SO(10) × S4 grand unified theory of flavour and leptogenesis

We propose a Grand Unified Theory of Flavour, based on SO(10) together with a non-Abelian discrete group S4, under which the unified three quark and lepton 16-plets are unified into a single triplet 3′. The model involves a further discrete group ℤ4R × ℤ43 which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublet-triplet splitting, and proton decay is shown to be under control. The Yukawa matrices are derived in detail, from renormalisable diagrams, and neutrino masses emerge from the type I seesaw mechanism. A full numerical fit is performed with 15 input parameters generating 19 presently constrained observables, taking into account supersymmetry threshold corrections. The model predicts a normal neutrino mass ordering with a CP oscillation phase of 260°, an atmospheric angle in the first octant and neutrinoless double beta decay with mββ = 11 meV. We discuss N2 leptogenesis, which fixes the second right-handed neutrino mass to be M2 ≃ 2 × 1011 GeV, in the natural range predicted by the model.