Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions

Relativistic dissipative fluid dynamics is a common tool to describe the space-time evolution of the strongly interacting matter created in ultrarelativistic heavy-ion collisions. For a proper comparison to experimental data, fluid-dynamical calculations have to be performed on an event-by-event basis. Therefore, fluid dynamics should be able to reproduce, not only the event-averaged momentum anisotropies, $<v_{n}>$, but also their distributions. In this paper, we investigate the event-by-event distributions of the initial-state and momentum anisotropies $\epsilon_n$ and $v_n$, and their correlations. We demonstrate that the event-by-event distributions of relative $v_n$ fluctuations are almost equal to the event-by-event distributions of corresponding $\epsilon_n$ fluctuations, allowing experimental determination of the relative anisotropy fluctuations of the initial state. Furthermore, the correlation $c(v_2,v_4)$ turns out to be sensitive to the viscosity of the fluid providing an additional constraint to the properties of the strongly interacting matter.