High-quality Peccei-Quinn symmetry from the interplay of vertical and horizontal gauge symmetries

Abstract We explore a class of axion models where an accidental $$\textrm{U}(1)$$ 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 $$m_a \in [2 \times 10^{-8}, 10^{-3}]\,\textrm{eV}$$ 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 $$m_a > rsim 0.01\,\textrm{eV}$$ m a ≳ 0.01 eV , and anomalon masses predicted below the $$\textrm{eV}$$ eV scale. We elaborate on anomalons’ cosmological production in the early universe, highlighting how measurements of $$\Delta N_\textrm{eff}$$ Δ N eff could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.