Abstract We explore a class of axion models where an accidental U (1) U (1) Peccei-Quinn (PQ) symmetry automatically emerges from the interplay of vertical (grand-unified) and horizontal (flavor) gauge symmetries. We study a specific Pati-Salam realization in detail, and aim to generalize the conclusions. We show that our specific model offers protection from PQ-violating operators to high dimension, and demonstrate that the model can reproduce the Standard Model flavor structure. A distinctive feature of the vertical-horizontal setup is the presence of parametrically light fermions, known as anomalons, which are introduced to cancel the gauge anomalies of the flavor symmetry. We also identify a major challenge to building a fully realistic model, most notably that of Landau poles in gauge couplings before the Planck scale. For the specific model investigated, the pre-inflationary PQ-breaking scenario predicts the axion mass window to be mₐ 2 10^-8, 10^-3\, eV m a ∈ 2 × 10 - 8, 10 - 3 eV. Conversely, a high-quality axion may be obtained instead in the post-inflationary scenario, with axion mass mₐ > rsim 0. 01\, eV m a ≳ 0. 01 eV, and anomalon masses predicted below the eV eV scale. We elaborate on anomalons’ cosmological production in the early universe, highlighting how measurements of Nₑff Δ N eff could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.
Luzio et al. (Mon,) studied this question.