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

Abstract

We demonstrate that only two ansätze can produce the features ofthe neutrino mixing angles. The first ansatz comes from thequark-lepton grand unification; νDi = VCKMνα issatisfied for left-handed neutrinos, where νDi ≡ (νD1,νD2,νD3) are the Dirac mass eigenstates andνα ≡ (νe,νμ,ντ) are the flavoureigenstates. The second ansatz comes from the assumption; νDi = Ubimaximalνi is satisfied between the Dirac masseigenstates νDi and the light Majorana neutrino masseigenstates νi ≡ (ν1,ν2,ν3), whereUbimaximal is the 3 × 3 rotation matrix that containstwo maximal mixing angles and a zero mixing. By these two ansätze,the Maki-Nakagawa-Sakata lepton flavour mixing matrix is given byUMNS = VCKM†Ubimaximal. We find that in thismodel the novel relation θsol + θ13 = π/4 issatisfied, where θsol and θ13 are solar andCHOOZ angle, respectively. This “Solar-CHOOZ Complementarity”relation indicates that only if the CHOOZ angle θ13 issizable, the solar angle θsol can deviate from the maximalmixing. Our predictions are θsol = 36°, θ13 = 9° and θatm = 45°, which are consistent withexperiments. We also infer the CP violation in neutrinooscillations. The leptonic Dirac CP phase δMNS ispredicted as sin δMNS ≃ Aλ2η, where A,λ,η are the CKM parameters in Wolfensteinparametrization. In contrast to the quark CP phase δCKM ≃ \U0001d4aa(1), the leptonic Dirac CP phase is very small,δMNS ≃ 0.8°. Furthermore, we remark that theratio of the Jarlskog CP violation factor for quarks and leptons isimportant, because the large uncertainty on η is cancelled outin the ratio, RJ ≡ JCKM/JMNS ≃ 4(2)1/2Aλ3 ≃ 5 × 10−2.