CP violation in bipair neutrino mixing

TL;DR

This paper investigates CP violation in bipair neutrino mixing, proposing modifications to account for observed non-zero reactor angle and analyzing implications for CP phases, with distinctions between two cases.

Contribution

It introduces a modification scheme to produce non-zero reactor angle in bipair neutrino mixing and analyzes its impact on CP-violating phases, distinguishing two cases.

Findings

The modified scheme can generate non-zero $ heta_{13}$ using charged lepton contributions.

Significant differences in CP phase structures are found between the two cases.

The model aligns with observed atmospheric mixing angle in one case but faces challenges with reactor angle observations.

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 $\sin^2\theta_{13} \neq 0$ 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.