On Deviations from Bimaximal Neutrino Mixing

The PMNS neutrino mixing matrix $U_{\rm PMNS}$ is in general a product of two unitary matrices $U_{\rm lep}$ and $U_{\nu}$ arising from the diagonalization of the charged lepton and neutrino mass matrices, $U_{\rm PMNS} = U^{\dagger}_{\rm lep} U_{\nu}$. Assuming that $U_{\nu}$ is a bimaximal mixing matrix, we investigate the possible forms of $U_{\rm lep}$. We identify three possible generic structures of $U_{\rm lep}$, 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 $\theta_{\rm sol}$, and of $|U_{e3}|^2 \equiv |(U_{\rm PMNS})_{e3}|^2$, are typically predicted, $\tan^2\theta_{\rm sol} \gtap 0.42$, $|U_{e3}|^2 \gtap 0.02$, while the atmospheric neutrino mixing angle $\theta_{\rm atm}$ can deviate noticeably from $\pi/4$, $\sin^22\theta_{\rm atm} \gtap 0.95$. The second corresponds to one of the mixing angles in $U_{\rm lep}$ being equal to $\pi/2$, and predicts practically maximal atmospheric neutrino mixing $\sin^2 2 \theta_{\rm atm} \simeq 1$. Large atmospheric neutrino mixing, $\sin^22\theta_{\rm atm} \gtap 0.95$, is naturally predicted by the third possible generic structure of $U_{\rm lep}$, which corresponds to all three mixing angles in $U_{\rm lep}$ 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.