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

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 $\sim \frac{m_{\mu }}{m_{\tau }}$.

14 pages, no figures. Material and references added and reorganized. Conclusions are unchanged

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