Parameterization of Pontecorvo-Maki-Nakagawa-Sakata Mixing Matrix based on CP-violating Bipair Neutrino Mixing

published in Modern Physics Letters A 30 (2015) 1550019-1550025 (Received date: Qctober 2014) with Jun Iizuka, Teruyuki Kitabayashi and Yuki Minagawa.

arXiv:1405.4045v1 (Title changed in the published version)

$CP violation in neutrino interactions is described by three phases contained in Pontecorvo-Maki-Nakagawa-Sakata mixing matrix ($U_{PMNS}$). We argue that the phenomenologocally consistent result of the Dirac CP violation can be obtained if $U_{PMNS}$ is constructed along bipair neutrino mixing scheme, namely, requiring that $ \left| U_{12} \right| = \left| U_{32} \right|~{\rm and}~\left| U_{22} \right| = \left| U_{23} \right|~\left(\rm case~1\right)$ and $ \left| U_{12} \right| = \left| U_{22} \right|~{\rm and}~\left| U_{32} \right| = \left| U_{33} \right|~\left(\rm case~2\right)$, where $U_{ij}$ stands for the $i$-$j$ matrix element of $U_{PMNS}$. As a results, the solar, atmospheric and reactor neutrino mixing angles $\theta_{12}$, $\theta_{23}$ and $\theta_{13}$, respectively, are correlated to satisfy $\cos 2{\theta _{12}} = \sin^2\theta_{23} - \tan^2\theta_{13}$ (case 1) or $\cos 2{\theta _{12}} = \cos^2\theta_{23} - \tan^2\theta_{13}$ (case 2). Furthermore, if Dirac CP violation is observed to be maximal, $\theta_{23}$ is determined by $\theta_{13}$ to be: $\sin^2\theta_{23} \approx \left( {\sqrt 2 - 1} \right)\left( {\cos^2\theta_{13} + \sqrt 2 \sin^2\theta_{13}} \right)$ (case 1) or $\cos^2\theta_{23} \approx \left( {\sqrt 2 - 1} \right)\left( {\cos^2\theta_{13} + \sqrt 2 \sin^2\theta_{13}} \right)$ (case 2). For the case of non-maximal Dirac CP violation, we perform numerical computation to show relations between the CP-violating Dirac phase and the mixing angles.$

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