  We study correlations between 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. Factorization
coefficients based on the ratio of such four-particle correlators allow the
independent measurement of the flow vector and flow magnitude factorization
breaking coefficient. Moreover, the correlation of the angles of flow harmonics
as a function of transverse momentum can be extracted. Results are compared to
preliminary data of the ALICE Collaboration. We also present predictions for
the momentum dependent factorization breaking coefficient between mixed flow
harmonics. The correlators with 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.
