On deviations from bimaximal neutrino mixing

Abstract

The PMNS neutrino mixing matrix U PMNS is in general a product of two unitary matrices U lep and U ν arising from the diagonalization of the charged lepton and neutrino mass matrices, U PMNS =U † lep U ν . Assuming that U ν is a bimaximal mixing matrix, we investigate the possible forms of U lep. We identify three possible generic structures of U lep, which are compatible with the existing data on neutrino mixing. One corresponds to a hierarchical “CKM-like” matrix. In this case relatively large values of the solar neutrino mixing angle θ sol, and of | U e3 | 2≡|( U PMNS) e3 | 2, are typically predicted, tan 2 θ sol≳0.42, | U e3 | 2≳0.02, while the atmospheric neutrino mixing angle θ atm can deviate noticeably from π/4, sin 22 θ atm≳0.95. The second corresponds to one of the mixing angles in U lep being equal to π/2, and predicts practically maximal atmospheric neutrino mixing sin 22 θ atm≃1. Large atmospheric neutrino mixing, sin 22 θ atm≳0.95, is naturally predicted by the third possible generic structure of U lep, which corresponds to all three mixing angles in U lep being large. We focus especially on the case of CP-non-conservation, analyzing it in detail. We show how the CP-violating phases, arising from the diagonalization of the neutrino and charged lepton mass matrices, contribute to the measured neutrino mixing observables.