One-loop Dirac neutrino mass and mixed axion/WIMP dark matter

We consider the Peccei-Quinn (PQ) mechanism as the one behind the Dirac neutrino masses when these are generated through the $d=5$ effective operator $\bar{L}\tilde{H}N_R\phi$ at one loop level, with $\phi$ being a Standard Model singlet scalar. In this setup, the PQ symmetry guarantees that the one-loop realization of such an effective operator gives the leading contribution to the Dirac neutrino masses by forbidding the contributions arising from its tree level realizations. All the mediators in the one-loop neutrino mass diagrams can be stabilized by a remnant $Z_N$ symmetry from the PQ symmetry breaking, thus forming a dark sector besides the axion sector and leading to mixed axion/WIMP dark matter scenarios.