Using spectator distributions to measure the initial geometry fluctuation

TL;DR

This paper investigates how spectator distributions can be used to measure initial geometry fluctuations in symmetric collisions, revealing that higher harmonics are less sensitive to these fluctuations and that centrality affects eccentricity and momentum anisotropy.

Contribution

It introduces a new method using spectator differences to measure eccentricity fluctuations and analyzes their impact on final state momentum anisotropy in collisions.

Findings

Higher harmonics are less sensitive to transverse plane fluctuations.

Position fluctuations increase eccentricity and flow in central collisions.

Fluctuations decrease eccentricity in semi-central and peripheral collisions.

Abstract

A study of eccentricity ($\varepsilon_{n}$) fluctuations and its possible impact on final state momentum anisotropy ($v_{n}$) for symmetric collisions are presented in the framework of Glauber model. Effect of fluctuations of nucleon's position on the initial geometry has been studied using a new method, where the difference between oppositely moving spectators is taken as a measurement of eccentricity fluctuations. This study shows that higher harmonics ($n$ =3, 4 and 5) of eccentricity are less sensitive to fluctuations in transverse plane compared to the 2$^{nd}$ harmonic. Position fluctuations in transverse plane will increase $\varepsilon_{2}$ and hence possibly $v_{2}$ for the most central nucleus-nucleus collisions. For semi-central and peripheral collisions, the fluctuations have opposite effect, it deceases the eccentricity $\varepsilon_{2}$. The fluctuation of initial geometry can be studied in collider experiments by studying the spectator distribution on the both sides of the beam.