Higher-order symmetry plane correlations in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV

The correlations between event-by-event fluctuations of symmetry planes are measured in Pb$-$Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV recorded by the ALICE detector at the Large Hadron Collider. This analysis is conducted using the Gaussian Estimator technique, which is insensitive to biases from correlations between different flow amplitudes. The study presents, for the first time, the centrality dependence of correlations involving up to five different symmetry planes. The correlation strength varies depending on the harmonic order of the symmetry plane and the collision centrality. Comparisons with measurements from lower energies indicate no significant differences within uncertainties. Additionally, the results are compared with hydrodynamic model calculations. Although the model predictions provide a qualitative explanation of the experimental results, they overestimate the data for some observables. This is particularly true for correlators that are sensitive to the non-linear response of the medium to initial-state anisotropies in the collision system. As these new correlators provide unique information - independent of flow amplitudes - their usage in future model developments can further constrain the properties of the strongly-interacting matter created in ultrarelativistic heavy-ion collisions.