https://doi.org/10.1140/epjc/s10052-019-6549-2
Regular Article - Theoretical Physics
Non-Bessel–Gaussianity and flow harmonic fine-splitting
1
Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
2
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
3
Physik Department, Technische Universität München, James Franck Str. 1, 85748, Garching, Germany
* e-mail: s.f.taghavi@tum.de
Received:
10
June
2018
Accepted:
27
December
2018
Published online:
29
January
2019
Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution 
and 2k-particle cumulants 
. In the present study, we systematically connect these observables to each other by employing a Gram–Charlier A series. We quantify the deviation of 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 
, ones that are more natural to use to study near Bessel–Gaussian distributions. These new cumulants are obtained from where the collision geometry effect is extracted from it. By exploiting 
, we introduce a new set of estimators for averaged ellipticity 
, ones which are more accurate compared to 
for 
. As another application of , we show that we are able to restrict the phase space of 
, 
and 
by demanding the consistency of and with equation. The allowed phase space is a region such that 
and 
, which is compatible with the experimental observations.
© The Author(s), 2019
