Fluctuation of the initial condition from Glauber models

TL;DR

This paper examines the fluctuations of initial conditions in heavy-ion collisions using Glauber models, revealing model dependence and providing analytic estimates for fluctuation ratios, with implications for jet quenching and flow coefficients.

Contribution

It offers a comparative analysis of initial condition fluctuations across different Glauber models and derives an analytic formula for fluctuation ratios at central collisions.

Findings

Fluctuation measures depend significantly on the Glauber model used.

The scaled standard deviation of epsilon* ranges from ~0.5 in central to 0.3-0.4 in peripheral collisions.

Analytic estimate for fluctuation ratio at zero impact parameter is approximately 0.52.

Abstract

We analyze measures of the azimuthal asymmetry, in particular the participant harmonic moments, epsilon*, in a variety of Glauber-like models for the early stage of collisions at RHIC. Quantitative comparisons indicate substantial model dependence for epsilon*, reflecting different effective number of sources, while the dependence of the scaled standard deviation sigma(epsilon*)/epsilon* on the particular Glauber model is weak. For all the considered models the values of sigma(epsilon*)/epsilon* range from ~0.5 for the central collisions to ~0.3-0.4 for peripheral collisions. These values, dominated by statistics, change only by 10-15% from model to model. For central collisions and in the absence of correlations between the location of sources we obtain through the use of the central limit theorem the simple analytic formula sigma(epsilon*)/epsilon*(b=0) ~ \sqrt{4/pi-1} ~ 0.52$, independent on the collision energy, mass number, or the number of sources. We investigate the shape-fluctuation effects for jet quenching and find they are important only for very central events. Finally, we list some remarks and predictions from smooth hydrodynamics on higher flow coefficients and their fluctuations, in particular sigma(v_4)/v_4=2 sigma(v_2)/v_2.