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

## TL;DR

This paper presents a renormalisable supersymmetric GUT model combining $ ext{Delta}(27)$ family symmetry and $SO(10)$, predicting neutrino properties and CP violation consistent with experimental data.

## Contribution

It introduces a novel $ ext{Delta}(27)$-based SUSY GUT model with spontaneous CP violation and specific neutrino mass and mixing predictions.

## Key findings

- Predicts a normal neutrino mass hierarchy with $m_1 \,\sim\, 0.3$ meV.
- Achieves $CP$-violating phase $\,\delta^l \approx 280^{\circ}$.
- Aligns neutrino parameters within $1\sigma$ of experimental values.

## 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{\phi} $ 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.