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

Junpei Harada

doi:10.1209/epl/i2006-10101-2

paper

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

arXiv:hep-ph/0512294 · doi:10.1209/epl/i2006-10101-2

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; $ν_{D i} = V_{C K M} ν_{α}$ is satisfied for left-handed neutrinos, where $ν_{D i}$ are the Dirac mass eigenstates and $ν_{α}$ are the flavour eigenstates. The second ansatz comes from the assumption; $ν_{D i} = U_{bima x ima l} ν_{i}$ is satisfied between the Dirac mass eigenstates $ν_{D i}$ and the light Majorana neutrino mass eigenstates $ν_{i}$ , where $U_{bima x ima l}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matrix is given by $U_{M N S} = V_{C K M}^{†} U_{bima x ima l}$ . We find that in this model the novel relation $θ_{so l} + θ_{13} = π /4$ is satisfied, where $θ_{so l}$ 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 $θ_{so l}$ can deviate from the maximal mixing. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase $δ_{M N S}$ is predicted as $sin δ_{M N S} ≃ A λ^{2} η$ , 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, $R_{J} \equiv J_{C K M} / J_{M N S} ≃ 42 A λ^{3} ≃ 5 \times 1 0^{- 2}$ .

arXiv comment9 pages, no figures; v2 references added, v3 references added

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

Abstract

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