The Fate of the Initial State Fluctuations in Heavy Ion Collisions. III The Second Act of Hydrodynamics

TL;DR

This paper analytically studies how small initial fluctuations evolve hydrodynamically in heavy ion collisions, incorporating viscosity effects and comparing results with experimental data to understand the Quark-Gluon plasma's behavior.

Contribution

It provides a comprehensive analytical framework for propagating small perturbations in hydrodynamic models of heavy ion collisions, including viscous effects and specific flow solutions.

Findings

Viscosity significantly alters the spectra and correlations of emitted particles.

Analytical solutions for perturbations are derived for Gubser flow, enabling detailed comparison with data.

Good agreement with STAR experimental data for large viscosity values.

Abstract

Hydrodynamical description of the "Little Bang" in heavy ion collisions is surprisingly successful, mostly due to the very small viscosity of the Quark-Gluon plasma. In this paper we systematically study the propagation of small perturbations, also treated hydrodynamically. We start with a number of known techniques allowing for analytic calculation of the propagation of small perturbations on top of the expanding fireball. The simplest approximation is the "geometric acoustics", which substitutes the wave equation by mechanical equations for the propagating "phonons". Next we turn to the case in which variables can be separated, in which case one can obtain not only the eikonal phases but also amplitudes of the perturbation. Finally, we focus on the so called Gubser flow, a particular conformal analytic solution for the fireball expansion, on top of which one can derive closed equations for small perturbations. Perfect hydrodynamics allows all variables to be separated and all equations to be solved in terms of known special functions. We can thus collect the analytical expression for all the harmonics and reconstruct the complete Green function of the problem. In the viscous case the equations still allow for variable separation, but one of the equations has to be solved numerically. We still can collect all the harmonics and show real-time perturbation evolution, observing viscosity-induced changes in the spectra and the correlation functions of secondaries. We end up by comparing the calculated angular shape of the correlation function to the STAR experimental data, and find, for sufficiently large viscosity, a surprisingly good agreement.