Neutrino oscillations: status and prospects for the determination of neutrino mass ordering and the leptonic $CP$-violation phase

This review is devoted to the 110th anniversary of the birth of Bruno Pontecorvo, an outstanding physicist who made an invaluable contribution to the development of modern neutrino physics, having predicted, inter alia, nonzero neutrino masses, mixing, and oscillations that were experimentally discovered in the early 2000s. Significant progress has been made over 20 years of experiments in determining the parameters of three-flavor neutrino oscillations. The status of and prospects for establishing neutrino mass ordering and the leptonic $CP$-violation phase $(\delta _{CP})$, unknown parameters of this theory, are discussed. It is expected that they will be measured in long-baseline experiments in the next decade. The ongoing accelerator experiments NOvA and T2K, which are currently the most sensitive to neutrino mass ordering and $\delta _{CP}$, are described in detail. For ease of comparison, NOvA and T2K techniques and results, including all aspects of data collection and analysis, are presented on a stage-by-stage basis. Possible reasons for the disagreement between the $\delta _{CP}$ values measured by NOvA and T2K are discussed. Future accelerator (DUNE and Hyper-Kamiokande) and reactor (JUNO) megaprojects are considered, along with experiments designed to use atmospheric neutrinos: IceCube Upgrade, KM3NeT (ORCA), and ICAL at INO, which can measure unknown oscillation parameters and refine the ones already determined.