Vanishing Higgs Potential in Minimal Dark Matter Models

TL;DR

This paper investigates whether the multiple point criticality principle can be realized in minimal dark matter models with an $SU(2)_L$ charged particle, finding that only triplet extensions can achieve this at high energy scales.

Contribution

It demonstrates that only $SU(2)_L$ triplet extensions of the Standard Model can realize the multiple point criticality principle at high scales, providing specific conditions for triplet fermions and scalars.

Findings

MPP realized at $ oughly 10^{16}$ GeV for triplet Majorana fermion with $M_t oughly 172$ GeV.

MPP can be satisfied for $10^{16}$ to $10^{17}$ GeV in triplet scalar models.

Realization of MPP depends on the Higgs-DM coupling and top quark mass.

Abstract

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.