# Strong CP problem with low-energy emergent QCD: The 4321 case

## TL;DR

This paper explores how low-energy emergent QCD within $U_1$ vector leptoquark models addresses the strong CP problem, predicts axions linked to B-physics anomalies, and connects to dark matter and neutrino mass generation.

## Contribution

It demonstrates that minimal gauge models with $U_1$ require two axions for the Peccei-Quinn solution and links axion phenomenology to B-physics hints and neutrino mass generation.

## Key findings

- Two axions are needed in minimal models to solve the strong CP problem.
- Predicted axion properties align with B-physics anomalies and dark matter.
- A UV completion connects axion physics to neutrino mass generation.

## Abstract

We analyze the strong CP problem and the implications for axion physics in the context of $U_1$ vector leptoquark models, recently put forward as an elegant solution to the hints of lepton flavor universality violation in B-meson decays. It is shown that in minimal gauge models containing the $U_1$ as a gauge boson, the Peccei-Quinn solution of the strong CP problem requires the introduction of two axions. Characteristic predictions for the associated axions can be deduced from the model parameter space hinted by B-physics, allowing the new axion sector to account for the dark matter of the Universe. We also provide a specific ultraviolet completion of the axion sector that connects the Peccei-Quinn mechanism to the generation of neutrino masses.