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

Ning Chen, Jianan Tian, Bin Wang

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.

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

Abstract

We study the nonmaximal symmetry breaking patterns of allowed in a supersymmetric theory with the affine Lie algebra of , 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 . We also prove that a separate nonmaximal symmetry breaking pattern of is unrealistic due to the additional massless vectorlike quarks in the spectrum.

Paper Structure

This paper contains 20 sections, 88 equations, 4 figures, 15 tables.

Table of Contents

  1. INTRODUCTION
  2. THE SSW SYMMETRY BREAKING PATTERN
  3. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) fermions
  4. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) Higgs fields
  5. RGEs of the SSW symmetry breaking pattern
  6. THE SWS SYMMETRY BREAKING PATTERN
  7. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) fermions
  8. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) Higgs fields
  9. RGEs of the SWS symmetry breaking pattern
  10. THE WSS SYMMETRY BREAKING PATTERN
  11. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) fermions
  12. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) Higgs fields
  13. RGEs of the WSS symmetry breaking pattern
  14. THE WWW SYMMETRY BREAKING PATTERN
  15. Decompositions of the ${\mathfrak{s} \mathfrak{u}}$(8) fermions
  16. ...and 5 more sections

Figures (4)

  • Figure 1: The two-loop RGEs of the ${\mathfrak{s} \mathfrak{u}}(8)$ setup according to the SSW symmetry breaking pattern. The RG evolutions within $10^{3}\,{\rm GeV} \lesssim \mu \lesssim 10^{13}\,{\rm GeV}$ are hidden in order to highlight the behaviors in three intermediate symmetry breaking scales given by the benchmark point in Eq. \ref{['eq:benchmark SSW']}.
  • Figure 2: The two-loop RGEs of the ${\mathfrak{s} \mathfrak{u}}(8)$ setup according to the SWS symmetry breaking pattern. The RG evolutions within $10^{3}\,{\rm GeV} \lesssim \mu \lesssim 10^{13}\,{\rm GeV}$ are hidden in order to highlight the behaviors in three intermediate symmetry breaking scales given by the benchmark point in Eq. \ref{['eq:benchmark SWS']}.
  • Figure 3: The two-loop RGEs of the ${\mathfrak{s} \mathfrak{u}}(8)$ setup according to the WSS symmetry breaking pattern. The RG evolutions within $10^{3}\,{\rm GeV} \lesssim \mu \lesssim 10^{13}\,{\rm GeV}$ are hidden in order to highlight the behaviors in three intermediate symmetry breaking scales given by the benchmark point in Eq. \ref{['eq:benchmark WSS']}.
  • Figure 4: The two-loop RGEs of the ${\mathfrak{s} \mathfrak{u}}(8)$ setup according to the WWW symmetry breaking pattern. The RG evolutions within $10^{3}\,{\rm GeV} \lesssim \mu \lesssim 10^{13}\,{\rm GeV}$ are hidden in order to highlight the behaviors in three intermediate symmetry breaking scales given by the benchmark point in Eq. \ref{['eq:benchmark WWW']}.