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 $$\textrm{U}(1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>U</mml:mtext> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $$m_a \in [2 \times 10^{-8}, 10^{-3}]\,\textrm{eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo>]</mml:mo> </mml:mrow> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> . Conversely, a high-quality axion may be obtained instead in the post-inflationary scenario, with axion mass $$m_a &gt; rsim 0.01\,\textrm{eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>≳</mml:mo> <mml:mn>0.01</mml:mn> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> , and anomalon masses predicted below the $$\textrm{eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>eV</mml:mtext> </mml:math> scale. We elaborate on anomalons’ cosmological production in the early universe, highlighting how measurements of $$\Delta N_\textrm{eff}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:mrow> </mml:math> could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.