Neutrino mixing and CP violation from Dirac-Majorana bimaximal mixture and quark-lepton unification

We demonstrate that only two ansatz can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; ${\nu }_{Di}=V_{CKM}{\nu }_{\alpha }$ is satisfied for left-handed neutrinos, where ${\nu }_{Di}$ are the Dirac mass eigenstates and ${\nu }_{\alpha }$ are the flavour eigenstates. The second ansatz comes from the assumption; $\nu_{Di} = U_{bimaximal} \nu_{i}$issatisfiedbetweentheDiracmasseigenstates$\nu_{Di}$andthelightMajorananeutrinomasseigenstates$\nu_{i}$,where$U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matrix is given by $U_{MNS} = V_{CKM}^\dagger U_{bimaximal}$\mathrm{.}Wefindthatinthismodelthenovelrelation$\theta_{sol} + \theta_{13} = \pi/4$issatisfied,where$\theta_{sol}$and$\theta_{13}$ are solar and CHOOZ angle respectively. This “Solar-CHOOZ Complementarity” relation indicates that only if the CHOOZ angle ${\theta }_{13}$ is sizable, the solar angle ${\theta }_{sol}$ can deviate from the maximal mixing. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase ${\delta }_{MNS}$ is predicted as $\sin {\delta }_{MNS}\simeq A{\lambda }^2\eta$, where $A, \lambda, \eta$ are the CKM parameters in Wolfenstein parametrization. Furthermore, we remark that the ratio of the Jarlskog CP violation factor for quarks and leptons is important, because the large uncertainty on $\eta$ is cancelled out in the ratio, $R_J \equiv J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A \lambda^3 \simeq 5 \times 10^{-2}$.