Influence of fluctuating initial-state shape deformations in ultra-central collisions

It is a long standing puzzle that hydrodynamic calculations give larger elliptic flow for ultra-central Pb+Pb events than experiments. One explanation is that sampling from a single particle distribution in Glauber model generates too much shape fluctuation, which can be expected to be modified by NN correlations. We study the fluctuation of shape-deformation as currently implemented in MC-Glauber-like models and its consequences on the magnitude of eccentricities. We show that for both deformed and spherical species, there are large fluctuations in the deformation that emerge event-by-event. For each nucleonic configuration, we characterize the deformation with parameters $\beta$ and $\gamma$, calculated using quadruple moments. The second order eccentricity $\varepsilon_2$ shows a strong correlation with the E-by-E deformation $\beta$'s for ultra-central collisions. We further show, via acoustic scaling, with a moderate reduction of $\beta$ by rescaling, the eccentricities we get then agree with the measured values of $v_n$, for all experimentally available centrality bins. Therefore, the model provides eccentricities that describe experimental data, both where geometry dominates and where fluctuation dominates.