium, and we show that they mostly affect particles with a higher velocity than the fluid. For these, we derive relations between different flow harmonics, from which the functional form of the dissipative corrections could ultimately be reconstructed from experimental data.

Highlights

High-energy collisions of heavy nuclei, as performed at the Brookhaven relativistic heavy ion collider (RHIC) and the CERN large hadron collider (LHC), lead to the formation of an extended fireball, the evolution of which is to a large degree well modelled by the laws of relativistic fluid dynamics
Turning to fast particles (Sect. 4), we investigate the dissipative corrections from freeze out on anisotropic flow and find that by using relations between different flow harmonics, it may be possible to constrain the functional form of these effects from the data
In the previous two sections, we investigated the effect of the dissipative correction δ f to the phase space distribution of particles at freeze out on the particle spectrum

Summary

Introduction

High-energy collisions of heavy nuclei, as performed at the Brookhaven relativistic heavy ion collider (RHIC) and the CERN large hadron collider (LHC), lead to the formation of an extended fireball, the evolution of which is to a large degree well modelled by the laws of relativistic fluid dynamics (see e.g. Ref. [1] for a recent review). Dissipation affects the endpoint of the fluid evolution, that is, the transition from a continuous medium to a collection of particles This corresponds in so-called “hybrid models” to the switch from hydrodynamics to a particle transport model [10], or in a more simplified picture, which we shall hereafter adopt, to the sudden (kinetic) freeze out of the fluid into noninteracting particles. If the freezing-out fluid is dissipative, f contains extra terms, to ensure the continuity of the energy-momentum tensor at decoupling These corrections have been computed, in the case of a transition to an ideal single-component Boltzmann gas, for a fluid with finite shear [12] or bulk viscosity [13], or a conformal fluid obeying second-order dissipative hydrodynamics [14].

Saddle-point computation of the Cooper–Frye integral

Slow particles

Fast particles

Discussion