Neutrino mixings inSO(10)with type II seesaw mechanism andθ13

Abstract

We analyze a class of supersymmetric $SO(10)$ grand unified theories with a type II seesaw mechanism for neutrino masses, where the contribution to the Pontecorvo-Maki-Nakagawa-Sakata matrix from the neutrino sector has an exact tribimaximal form, dictated by a broken ${S}_{4}$ symmetry. The Higgs fields that determine the fermion masses are two $\mathbf{10}$ fields and one $\mathbf{126}$ field, with the latter simultaneously contributing to neutrino as well as charged fermion masses. Fitting charged fermion masses and the Cabibbo-Kobayashi-Maskawa mixings leads to corrections to the tribimaximal mixing that determine the final Pontecorvo-Maki-Nakagawa-Sakata matrix with the predictions ${\ensuremath{\theta}}_{13}\ensuremath{\simeq}4\ifmmode^\circ\else\textdegree\fi{}--6\ifmmode^\circ\else\textdegree\fi{}$ and a Dirac $CP$ phase between $\ensuremath{-}10\ifmmode^\circ\else\textdegree\fi{}$ and $+15\ifmmode^\circ\else\textdegree\fi{}$. We also show correlations between various mixing angles which can be used to test the model.