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

Abstract

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; $\nu_{Di} = U_{bimaximal} \nu_{i}$ is satisfied between the Dirac mass eigenstates $\nu_{Di}$ and the light Majorana neutrino mass eigenstates $\nu_{i}$, where $U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matrix is given by $U_{MNS} = V_{CKM}^\dagger U_{bimaximal}$. We find that in this model the novel relation $\theta_{sol} + \theta_{13} = \pi/4$ is satisfied, 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, $R_J \equiv J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A \lambda^3 \simeq 5 \times 10^{-2}$.