Towards a complete $\Delta (27)\times SO(10)$ SUSY GUT

Abstract

I discuss a renormalisable model based on $\Delta (27)$ family symmetry with an $SO(10)$ grand unified theory (GUT) with spontaneous geometrical $CP$ violation. The symmetries are broken close to the GUT breaking scale, yielding the minimal supersymmetric standard model. Low-scale Yukawa structure is dictated by the coupling of matter to $\Delta (27)$ antitriplets $\bar{\varphi }$ 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 $m_1\sim 0.3$ meV, $CP$-violating oscillation phase ${\delta }^l\approx 280^{\circ }$ and the remaining neutrino parameters all within $1\sigma$ of their best-fit experimental values.

Comments: Poster presented at NuPhys2016 (London, 12-14 December 2016). 4 pages, LaTeX