SO(10) x 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 S-4, under which the unified three quark and lepton 16-plets are unified into a single triplet 3'. The model involves a further discrete group Z(4)(R) x Z(4)(3) which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublettriplet 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 degrees, an atmospheric angle in the first octant and neutrinoless double beta decay with m beta beta = 11 meV. We discuss N-2 leptogenesis, which fixes the second right-handed neutrino mass to be M-2 similar or equal to 2 x 10(11) GeV, in the natural range predicted by the model.