Using spectator distributions to measure the initial geometry fluctuation

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A study of eccentricity (εₙ) fluctuations and its possible impact on final state momentum anisotropy (vₙ) 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 2nd harmonic. Position fluctuations in transverse plane will increase ε₂ and hence possibly v₂ for the most central nucleus-nucleus collisions. For semi-central and peripheral collisions, the fluctuations have opposite effect, it deceases the eccentricity ε₂. The fluctuation of initial geometry can be studied in collider experiments by studying the spectator distribution on the both sides of the beam.