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Translation of collision geometry fluctuations into momentum anisotropies in relativistic heavy-ion collisions

We develop a systematic framework for the study of the initial collision geometry fluctuations in relativistic heavy-ion collisions and investigate how they evolve through different stages of the fireball history and translate into final particle momentum anisotropies. We find in our event-by-event analysis that only the few lowest momentum anisotropy parameters survive after the hydrodynamical evolution of the system. The geometry of the produced medium is found to be affected by the pre-equilibrium evolution of the medium and the thermal smearing of the discretized event-by-event initial conditions, both of which tend to smear out the spatial anisotropies. We find such effects to be more prominent for higher moments than for lower moments. The correlations between odd and even spatial anisotropy parameters during the pre-equilibrium expansion are quantitatively studied and found to be small. Our study provides a theoretical foundation for the understanding of initial state fluctuations and the collective expansion dynamics in relativistic heavy-ion collisions.