Adjoint $SU(5)$ GUT model with $T_7$ flavor symmetry

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 $24$-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $m_{{\hat{I}}^2{\hat{I}}^2}=$ 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.

22 pages, 5 figures. Final version. To be published in Physical Review D