Towards a complete Δ(27) x SO(10) SUSY GUT

We propose a renormalizable model based on Delta(27) family symmetry with an SO(10) grand unified theory leading to a novel form of spontaneous geometrical CP violation. The symmetries, including Delta(27) and Z(9) x Z(12) x Z(4)(R), are broken close to the grand unified theory breaking scale to yield the minimal supersymmetric standard model with the standard R parity. SO(10) is broken via SU(5) with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing vacuum expectation value) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to Delta(27) antitriplets (phi) over bar of which the vacuum expectation values are aligned in the constrained sequential dominance 3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass between 0.32 and 0.38 meV, CP-violating oscillation phase delta(l) approximate to (275-280)degrees, and the remaining neutrino parameters all within 1 sigma of their best-fit experimental values.