Current and Future Neutrino Oscillation Constraints on Leptonic Unitarity

The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in the mixing of the active neutrino states. Motivated by the prospect that future experiments may provide a precise measurement of the lepton mixing matrix, we revisit current constraints on unitarity violation from oscillation measurements and project how next-generation experiments will improve our current knowledge. With the next-generation data, the normalizations of all rows and columns of the lepton mixing matrix will be constrained to $\lesssim$10\% precision, with the $e$-row best measured at $\lesssim$1\% and the $\tau$-row worst measured at ${\sim}10\%$ precision. The measurements of the mixing matrix elements themselves will be improved on average by a factor of $3$. We highlight the complementarity of DUNE, T2HK, JUNO, and IceCube Upgrade for these improvements, as well as the importance of $\nu_\tau$ appearance measurements and sterile neutrino searches for tests of leptonic unitarity.