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.

arXiv comment22 pages, 4 figures. Matches published version

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• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• An $S_4\times SU(5)$ SUSY GUT of flavour in 6d
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• A minimal non-supersymmetric SO(10) model with Peccei--Quinn symmetry
• $\mathbf{SO}(10)\times {\mathbf{S}}_4$ Grand Unified Theory of Flavour and Leptogenesis
• Tri-Direct CP in the Littlest Seesaw Playground
• Muon anomalies and the $SU(5)$ Yukawa relations
• Strong thermal $SO(10)$-inspired leptogenesis in the light of recent results from long-baseline neutrino experiments
• Effective alignments as building blocks of flavour models
• Effective alignments and the landscape of $S_4$ flavour models
• Exceptional Unification of Families and Forces
• Yukawa ratio predictions in non-renormalizable $\mathrm{SO}(10)$ GUT models
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Revisiting the Universal Texture Zero of Flavour: a Markov Chain Monte Carlo Analysis
• SO(10) unification with horizontal symmetry
• Flavor Symmetries in the Yukawa Sector of Non-Supersymmetric SO(10): Numerical Fits Using Renormalization Group Running
• Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$
• $SO(10)$ models with $A_4$ modular symmetry
• Resonant leptogenesis and TM${}_1$ mixing in minimal Type-I seesaw model with S${}_4$ symmetry