Adjoint $SU(5)$ GUT model with $T_{7}$ flavor symmetry

TL;DR

This paper introduces an $SU(5)$ GUT model with $T_{7}$ flavor symmetry that explains fermion masses, mixing, and neutrino properties, while remaining consistent with phenomenological constraints and potentially testable at colliders.

Contribution

It develops a novel $SU(5)$ GUT framework incorporating $T_{7}$ and multiple discrete symmetries to unify fermion mass generation and neutrino phenomenology.

Findings

Predicts neutrinoless double beta decay effective mass of 4-50 meV.

Achieves gauge coupling unification with TeV-scale colored fields.

Provides benchmark scenarios compatible with current experimental constraints.

Abstract

We propose an adjoint $SU(5)$ GUT model with a $T_{7}$ family symmetry and an extra $Z_{2}\otimes Z_{3}\otimes Z_{4}\otimes Z_{4}^{\prime }\otimes Z_{12}$ discrete group, that successfully describes the prevailing Standard Model fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the $Z_{3}\otimes Z_{4}\otimes Z_{12}$ symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type-I and type-III seesaw mechanisms mediated by the fermionic $SU(5)$ singlet and the adjoint $\mathbf{24}$-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $m_{\beta \beta }=$ 4 and 50 meV for the normal and the inverted neutrino spectra, respectively. We construct several benchmark scenarios, which lead to $SU(5)$ gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, proton decay, dark matter, etc. These scenarios contain TEV-scale colored fields, which could give rise to a visible signal or be stringently constrained at the LHC.