Probing hydrodynamics and the moments of the elliptic flow distribution in $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$ lead-lead collisions using higher-order cumulants

The $v_{2}$ cumulant values for the elliptic anisotropy harmonic, $v_{2}\{2k\}$, are determined up to the tenth order ($k = 5$) as a function of the collision centrality in $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$ lead-lead collisions. The data were obtained by the CMS experiment at the LHC. A fine splitting is observed for the coefficients, with $v_{2}\{2\} > v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\}$. The subtle differences in the higher order harmonics allow for a precise determination of the underlying hydrodynamics. Based on these results, centrality-dependent moments for the fluctuation-driven $v_{2}$ distribution are determined, including the skewness, the kurtosis and, for the first time, the superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial state geometry in high energy nuclear collisions.