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

TL;DR

This work develops a class of axion models in which a high-quality Peccei-Quinn symmetry emerges accidentally from the interplay between vertical (Pati-Salam) and horizontal (flavor) gauge symmetries. Focusing on a Pati-Salam realization with gauged SU(3)_{f_R}, it demonstrates PQ protection against dangerous operators, shows how SM flavor can be reproduced, and analyzes the spectrum and cosmology of parametrically light anomalons that cancel flavor anomalies. The axion sector is embedded in the extended scalar content, yielding a DFSZ-like coupling with a calculable decay constant f_a and two distinct mass windows for accidental (pre-/post-inflation) and high-quality PQ scenarios, while Landau-pole issues point to a need for UV completion. The cosmology of anomalons, including their potential as dark radiation or dark matter, provides novel low-energy probes via ΔN_eff and EDM/cosmological constraints, linking UV PQ dynamics to observable astrophysical and cosmological signals.

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 $ΔN_{\rm eff}$ could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.

Figures (9)

• Figure 1: Left panel: Iso-contours of $f_a$ in the $(V_\Delta, V_\chi)$ plane. The red area signals the region of parameter space where the PQ quality problem arises, with $|\theta_{\rm eff}|>10^{-10}$. The blue area is disfavored by astrophysical bounds, $f_a\gtrsim 2.3\times 10^8\,\mathrm{GeV}$ (cf. Sect. \ref{['eq:astrolimits']}). Along the dashed line, $V_\Delta=V_\chi\equiv V$ holds. Along the dotted line, $|\theta_{\rm eff}|$ acquires its minimal value compatible with astrophysical constraints. Right panel: Contribution to $|\theta_{\rm eff}|$ from operators whose projection on the VEVs is of the type $v^m V^n/\Lambda_{\rm UV}^{m+n-4}$, assuming $V_\Delta=V_\chi=V=3\sqrt{5}f_a$. In the red regions, $|\theta_{\rm eff}|>10^{-10}$ for the values of $V$ in the legend, which correspond color-wise to the red dots in the left panel. The black stars correspond to operators generated in our model which impose the strongest conditions for PQ quality, cf. Eq. (\ref{['eq:contributions-axion']}).
• Figure 2: The spectrum of neutrinos and anomalons as a function of the Pati-Salam breaking scale $V$ (left panel), and the upper bounds on parameters $l$ and $\tilde{l}$ from Eq. (\ref{['eq:parlimit-l']}) and \ref{['eq:parlimit-lt']} for mixing not to interfere with the spectrum approximation (right panel).
• Figure 3: Comparison of the size of contributions to $U_{L\perp}$ from Eq. (\ref{['eq:terms-LP']}) (left panel) and to $U_{L0}$ from Eq. (\ref{['eq:terms-L0']}) (right panel). Each contribution is proportional to one of the coefficients $c\in\{l,r,\tilde{l},\tilde{r}\}$. If $c\neq 1$, a contribution shifts by $\log_{10}|c|$; for $|c|<1$ the shift is downward.
• Figure 4: Contour plots for $\log_{10}$ of the size of mixing of L-neutrinos with anomalons. The upper row shows mixing with heavy anomalons $U_{L\perp}$ in the $l$-$r$ plane and benchmark values $\tilde{l}=\tilde{r}=10^{-3}$. The lower row shows mixing with light anomalons $U_{L0}$ in the $l$-$\tilde{l}$ plane and benchmark values $r=\tilde{r}=10^{-6}$. The columns represent three different values of the PS-breaking scale: $V=10^{9,11,14}\,\mathrm{GeV}$. The color coding is consistent for all plots, and the dashed lines represent where the contributions of the two terms from the $x$- and $y$-axis are equal, see main text.
• Figure 5: Axion-photon coupling (Eq. (\ref{['eq:axionph']}) with $E/N = 8/3$) as a function of the axion mass. Current limits and future sensitivities are represented by filled and shaded regions, respectively. A high-quality PQ symmetry is obtained for $m_a \gtrsim 0.01\,\mathrm{eV}$ (light blue line) in the post-inflationary PQ-breaking scenario. An accidental PQ symmetry (not addressing the PQ-quality problem) corresponds to the intervals $m_a \in [2 \times 10^{-8}, 10^{-3}]\,\mathrm{eV}$ in the pre-inflationary PQ-breaking scenario (black line) and $m_a \in [2.8 \times 10^{-5}, 0.01]\,\mathrm{eV}$ in the post-inflationary PQ-breaking scenario (blue/dashed line). Axion limits adapted from AxionLimits.