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

TL;DR

This paper investigates the two-loop renormalization group equations of an SU(8) gauge theory with a specific symmetry breaking pattern, analyzing gauge coupling evolution and unification challenges within this framework.

Contribution

It provides a detailed analysis of the gauge coupling evolution in an SU(8) model with maximal symmetry breaking, highlighting the need for additional fields for unification.

Findings

Two-loop RGEs do not achieve gauge unification with minimal setup.

Additional adjoint Higgs fields are required for unification.

Gravity-induced dimension-5 terms influence the gauge coupling evolution.

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.