Two simple textures of the magic neutrino mass matrix

Abstract

The Tri-Bimaximal (TBM) mixing predicts a vanishing ${\theta }_{13}$. This can be attributed to the inherited $\mu -\tau$ symmetry of TBM mixing. We break its $\mu -\tau$ symmetry by adding a complex magic matrix with one variable to TBM neutrino mass matrix with one vanishing eigenvalue. We present two such textures and study their phenomenological implications.