Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting

Abstract: Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution $p(v_n)$ and $2k$-particle cumulants $c_n{2k}$. In the present study, we systematically connect these observables to each other by employing Gram-Charlier A series. We quantify the deviation of $p(v_n)$ from Bessel-Gaussianity in terms of flow harmonic fine-splitting. Subsequently, we show that the corrected Bessel-Gaussian distribution can fit the simulated data better than the Bessel-Gaussian distribution in the more peripheral collisions. Inspired by Gram-Charlier A series, we introduce a new set of cumulants $q_n{2k}$ that are more natural to study distributions near Bessel-Gaussian. These new cumulants are obtained from $c_n{2k}$ where the collision geometry effect is extracted from it. By exploiting $q_2{2k}$, we introduce a new set of estimators for averaged ellipticity $\bar{v}_2$ which are more accurate compared to $v_2{2k}$ for $k>1$. As another application of $q_2{2k}$, we show we are able to restrict the phase space of $v_2{4}$, $v_2{6}$ and $v_2{8}$ by demanding the consistency of $\bar{v}_2$ and $v_2{2k}$ with $q_2{2k}$ equation. The allowed phase space is a region such that $v_2{4}-v_2{6}\gtrsim 0$ and $12 v_2{6}-11v_2{8}-v_2{4}\gtrsim 0$, which is compatible with the experimental observations.