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Flavor in Ninths and a Discrete Gauge Origin of the QCD Axion

Vernon Barger

Abstract

Quark and lepton hierarchies are organized by rational powers of a single parameter in units of one ninth. We show that this ``flavor in ninths'' structure points to a discrete $\mathbb{Z}_{18}$ gauge origin of Froggatt--Nielsen symmetry, whose $\mathbb{Z}_9$ subgroup controls the flavor lattice. Identifying the flavon with the Peccei--Quinn field, the same symmetry stabilizes the QCD axion, enforces $N_{\rm DW}=1$, and predicts $E/N=8/3$ (or $2$ with light higgsinos). The lowest Planck-suppressed operator appears at dimension eighteen, naturally solving the axion quality problem. For $f_a\sim(5$--$8)\times10^{11}$ GeV the axion accounts for dark matter and lies within near-term haloscope reach.

Flavor in Ninths and a Discrete Gauge Origin of the QCD Axion

Abstract

Quark and lepton hierarchies are organized by rational powers of a single parameter in units of one ninth. We show that this ``flavor in ninths'' structure points to a discrete gauge origin of Froggatt--Nielsen symmetry, whose subgroup controls the flavor lattice. Identifying the flavon with the Peccei--Quinn field, the same symmetry stabilizes the QCD axion, enforces , and predicts (or with light higgsinos). The lowest Planck-suppressed operator appears at dimension eighteen, naturally solving the axion quality problem. For -- GeV the axion accounts for dark matter and lies within near-term haloscope reach.
Paper Structure (7 sections, 19 equations, 1 figure, 1 table)

This paper contains 7 sections, 19 equations, 1 figure, 1 table.

Table of Contents

  1. I. Introduction
  2. II. Ninths Structure and Textures
  3. III. Z18 Origin, Ninths Substructure, and Anomaly Consistency
  4. IV. Axion Quality from Ninths and NDW=1
  5. V. E/N and Axion Phenomenology
  6. VI. Unified Picture
  7. Acknowledgments

Figures (1)

  • Figure 1: $\mathbb{Z}_9$ flavor subgroup of $\mathbb{Z}_{18}$. The generators $(1,2,4)$ span all residues mod 9, enabling suppressions quantized in $1/9$.