On Minimal Dark Matter coupled to the Higgs

We provide a unified presentation of extensions of the Minimal Dark Matter framework in which new fermionic electroweak multiplets are coupled to each other via the Standard Model Higgs doublet. We study systematically the generic features of all the possibilities, starting with a singlet and two doublets (akin to Bino-Higgsino dark matter) up to a Majorana quintuplet coupled to two Weyl quadruplets. We pay special attention to this last case, since it has not yet been discussed in the literature. We estimate the parameter space for viable dark matter candidates. This includes an estimate for the mass of a quasi-pure quadruplet dark matter candidate taking into account the Sommerfeld effect. We also argue how the coupling to the Higgs can bring the Minimal Dark Matter scenario within the reach of present and future direct detection experiments.