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.

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.