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; $ν_{Di} = V_{CKM} ν_α$ is satisfied for left-handed neutrinos, where $ν_{Di}$ are the Dirac mass eigenstates and $ν_α$ are the flavour eigenstates. The second ansatz comes from the assumption; $ν_{Di} = U_{bimaximal} ν_{i}$ is satisfied between the Dirac mass eigenstates $ν_{Di}$ and the light Majorana neutrino mass eigenstates $ν_{i}$, 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 $θ_{sol} + θ_{13} = π/4$ is satisfied, where $θ_{sol}$ and $θ_{13}$ are solar and CHOOZ angle respectively. This "Solar-CHOOZ Complementarity" relation indicates that only if the CHOOZ angle $θ_{13}$ is sizable, the solar angle $θ_{sol}$ can deviate from the maximal mixing. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase $δ_{MNS}$ is predicted as $\sin δ_{MNS} \simeq A λ^2 η$, where $A, λ, η$ 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 $η$ is cancelled out in the ratio, $R_J \equiv J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A λ^3 \simeq 5 \times 10^{-2}$.