From axion quality and naturalness problems to a high-quality Z_N QCD relaxion

We highlight general issues associated with quality and naturalness problems in theories of light QCD axions, axionlike particles, and relaxions. We show that the presence of Planck-suppressed operators generically lead to scalar coupling of axions with the Standard Model. We present a new class of 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.