Vanishing Higgs Potential in Minimal Dark Matter Models
  We consider the Standard Model with a new particle which is charged under
$SU(2)_{L}$ 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
$V_{\text{eff}}(\phi)$ and its derivative $dV_{\text{eff}}(\phi)/d\phi$ 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 $SU(2)_L$ triplet extensions can realize the MPP. More concretely, in the
case of the triplet Majorana fermion, the MPP is realized at the scale
$\phi={\cal{O}}(10^{16}\text{GeV})$ if the top mass $M_{t}$ is around $172$
GeV. On the other hand, for the real triplet scalar, the MPP can be satisfied
for $10^{16}\text{ GeV}\lesssim\phi\lesssim10^{17}$GeV and $172\text{
GeV}\gtrsim M_{t}\gtrsim171$ GeV, depending on the coupling between the Higgs
and DM.
