Factorization breaking for higher moments of harmonic flow

We study correlations between the harmonic flow vectors squared measured at different transverse momenta. One of the flow harmonics squared is taken at a fixed transverse momentum and correlated to the momentum averaged harmonic flow squared of the same order. Such four particle correlators, dependent on transverse momentum, have been recently measured experimentally. The correlation based on four-particle correlators allows the independent measurement of the flow vector and flow magnitude correlation coefficient. Also, the correlation of the harmonic flow angles as a function of transverse momentum can be extracted. Results are compared to the preliminary data of the ALICE Collaboration. We also present the predictions for the momentum dependent correlation coefficient between mixed flow harmonics. The correlations between squares of mixed harmonics can serve as a way to independently measure the flow vector, flow magnitude, and flow angle correlations, and could be used to gain additional information on the fluctuating initial state and the dynamics in heavy-ion collisions.