An extension of tribimaximal lepton mixing

Abstract

Harrison, Perkins and Scott have proposed simple charged lepton and neutrino mass matrices that lead to the tribimaximal mixing ${U}_{\mathrm{TBM}}$. We consider in this work an extension of the mass matrices so that the leptonic mixing matrix becomes ${U}_{\mathrm{PMNS}}={V}_{L}^{\ensuremath{\ell}\ifmmode\dagger\else\textdagger\fi{}}{U}_{\mathrm{TBM}}W$, where ${V}_{L}^{\ensuremath{\ell}}$ is a unitary matrix needed to diagonalize the charged lepton mass matrix and $W$ measures the deviation of the neutrino mixing matrix from the bimaximal form. Hence, corrections to ${U}_{\mathrm{TBM}}$ arise from both charged lepton and neutrino sectors. Following our previous work to assume a Qin-Ma-like parametrization ${V}_{\mathrm{QM}}$ for the charged lepton mixing matrix ${V}_{L}^{\ensuremath{\ell}}$ in which the $CP$-odd phase is approximately maximal, we study the phenomenological implications in two different scenarios: ${V}_{L}^{\ensuremath{\ell}}={V}_{\mathrm{QM}}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${V}_{L}^{\ensuremath{\ell}}={V}_{\mathrm{QM}}$. We find that the latter is more preferable, though both scenarios are consistent with the data within $3\ensuremath{\sigma}$ ranges. The predicted reactor neutrino mixing angle ${\ensuremath{\theta}}_{13}$ in both scenarios is consistent with the recent T2K and MINOS data. The leptonic $CP$ violation characterized by the Jarlskog invariant $J$ is generally of order ${10}^{\ensuremath{-}2}$.