Deviation from Tri-Bimaximal Neutrino mixing from the Charged Lepton Sector

TL;DR

This paper investigates how deviations from tri-bimaximal neutrino mixing can arise from corrections in the charged lepton sector, focusing on symmetry breaking effects and their impact on mixing angles.

Contribution

It introduces a model with specific $Z_2$ symmetries in charged lepton and neutrino sectors to analyze deviations from TBM mixing due to symmetry breaking.

Findings

$ heta_{13}$ is related to deviations in $ heta_{12}$.

Deviation of $ heta_{23}$ is proportional to $m_{bc}/m_{ au}$.

The model quantifies how charged lepton corrections affect neutrino mixing angles.

Abstract

The tri-bimaximal mixing matrix is most likely the leading order term in the description of leptonic mixing. We derive deviations from tri-bimaximal mixing(TBM) due to corrections from the charged lepton sector. We assume a decoupled 2-3 symmetry, which is a $Z_2$ symmetry, in the charged lepton sector and another $Z_2$ symmetry in the neutrino sector. The TBM is obtained in the flavor symmetric limit. We consider deviations from the TBM form arising from the breaking of the 2-3 symmetry in the charged lepton sector but do not consider deviations from the breaking of the flavor symmetry in the neutrino sector. In particular we find the size of $\sin{\theta_{13}}$ to be related to the deviation $\sin{\theta_{12}}$ from $\sqrt{1/3}$ while the deviation of $\sin{\theta_{23}}$ from its tri-bimaximal value is $ \sim {m_{\mu} \over m_{\tau}}$.