Are axion solutions to the CP problem fine-tuned?

Abstract

We begin with an overview on fine-tuning and naturalness arguments in particle physics. We then turn our attention to the CP violating angle $ heta$ in the Standard Model, which was historically considered to be unnaturally tiny. We discuss possible differences in interpretation of fine-tuning when this angle is treated as an unknown parameter in the Standard Model versus a randomly chosen ground state in the vacuum. Lastly, we consider axion solutions to the CP problem. Paying attention to the axion quality problem, we ponder whether axion solutions themselves suffer from fine-tuning.