Dark matter stability and one-loop neutrino mass generation based on Peccei-Quinn symmetry

We propose a model which is a simple extension of the KSVZ invisible axion model with an inert doublet scalar. Peccei-Quinn symmetry forbids tree-level neutrino mass generation and its remnant $Z_2$ symmetry guarantees dark matter stability. The neutrino masses are generated by one-loop effects as a result of the breaking of Peccei-Quinn symmetry through a nonrenormalizable interaction. Although the low energy effective model coincides with an original scotogenic model which contains right-handed neutrinos with large masses, it is free from the strong $CP$ problem.