Minimal extension of tribimaximal mixing and generalizedZ2×Z2symmetries

Abstract

We discuss consequences of combining the effective ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry of the tribimaximal neutrino mass matrix with the $CP$ symmetry. Imposition of such generalized ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to a nonzero ${\ensuremath{\theta}}_{13}$ and maximal atmospheric mixing angle and $CP$ violating phase. It is shown that an effective generalized ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry of the mass matrix can arise from the ${A}_{4}$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle ${\ensuremath{\theta}}_{13}$.