Properties of quark-gluon plasma (QGP) produced in heavy-ion collisions can be inferred via its hydrodynamic response to the anisotropies in the initial-state geometry. This phenomenon is known as collective anisotropic flow and its measurements were crucial in establishing the perfect-liquid paradigm about QGP properties. Experimentally, the most precise flow results in the past two decades have been obtained with multiparticle correlations and cumulants, which are in heavy-ion collisions robust against unwanted systematic biases characteristic for other analysis techniques. However, in the flow measurements in small-collision systems multiparticle techniques are also not reliable.
To make further progress, we reconcile for the first time the strict mathematical formalism of multivariate cumulants with the usage of cumulants in anisotropic flow analyses in high-energy nuclear collisions . This reconciliation yields to the next generation of observables to be used in flow analyses: symmetric and asymmetric cumulants of flow amplitudes, event-by-event cumulants of azimuthal angles, and cumulants of symmetry plane correlations. We demonstrate that each higher-order cumulant of flow amplitudes extracts information which is inaccessible at lower orders, and therefore their measurements by definition provide new and independent constraints on the QGP properties . The new event-by-event cumulants of azimuthal angles have the potential to disentangle flow and non-flow contributions in the measured correlations. To achieve that goal, we present the first analytic solutions for the long-standing problem of combinatorial background in the measured correlations .
Predictions from state-of-the-art theoretical models for these new flow observables are presented as well.
 A. Bilandzic, M. Lesch, C. Mordasini and S. F. Taghavi, arXiv:2101.05619
 ALICE Collaboration, Phys. Rev. Lett. 127, 092302 (2021), arXiv: 2101.02579
 A. Bilandzic, arXiv:2106.05760