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

Abstract

The relation between the mixing matrices of leptons and quarks: $U_{\mathrm{PMNS}}\approx V_{\mathrm{CKM}}^{†}{U}_0$, where $U_0$ is a matrix of special forms (e.g. BM, TBM), can be a clue for understanding the lepton mixing and neutrino masses. It may imply the Grand unification and existence of a hidden sector with certain symmetry which 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 ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$. 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 $SO(10)$ GUT with the $S_4$ flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of CP phase $144^{\circ }\lesssim {\delta }_{\mathrm{CP}}\lesssim 210^{\circ }$ in the minimal version.

Comments: 19 pages, 1 figure, Consideration of the CKM mixing in sect. V modified, references added