From axion quality and naturalness problems to a high-quality $\mathbb{Z}_{N}$ QCD relaxion

Abstract: We highlight general issues associated with quality and naturalness problems in theories of light QCD-axions, axion-like particles, and relaxions. We show the presence of Planck-suppressed operators generically lead to scalar coupling of axions with the Standard model. We present a new class of $\mathbb Z_{N}$ QCD relaxion models that can address both the QCD relaxion CP problem as well as its quality problem. This new class of models also leads to interesting experimental signatures, which can be searched for at the precision frontier.