Closing in on minimal dark matter and radiative neutrino masses

We study one-loop radiative neutrino mass models in which one of the beyond-the-
standard model fi elds is either a hypercharge-zero fermion quintet (minimal dark matter)
or a hypercharge-zero scalar septet. By systematically classifying all possible one-loop
such models we identify various processes that render the neutral component of these representations (dark matter) cosmologically unstable. Thus, our fi ndings show that these
scenarios are in general not reconcilable with dark matter stability unless tiny couplings
or additional ad hoc symmetries are assumed, in contrast to minimal dark matter models
where stability is entirely due to the standard model gauge symmetry. For some variants
based on higher-order loops we find that alpha_ 2 reaches a Landau pole at rather low scales,
a couple orders of magnitude from the characteristic scale of the model itself. Thus, we
argue that some of these variations although consistent with dark matter stability and
phenomenological constraints are hard to reconcile with perturbativity criteria.