Non-Bessel–Gaussianity and flow harmonic fine-splitting

Abstract

Abstract Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution $$p(v_n)$$ p(vn) and 2k-particle cumulants $$c_n\{2k\}$$ cn{2k} . In the present study, we systematically connect these observables to each other by employing a Gram–Charlier A series. We quantify the deviation of $$p(v_n)$$ p(vn) from Bessel–Gaussianity in terms of harmonic fine-splitting of the flow. 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 the Gram–Charlier A series, we introduce a new set of cumulants $$q_n\{2k\}$$ qn{2k} , ones that are more natural to use to study near Bessel–Gaussian distributions. These new cumulants are obtained from $$c_n\{2k\}$$ cn{2k} where the collision geometry effect is extracted from it. By exploiting $$q_2\{2k\}$$ q2{2k} , we introduce a new set of estimators for averaged ellipticity $$\bar{v}_2$$ v¯2 , ones which are more accurate compared to $$v_2\{2k\}$$ v2{2k} for $$k>1$$ k>1 . As another application of $$q_2\{2k\}$$ q2{2k} , we show that we are able to restrict the phase space of $$v_2\{4\}$$ v2{4} , $$v_2\{6\}$$ v2{6} and $$v_2\{8\}$$ v2{8} by demanding the consistency of $$\bar{v}_2$$ v¯2 and $$v_2\{2k\}$$ v2{2k} with $$q_2\{2k\}$$ q2{2k} equation. The allowed phase space is a region such that $$v_2\{4\}-v_2\{6\}\gtrsim 0$$ v2{4}-v2{6}≳0 and $$12 v_2\{6\}-11v_2\{8\}-v_2\{4\}\gtrsim 0$$ 12v2{6}-11v2{8}-v2{4}≳0 , which is compatible with the experimental observations.