Flavor unification, dark matter, proton decay and other observable predictions with low-scale $S_4$ symmetry

TL;DR

This paper demonstrates how non-supersymmetric $SO(10)$ grand unified theories with low-scale $S_4$ flavor symmetry can achieve gauge coupling unification, predict dark matter candidates, and provide observable proton decay signals.

Contribution

It introduces a novel low-scale flavor symmetric GUT model with $S_4$, showing successful gauge unification, dark matter stability, and testable proton decay predictions.

Findings

Successful gauge coupling unification with specific fermionic dark matter candidates.

Predicted proton lifetime within reach of current or future experiments.

Identified signatures of grand unification in dark matter and scalar particles.

Abstract

We show how gauge coupling unification is successfully implemented through non-supersymmetric grand unified theory, $SO(10)\times G_f (~G_f=S_4, SO(3)_f, SU(3)_f)$, using low-scale flavor symmetric model of the type $SU(2)_L\times U(1)_Y$ $ \times SU(3)_C \times S_4$ recently proposed by Hagedorn, Lindner, and Mohapatra, while assigning matter-parity discrete symmetry for the dark matter stability. For gauge coupling unification in the single-step breaking case, we show that a color-octet fermion and a hyperchargeless weak-triplet fermionic dark matter are the missing particles needed to complete its MSSM-equivalent degrees of freedom. When these are included the model automatically predicts the nonsupersymmetric grand unification with a scale identical to the minimal supersymmetric standard model/grand unified theory scale. We also find a two-step breaking model with Pati-Salam intermediate symmetry where the dark matter and a low-mass color-octet scalar or the fermion are signaled by grand unification. The proton-lifetime predictions are found to be accessible to ongoing or planned searches in a number of models. We discuss grand unified origin of the light fermionic triplet dark matter, the color-octet fermion, and their phenomenology.