Explaining higher-order correlations between elliptic and triangular flow

TL;DR

This paper reveals a simple underlying structure in complex flow cumulants in heavy-ion collisions, linking higher-order correlations to the mean elliptic flow and geometric collision features.

Contribution

It derives analytic relations between cumulants of different orders, explaining their behavior and providing predictions for higher-order cumulants in Pb+Pb collisions.

Findings

Cumulants' changes are determined by mean elliptic flow from collision geometry.

Derived simple analytic relations between different order cumulants.

Predicted higher-order cumulants that have not yet been experimentally analyzed.

Abstract

The ALICE and CMS Collaborations have analyzed a number of cumulants mixing elliptic flow ($v_2$) and triangular flow ($v_3$), involving up to $8$ particles, in Pb+Pb collisions at the LHC. We unravel an unexpected simplicity in these complex mathematical quantities for collisions at fixed impact parameter. We show that as one increases the order in $v_2$, for a given order in $v_3$, the changes in the cumulants are solely determined by the mean elliptic flow in the reaction plane, which originates from the almond-shaped geometry of the overlap area between the colliding nuclei. We derive simple analytic relations between cumulants of different orders on this basis. These relations are in good agreement with recent data from the CMS Collaboration. We argue that agreement will be further improved if the analysis is repeated with a finer centrality binning. We make quantitative predictions for cumulants of order 10 which have not yet been analyzed.