The gauge coupling evolutions of an ${\rm SU}(8)$ theory with the maximally symmetry breaking pattern

Abstract

We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an ${\rm SU}(8)$ theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate the observed SM quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern through its maximally breaking pattern. The field theoretical two-loop RGEs can not achieve the gauge coupling unification with the minimal setup, unless additional adjoint Higgs fields as well as the gravity-induced $d=5$ term to the ${\rm SU}(8)$ field strength term are included.