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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03631 |
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Table of Contents:
- 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 domain-wall number $N_{\rm DW}=1$, and predicts the axion--photon coupling through the anomaly ratio $E/N=8/3$ (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.