Accidental Peccei-Quinn Symmetry From Gauged U(1) and a High Quality Axion

TL;DR

This paper develops models with a gauged U(1) symmetry that naturally produce a high-quality axion, solving the strong CP problem while avoiding cosmological issues like domain wall problems.

Contribution

It introduces explicit models with anomaly-free gauged U(1) symmetries that generate accidental PQ symmetries, enhancing axion quality and providing testable predictions.

Findings

Models produce axions with distinct couplings to electrons and nucleons.

All models have a domain wall number of one, avoiding cosmological domain wall problems.

The models offer hybrid KSVZ-DFSZ axions with potential for experimental verification.

Abstract

We construct explicit models that solve the axion quality problem originating from quantum gravitational effects. The general strategy we employ is to supplement the Standard Model and its grand unified extensions by an anomaly-free axial $U(1)_a$ symmetry that is gauged. We show that for several choices of the gauge quantum numbers of the fermions, this setup leads to an accidental $U(1)$ symmetry with a QCD anomaly which can be identified as the Peccei-Quinn (PQ) symmetry that solves the strong CP problem. The $U(1)_a$ gauge symmetry controls the amount of explicit PQ symmetry violation induced by quantum gravity, resulting in a high quality axion. We present two classes of models employing this strategy. In the first class (models I and II), the axial $U(1)_a$ gauge symmetry acts on vector-like quarks leading to an accidental KSVZ-type axion. The second class (model III) is based on $SO(10)$ grand unified theory extended by a gauged $U(1)_a$ symmetry that leads to a hybrid KSVZ--DFSZ type axion. The couplings of the axion to the electron and the nucleon are found to be distinct in this class of hybrid models from those in the KSVZ and DFSZ models, when the axion is identified as the dark matter of the universe, which can be used to test these models. Interestingly, all models presented here have domain wall number of one, which is free of cosmological problems that typically arise in axion models.