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 $\mathrm{U}(1)$ 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 $m_a \in [2 \times 10^{-8}, 10^{-3}]\,\mathrm{eV}$. Conversely, a high-quality axion may be obtained instead in the post-inflationary scenario, with axion mass $m_a \gtrsim 0.01\,\mathrm{eV}$, and anomalon masses predicted below the $\mathrm{eV}$ scale. We elaborate on anomalons' cosmological production in the early universe, highlighting how measurements of $\Delta N_{\rm eff}$ could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.