Nonmaximal symmetry breaking patterns in the supersymmetric $\widehat {\mathfrak{s} \mathfrak{u}}(8)_{k_U =1}$ theory

TL;DR

This paper investigates specific symmetry breaking patterns in a supersymmetric affine Lie algebra model to explain quark/lepton mass hierarchies and mixing, finding viable unification scenarios and ruling out certain patterns due to unwanted particles.

Contribution

It introduces nonmaximal symmetry breaking patterns in an affine Lie algebra framework relevant to particle physics, proposing a model that explains mass hierarchies and mixing.

Findings

Three gauge couplings unify below the Planck scale.

A specific symmetry breaking pattern is ruled out due to extra massless particles.

Unification relations are derived from the affine Lie algebra at level 1.

Abstract

We study the nonmaximal symmetry breaking patterns of ${\mathfrak{s} \mathfrak{u}}(8) \to \mathfrak{g}_{531}/\mathfrak{g}_{351}$ allowed in a supersymmetric theory with the affine Lie algebra of $\widehat {\mathfrak{s} \mathfrak{u}}(8)_{k_U=1}$, which was recently proposed to explain the three-generational standard model quark/lepton mass hierarchies as well as the Cabbibo-Kobayashi-Maskawa mixing pattern. Three gauge couplings are found to achieve the unification below the Planck scales, according to the unification relations determined by the affine Lie algebra at level of $1$. We also prove that a separate nonmaximal symmetry breaking pattern of ${\mathfrak{s} \mathfrak{u}}(8) \to \mathfrak{g}_{621}$ is unrealistic due to the additional massless vectorlike quarks in the spectrum.