https://doi.org/10.1140/epjc/s10052-025-15175-w
Regular Article - Theoretical Physics
High-quality Peccei-Quinn symmetry from the interplay of vertical and horizontal gauge symmetries
1
Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via F. Marzolo 8, 35131, Padova, Italy
2
Instituto de Física Corpuscular (IFIC), Universitat de València-CSIC, Parc Científic UV, C/ Catedrático José Beltrán 2, 46980, Paterna, Spain
3
Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, C.P. 13, 00044, Frascati, Italy
Received:
2
September
2025
Accepted:
5
December
2025
Published online:
5
January
2026
We explore a class of axion models where an accidental
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
![$$m_a \in [2 \times 10^{-8}, 10^{-3}]\,\textrm{eV}$$](/articles/epjc/abs/2026/01/10052_2025_Article_15175/10052_2025_Article_15175_tex_eq2.png)
. Conversely, a high-quality axion may be obtained instead in the post-inflationary scenario, with axion mass
, and anomalon masses predicted below the
scale. We elaborate on anomalons’ cosmological production in the early universe, highlighting how measurements of
could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
