$\mathbf{SO(10)}\times \mathbf{S_4} $ Grand Unified Theory of Flavour and Leptogenesis

TL;DR

This paper presents a Grand Unified Theory of Flavour based on $SO(10)$ and $S_4$, integrating quark and lepton families, deriving neutrino masses via type I seesaw, and successfully fitting experimental data including leptogenesis predictions.

Contribution

It introduces a novel $SO(10) imes S_4$ GUT model with detailed Yukawa structures, flavon alignments, and a comprehensive fit to neutrino and quark data, including leptogenesis.

Findings

Predicts normal neutrino mass ordering with specific CP phase.

Provides a detailed fit to 19 observables with 15 parameters.

Identifies the second right-handed neutrino mass for leptogenesis.

Abstract

We propose a Grand Unified Theory of Flavour, based on $SO(10)$ together with a non-Abelian discrete group $S_4$, under which the unified three quark and lepton 16-plets are unified into a single triplet $3'$. The model involves a further discrete group $ \mathbb{Z}_4^R\times \mathbb{Z}_4^3$ which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublet-triplet splitting, and proton decay is shown to be under control. The Yukawa matrices are derived in detail, from renormalisable diagrams, and neutrino masses emerge from the type I seesaw mechanism. A full numerical fit is performed with 15 input parameters generating 19 presently constrained observables, taking into account supersymmetry threshold corrections. The model predicts a normal neutrino mass ordering with a CP oscillation phase of $260^{\circ}$, an atmospheric angle in the first octant and neutrinoless double beta decay with $m_{\beta \beta}= 11$ meV. We discuss $N_2$ leptogenesis, which fixes the second right-handed neutrino mass to be $M_2\simeq 2\times 10^{11}$ GeV, in the natural range predicted by the model.