A Tale of Two-U(1) Axion Models

Understand

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.