The Planck scale, the Higgs mass and scalar dark matter

TL;DR

This paper explores how adding a dark matter scalar to the Standard Model can extend its validity up to the Planck scale and accommodate the observed Higgs mass, using Renormalization Group analysis.

Contribution

It introduces a toy model with a dark matter scalar coupled to the Higgs-top sector, showing how it can lower the Higgs mass bound and extend the model's validity.

Findings

Dark matter scalar can lower the Higgs mass lower bound.

Higher-order couplings can increase the ultraviolet cutoff scale.

Model can account for the full dark matter relic density.

Abstract

This study is inspired by a scenario, in which the Standard Model, enhanced by an additional dark matter scalar, could be extended up to the Planck scale, while accommodating the low measured value of the Higgs mass. To that end, we study a toy model for a gauge singlet dark matter scalar coupled to the Higgs-top-quark sector of the Standard Model. Using functional methods to derive Renormalization Group flow equations in that model, we examine several choices for the ultraviolet, bare potential in the Higgs-dark-matter sector. Our results indicate that the dark matter scalar can decrease the lower bound on the Higgs mass in the Standard Model. We then use the fact that higher-order couplings which are driven to tiny values by the Renormalization Group flow towards low energies can easily be of order one at the ultraviolet cutoff scale. Our study indicates that the inclusion of these couplings can significantly increase the ultraviolet cutoff scale and therefore the range of validity of the model while yielding a low value for the Higgs mass in the infrared. This is achieved within a setting where the dark matter scalar accounts for the complete dark matter relic density in our universe.