Explaining higher-order correlations between elliptic and triangular flow

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.