Scalar dark matter multiplet of global $O(N)$ symmetry

TL;DR

This paper explores scalar dark matter models with global $O(N)$ symmetry, analyzing their parameter space under experimental and theoretical constraints, and finds that only the model with a scalar mediator can maintain vacuum stability and perturbativity up to high scales.

Contribution

It introduces and compares two scalar dark matter models with $O(N)$ symmetry, highlighting the conditions for vacuum stability and perturbativity in each.

Findings

Type I model cannot achieve stable electroweak vacuum.

Type II model can have a stable vacuum and perturbative couplings up to the Planck scale.

Constraints from Higgs decay, relic abundance, and scattering cross section are applied.

Abstract

We study two types of models involving a scalar dark matter multiplet of global $O(N)$ symmetry. These models are distinguished by the absence (Type I) or presence (Type II) of a scalar mediator with $Z_{2}$ symmetry. We derive the allowed regions for the dark matter mass and new scalar couplings based on constraints from Higgs invisible decay, the relic abundance of dark matter, and the spin-independent dark matter-nucleon scattering cross section. Within the allowed parameter space, we also discuss the vacuum stability of the Higgs potential and the perturbativity of the scalar couplings in both models. We find that the Type I model cannot achieve stable electroweak vacuum, whereas the Type II model can have both a stable vacuum and perturbative couplings up to the Planck scale.