Parity Problem of the Scotogenic Neutrino Model

We show that Ma's scotogenic model, which is arguably one of the simplest settings containing a Dark Matter candidate and generating a naturally suppressed active neutrino mass at 1-loop level, suffers from a potentially severe hierarchy-type problem. In case the right-handed neutrinos involved have sufficiently large masses, they can via loop effects drive the mass parameter of the inert scalar contained in the model towards negative values. This behaviour leads to a breaking of the $\mathbb{Z}_2$ parity symmetry built into the model which is paramount to keeping the setting consistent at low energies - without it the model would lose its Dark Matter candidate and the neutrino mass would not be naturally suppressed. Thus, if the breaking occurs at a sufficiently low scale, it could potentially spoil the success of the whole model. Trying to avoid this consistency problem leads to a new constraint on the model parameter space which has not yet been described in the literature.