Kurtosis of elliptic flow fluctuations

Elliptic flow ($v_2$) in ultrarelativistic nucleus-nucleus collisions fluctuates event to event, both in magnitude and in orientation with respect to the reaction plane. Even though the reaction plane is not known event to event in experiment, we show that the statistical properties of $v_2$ fluctuations in the reaction plane can be precisely extracted from experimental data. Previous studies have shown how to measure the mean, variance and skewness using the first three cumulants $v_2\{2\}$, $v_2\{4\}$ and $v_2\{6\}$. We complement these studies by providing a formula for the kurtosis, which requires an accurate determination of the next cumulant $v_2\{8\}$. Using existing data, we show that the kurtosis is positive for most centralities, in contrast with the kurtosis of triangular flow fluctuations, which is negative. We argue that these features are robust predictions of fluid-dynamical models.