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

TL;DR

This paper presents a renormalisable $\Delta(27) \times SO(10)$ SUSY GUT model that naturally explains neutrino masses, mixing, and CP violation, aligning well with experimental data and predicting specific neutrino parameters.

Contribution

It introduces a novel SUSY GUT model with $\Delta(27)$ family symmetry and spontaneous geometrical CP violation, achieving realistic fermion masses and mixings within a unified framework.

Findings

Predicts a normal neutrino mass hierarchy with $m_1=0.13$ meV.

Aligns PMNS mixing angles with experimental best-fit values.

Provides specific predictions for neutrino oscillation phase $\delta^l \approx -90^{\circ}$.

Abstract

We propose a renormalisable model based on $\Delta(27)$ family symmetry with an $SO(10)$ grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries, including $\Delta(27)$ and $\mathbb{Z}_{9} \times \mathbb{Z}_{12} \times \mathbb{Z}_{4}^{R}$, are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model (MSSM) 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 VEV) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to $ \Delta(27) $ antitriplets $ \bar{\phi} $ whose VEVs are aligned in the CSD3 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 $ m_1 = 0.13 $ meV and the PMNS mixing parameters $\theta^l_{13} \approx 8.35^{\circ}$, $\theta^l_{12}\approx 34^{\circ}$, $\theta^l_{23}\approx 43^{\circ}$ and an oscillation phase $\delta^l\approx -90^{\circ}$.