Parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix based on CP-violating bipair neutrino mixing

Abstract

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 $|U_{12}|=|U_{32}|\mathrm{and}|U_{22}|=|U_{23}|(case1)$ and $|U_{12}|=|U_{22}|\mathrm{and}|U_{32}|=|U_{33}|(case2)$, 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: ${\sin }^2{\theta }_{23}\approx (\sqrt{2}-1)({\cos }^2{\theta }_{13}+\sqrt{2}{\sin }^2{\theta }_{13})$ (case 1) or ${\cos }^2{\theta }_{23}\approx (\sqrt{2}-1)({\cos }^2{\theta }_{13}+\sqrt{2}{\sin }^2{\theta }_{13})$ (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.

Comments: 7 pages, 3 figures, version to appear in Modern Physics Letters A