  Higher order symmetric cumulants of global collective observables in heavy
ion collisions are studied. The symmetric cumulants can be straightforwardly
constructed for scalar observables: the average transverse momentum, the
multiplicity, and the squares of harmonic flow vectors. Third and fourth order
cumulants are calculated in the hydrodynamic model. A linear predictor of the
average transverse momentum and harmonic flow coefficients in a collision is
used to predict the value of the cumulants from the moments of the initial
distribution. The symmetric cumulants divided by the averages (or the standard
deviations) of the considered observables can be used as a fine tool to study
correlations present in the initial state of the collision.
