Vanishing Higgs potential in minimal dark matter models

We consider the Standard Model with a new particle which is charged under SU(2)LSU(2)L with the hypercharge being zero. Such a particle is known as one of the dark matter (DM) candidates. We examine the realization of the multiple point criticality principle (MPP) in this class of models. Namely, we investigate whether the one-loop effective Higgs potential Veff(ϕ)Veff(ϕ) and its derivative dVeff(ϕ)/dϕdVeff(ϕ)/dϕ can become simultaneously zero at around the string/Planck scale, based on the one/two-loop renormalization group equations. As a result, we find that only the SU(2)LSU(2)L triplet extensions can realize the MPP. More concretely, in the case of the triplet Majorana fermion, the MPP is realized at the scale ϕ=O(1016 GeV)ϕ=O(1016 GeV) if the top mass MtMt is around 172 GeV. On the other hand, for the real triplet scalar, the MPP can be satisfied for 1016 GeV≲ϕ≲1017 GeV1016 GeV≲ϕ≲1017 GeV and 172 GeV≳Mt≳171 GeV172 GeV≳Mt≳171 GeV, depending on the coupling between the Higgs and DM.