Using spectator distributions to measure the initial geometry fluctuation

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.