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

TL;DR

This paper links a flavor hierarchy pattern to a discrete gauge symmetry that stabilizes the QCD axion, predicts its coupling, and addresses the axion quality problem, with implications for dark matter detection.

Contribution

It proposes a discrete $ ext{Z}_{18}$ gauge origin for flavor structure and the QCD axion, connecting flavor hierarchies to axion stability and observable properties.

Findings

The flavor structure suggests a $ ext{Z}_9$ subgroup controlling flavor lattice.

The model predicts an axion-photon coupling ratio $E/N=8/3$ (or 2 with higgsinos).

The lowest Planck-suppressed operator appears at dimension eighteen, solving the axion quality problem.

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 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.