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_{\nu} arising from the diagonalization of the charged lepton and neutrino mass matrices, U_{PMNS} = U^{\dagger}_{lep} U_{\nu}. Assuming that U_{\nu} 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 \theta_{sol}, and of |U_{e3}|^2, are typically predicted, \tan^2\theta_{sol} \gtap 0.42, |U_{e3}|^2 \gtap 0.02, while the atmospheric neutrino mixing angle \theta_{atm} can deviate noticeably from \pi/4, \sin^2 2\theta_{atm} \gtap 0.95. The second corresponds to one of the mixing angles in U_{lep} being equal to \pi/2, and predicts practically maximal atmospheric neutrino mixing \sin^2 2\theta_{atm} \simeq 1. Large atmospheric neutrino mixing, \sin^2 2\theta_{atm} \gtap 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-nonconservation, 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.