Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices

TL;DR

This paper investigates how small orthogonal rotations can correct neutrino mixing matrices to align with observed mixing angles, identifying specific rotation schemes that fit experimental data within 1σ and 2σ ranges.

Contribution

It introduces a systematic analysis of rotation-based corrections to TBM, BM, and DC matrices, identifying schemes that successfully match experimental neutrino mixing angles.

Findings

Certain rotation schemes fit all angles within 1σ.

Some schemes match angles within 2σ.

Other schemes are less successful or excluded.

Abstract

In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $\theta_{13}$ and checking the consistency with other neutrino mixing angles. The corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}\cdot U \cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}\cdot U \cdot R_{23}$, $R_{12}\cdot U \cdot R_{13}$ for BM and $R_{13}\cdot U \cdot R_{13}$ for TBM perturbative case successfully fit all neutrino mixing angles within $1\sigma$ range. The perturbed PMNS matrix $R_{12}\cdot U \cdot R_{13}$ for DC, TBM and $R_{23}\cdot U \cdot R_{23}$ for TBM case is successful in producing mixing angles at 2$\sigma$ level. The other rotation schemes are either excluded or successful in producing mixing angles at $3\sigma$ level.