A Tale of Two-U(1) Axion Models

TL;DR

This paper classifies and analyzes two-U(1) axion models that address the strong CP and quality problems, introducing a moose diagram method to understand phase cancellations and exploring implications for axion mass spectra.

Contribution

It provides a unified classification of mixed two-U(1) models for solving strong CP issues and introduces a novel moose diagram approach to relate CP phases.

Findings

The lightest axion remains the QCD axion in these models.

A Z2 symmetry can enhance the axion mass spectrum.

The framework can be extended to multi-axion scenarios.

Abstract

The $U(1)$ global symmetry to solve the strong $CP$ problem could be the remnant of multi-$U(1)$ symmetries from QCD and hidden strong dynamics. Both Peccei-Quinn $U(1)$ and dynamical $U(1)$ are described uniformly, based on which we classify various mixed two-$U(1)$ models to solve both strong $CP$ and quality problems. We propose a moose diagram method with different fermion assignments to directly read relations between $CP$ phases, which illustrate how strong $CP$ problem is solved in terms of cancellation between $CP$ phases. In two axion models, we find the lightest axion is still same as QCD axion at infrared region, while one axion model with $Z_2$ symmetry enhances the axion mass spectrum. Our discussions can be extended to multi-axion cases.