A perturbative approach to the hydrodynamics of heavy ion collisions

TL;DR

This paper introduces a perturbative method for modeling the hydrodynamic evolution of fluctuations in heavy ion collisions, enabling detailed analysis of initial state effects and mode interactions.

Contribution

It presents a systematic perturbative expansion approach for hydrodynamic fluctuations, facilitating the study of mode propagation and interactions in heavy ion collision simulations.

Findings

Fluid dynamic propagation of fluctuations can be modeled with background-fluctuation splitting.

The method allows order-by-order solutions for evolution equations.

It enables analysis of mode interactions and particle spectra.

Abstract

Initial fluctuations in hydrodynamic fields such as energy density or flow velocity give access to understanding initial state and equilibration physics as well as thermodynamic and transport properties. We provide evidence that the fluid dynamic propagation of fluctuations of realistic size can be based on a background-fluctuation splitting and a systematic perturbative expansion in the fluctuating fields. Initial conditions are characterized by a Bessel-Fourier expansion for single events, event-by-event correlations and probability distributions. The evolution equations can be solved order-by-order in the expansion which allows to study the fluid dynamical propagation of single modes, the study of interaction effects between modes, the determination of the associated particle spectra and the generalization of the whole program to event-by-event correlations and distributions.