CP violation in bipair neutrino mixing

Abstract

There are experimentally determined two best-fit points for the atmospheric neutrino mixing angle ${\theta }_{23}$: ${\sin }^2{\theta }_{23}=0.413$ (case A) and ${\sin }^2{\theta }_{23}=0.594$ (case B). In the bipair neutrino mixing scheme, we predict ${\sin }^2{\theta }_{23}=\sqrt{2}-1$ (case 1) to be consistent with the case A and ${\sin }^2{\theta }_{23}=2-\sqrt{2}$ (case 2) to be consistent with the case B. If the case B is realized in nature, the bipair neutrino mixing provides a unique neutrino model consistent with the observation ${\sin }^2{\theta }_{23}=0.594$. However, the reactor neutrino mixing angle ${\theta }_{13}$ is predicted to be ${\sin }^2{\theta }_{13}=0$, which is inconsistent with the observation. We propose a new modification scheme to yield ${\sin }^2{\theta }_{13}\ne 0$ utilizing the charged lepton contribution and study its effect on both of CP-violating Dirac and Majorana phases, which is numerically estimated. It is found that there appear striking differences between the case 1 and the case 2 in their phase structure.

Comments: 10 pages, 12 figures. Accepted for publication in Physics Letters B