Neutrino mixing in SO(10) GUTs with a non-Abelian flavor symmetry in the hidden sector

The relation between the mixing matrices of leptons and quarks, U-PMNS approximate to V-CKM(dagger) U-0, where U-0 is a matrix of special forms [e.g., bimaximal (BM) and tribimaximal], can be a clue for understanding the lepton mixing and neutrino masses. It may imply the grand unification and the existence of a hidden sector with certain symmetry that generates U-0 and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain U-0. The residual symmetries of both the visible and hidden sectors are Z(2) x Z(2). Their embedding in a unified flavor group is considered. We find that there are only several possible structures of U-0, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the SO(10) grand unified theory with the S-4 flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of CP phase 144 degrees less than or similar to delta(CP) less than or similar to 210 degrees in the minimal version.