# A natural $ S_4 \times SO(10) $ model of flavour

## TL;DR

This paper presents a natural supersymmetric grand unified theory based on $S_4 imes SO(10)$ that explains fermion masses and mixings, predicts a normal neutrino hierarchy, and addresses Higgs and proton decay issues.

## Contribution

It introduces a novel $S_4 imes SO(10)$ model with hierarchical flavon vacuum alignments, accurately fitting fermion data and predicting leptonic CP phases, while solving Higgs and proton decay problems.

## Key findings

- Accurately fits all quark and lepton data
- Predicts leptonic CP phase within specific intervals
- Provides mechanisms for Higgs $ ext{μ}$ term and proton stability

## Abstract

We propose a natural $ S_4 \times SO(10) $ supersymmetric grand unified theory of flavour with an auxiliary $\mathbb{Z}_4^2 \times \mathbb{Z}_4^R$ symmetry, based on small Higgs representations (nothing larger than an adjoint) and hence a type-I seesaw mechanism. The Yukawa structure of all fermions is determined by the hierarchical vacuum expectation values of three $ S_4 $ triplet flavons, with CSD3 vacuum alignments, where up-type quarks and neutrinos couple to one Higgs $\mathbf{10}$, and the down-type quarks and charged leptons couple to a second Higgs $\mathbf{10}$. The Yukawa matrices are obtained from sums of low-rank matrices, where each matrix in the sum naturally accounts for the mass of a particular family, as in sequential dominance in the neutrino sector, which predicts a normal neutrino mass hierarchy. The model accurately fits all available quark and lepton data, with predictions for the leptonic $CP$ phase in 95$\%$ credible intervals given by $ 281^\circ < \delta^\ell < 308^\circ $ and $ 225^\circ < \delta^\ell < 253^\circ $. The model reduces to the MSSM, with the two Higgs doublets emerging from the two Higgs $\mathbf{10}$s without mixing, and we demonstrate how a $\mu$ term of $\mathcal{O}$(TeV) can be realised, as well as doublet-triplet splitting, with Planck scale operators controlled by symmetry, leading to acceptable proton decay.

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Source: https://tomesphere.com/paper/1705.01555