RGE of a Cold Dark Matter Two-Singlet Model

Abstract

We study via the renormalization group equations at one-loop order the perturbativity and vacuum stability of a two-singlet model of cold dark matter (DM) that consists in extending the Standard Model with two real gauge-singlet scalar fields. We then investigate the regions in the parameter space in which the model is viable. For this, we require the model to reproduce the observed DM relic density abundance, to comply with the measured XENON 100 direct-detection upper bounds, and to be consistent with the RGE perturbativity and vacuum-stability criteria up to $40\mathrm{TeV}$. For small mixing angle $\theta $ between the physical Higgs $h$ and auxiliary field, and DM-$h$ mutual coupling constant $\lambda_{0}^{(4)}$, we find that the auxiliary-field mass is confined to the interval $116\mathrm{GeV}-138\mathrm{GeV}$ while the DM mass is mainly confined to the region above $57\mathrm{GeV}$. Increasing $\theta $ enriches the existing viability regions without relocating them, while increasing $\lambda_{0}^{(4)}$ shrinks them with a tiny relocation. We show that the model is consistent with the recent Higgs boson-like discovery by the ATLAS and CMS experiments, while very light dark matter (masses below $5\mathrm{GeV}$) is ruled out by the same experiments.