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

## TL;DR

This paper explores how non-abelian flavor symmetries in the hidden sector of SO(10) GUTs can explain lepton and quark mixing patterns, predicting specific neutrino CP phases and mixing matrices like BM and those involving the golden ratio.

## Contribution

It introduces a residual symmetry approach within SO(10) GUTs to derive specific forms of the lepton mixing matrix, including the Bimaximal (BM) scenario, with detailed model realization and predictions.

## Key findings

- Predicted CP phase range: 144° to 210°.
- Identified possible mixing structures including BM and golden ratio matrices.
- Presented a realization of the BM scenario within SO(10) GUTs with S4 flavor symmetry.

## Abstract

The relation between the mixing matrices of leptons and quarks: $U_{\rm{PMNS}} \approx V_{\rm{CKM}}^\dagger U_0$, 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 $144^{\circ}\lesssim\delta_{\rm CP}\lesssim 210^{\circ}$ in the minimal version.