The Importance of Correlations and Fluctuations on the Initial Source Eccentricity in High-Energy Nucleus-Nucleus Collisions

TL;DR

This paper analyzes how correlations and fluctuations influence the initial source eccentricity in high-energy nucleus-nucleus collisions, emphasizing the importance of event-by-event fluctuations and deriving analytical expressions for participant eccentricity cumulants.

Contribution

It introduces analytical formulas for participant eccentricity cumulants considering correlations, and compares them with Monte Carlo Glauber simulations to highlight deviations from smooth matter assumptions.

Findings

Participant eccentricity is robust against density parameter variations.

Fluctuations in $v_2$ are mainly sensitive to RMS values due to event-plane resolution.

Fourth order cumulant deviates significantly from smooth distribution estimates.

Abstract

In this paper, we investigate various ways of defining the initial source eccentricity using the Monte Carlo Glauber (MCG) approach. In particular, we examine the participant eccentricity, which quantifies the eccentricity of the initial source shape by the major axes of the ellipse formed by the interaction points of the participating nucleons. We show that reasonable variation of the density parameters in the Glauber calculation, as well as variations in how matter production is modeled, do not significantly modify the already established behavior of the participant eccentricity as a function of collision centrality. Focusing on event-by-event fluctuations and correlations of the distributions of participating nucleons we demonstrate that, depending on the achieved event-plane resolution, fluctuations in the elliptic flow magnitude $v_2$ lead to most measurements being sensitive to the root-mean-square, rather than the mean of the $v_2$ distribution. Neglecting correlations among participants, we derive analytical expressions for the participant eccentricity cumulants as a function of the number of participating nucleons, $\Npart$,keeping non-negligible contributions up to $\ordof{1/\Npart^3}$. We find that the derived expressions yield the same results as obtained from mixed-event MCG calculations which remove the correlations stemming from the nuclear collision process. Most importantly, we conclude from the comparison with MCG calculations that the fourth order participant eccentricity cumulant does not approach the spatial anisotropy obtained assuming a smooth nuclear matter distribution. In particular, for the Cu+Cu system, these quantities deviate from each other by almost a factor of two over a wide range in centrality.