Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions

TL;DR

This paper introduces a Bessel-Fourier decomposition method to comprehensively characterize initial fluctuations in heavy-ion collision hydrodynamics, enabling mode-by-mode propagation and statistical analysis of event ensembles.

Contribution

It presents a novel decomposition technique for initial fluctuations, allowing detailed mode analysis and demonstrating Gaussianity in Monte Carlo Glauber model event distributions.

Findings

Fluctuations can be ordered by wavelength.

Mode-by-mode propagation is feasible.

Event distributions are approximately Gaussian.

Abstract

Event-by-event fluctuations in the initial conditions for a hydrodynamical description of heavy-ion collisions are characterized. We propose a Bessel-Fourier decomposition with respect to the azimuthal angle, the radius in the transverse plane and rapidity. This allows for a complete characterization of fluctuations in all hydrodynamical fields including energy density, pressure, fluid velocity, shear stress and bulk viscous pressure. It has the advantage that fluctuations can be ordered with respect to their wave length and that they can be propagated mode-by-mode within the hydrodynamical formalism. Event ensembles can then be characterized in terms of a functional probability distribution. For the event ensemble of a Monte Carlo Glauber model, we provide evidence that the latter is close to Gaussian form, thus allowing for a particularly simple characterization of the event distribution.