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

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 $10$, and the down-type quarks and charged leptons couple to a second Higgs $10$. 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 $10$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.

22 pages, 4 figures. Matches published version