Higgs and Dark Matter Hints of an Oasis in the Desert

TL;DR

This paper explores the implications of dark matter interactions with the Higgs boson, revealing that such interactions can destabilize the electroweak vacuum and require new physics at accessible energy scales, which are testable experimentally.

Contribution

It provides a detailed analysis of how Higgs-dark matter interactions constrain new physics scales and offers explicit two-loop RGEs and threshold corrections for various models.

Findings

Dark matter-Higgs interactions can destabilize the electroweak vacuum.

New physics must appear below the Planck scale, often within 10-1000 TeV.

The parameter space is testable with upcoming experiments.

Abstract

Recent LHC results suggest a standard model (SM)-like Higgs boson in the vicinity of 125 GeV with no clear indications yet of physics beyond the SM. At the same time, the SM is incomplete, since additional dynamics are required to accommodate cosmological dark matter (DM). In this paper we show that interactions between weak scale DM and the Higgs which are strong enough to yield a thermal relic abundance consistent with observation can easily destabilize the electroweak vacuum or drive the theory into a non-perturbative regime at a low scale. As a consequence, new physics--beyond the DM itself--must enter at a cutoff well below the Planck scale and in some cases as low as O(10 - 1000 TeV), a range relevant to indirect probes of flavor and CP violation. In addition, this cutoff is correlated with the DM mass and scattering cross-section in a parameter space which will be probed experimentally in the near term. Specifically, we consider the SM plus additional spin 0 or 1/2 states with singlet, triplet, or doublet electroweak quantum numbers and quartic or Yukawa couplings to the Higgs boson. We derive explicit expressions for the full two-loop RGEs and one-loop threshold corrections for these theories.