Examination of pairs in neutrino mixing matrix

TL;DR

This paper analyzes pairs of elements in the neutrino mixing matrix to identify patterns consistent with experimental data, proposing new mixing patterns and constraining CP-violation phases.

Contribution

It introduces a method to identify pairs in the neutrino mixing matrix and suggests new mixing patterns aligned with current experimental results.

Findings

Tri-maximal mixing in ν₂ is favorable.

μ-τ interchange symmetry is supported.

Maximal CP-violation is compatible with data.

Abstract

We exam the pairs of neutrino mixing matrix and suggest pairs that can be used in the construction of new mixing patterns, with "pair" denoting the equality of the modulus of a pair of matrix elements. The results show that the tri-maximal mixing in $\nu_2$ and the $\mu$-$\tau$ interchange symmetry are good choices under current experimental results. The two cases of bi-pair mixing pattern depend on the mass hierarchy of neutrinos. We also derive constraints on the CP-phase by the pairs. The results are compatible with the maximal CP-violation in most cases that are both self-consistent and consistent with experimental results.