Abstract
We propose a renormalisable model based on Δ(27) family symmetry with an SO(10) grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model with standard R-parity. Low-scale Yukawa structure is dictated by the coupling of matter to Δ(27) antitriplets whose vacuum expectation values are aligned in the CSD3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass m1 ∼ 0.3 meV, CP-violating oscillation phase δl ≈ 280° and the remaining neutrino parameters all within 1σ of their best-fit experimental values.
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