Perturbation to TBM mixing and its phenomenological implications

TL;DR

This paper explores how small perturbations to the Tri-bimaximal mixing matrix can explain the observed non-zero reactor angle and predicts related phenomenological parameters, aligning theory with recent experimental data.

Contribution

It introduces a specific perturbation scheme to TBM mixing and derives constraints on parameters to fit observed neutrino mixing angles and CP violation.

Findings

Allowed parameter ranges for perturbations consistent with data

Predicted Dirac CP phase can vary between 0 and -π/2

Effective Majorana mass remains below experimental limits

Abstract

To accommodate the recently observed non-zero reactor mixing angle $\theta_{13}$, we consider the lepton mixing matrix as Tri-bimaximal mixing (TBM) form in the leading order along with a perturbation in neutrino sector. The perturbation is taken to be a rotation in 23 plane followed by a rotation in 13 plane, i.e., $R_{23}(\theta_{23}')R_{13}(\theta_{13}',\phi)$. We obtain the allowed values of the parameters $\theta_{23}'$, $\theta_{13}'$ and $\phi$, which can accommodate all the observed mixing angles consistently and calculate the phenomenological observables such as the Dirac CP violating phase ($\delta_{CP}$), Jarlskog invariant ($J_{CP}$), effective majorana mass $M_{ee}^{\nu}$, and $m_{\nu_e}$, the electron neutrino mass. We find that $\delta_{CP}$ can take any values between $0$ and $-\pi/2$ and $M_{ee}^{\nu}$ always comes below its experimental upper limit.