Higgs and Dark Matter Hints of an Oasis in the Desert

TL;DR

The paper addresses how Higgs-portal dark matter, compatible with a 125 GeV Higgs, impacts vacuum stability and the need for new physics below the Planck scale. It develops two-loop RGEs and one-loop thresholds for SM extensions with DM multiplets, linking the relic abundance and direct detection constraints to the ultraviolet cutoff Λ. A key finding is that fermionic DM tends to destabilize the vacuum and pushes Λ down to around 10^4 GeV, while scalar DM can stabilize the vacuum and allow higher Λ within perturbativity, with the exact scale tied to DM mass and cross-section. These results imply a testable connection between DM phenomenology and high-scale completion, suggesting flavor/CP-violating probes and future direct detection experiments as avenues to indirectly explore the UV dynamics associated with the Higgs sector.

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.

Figures (13)

• Figure 1: Vacuum structure of the SM as a function of the Higgs boson mass. Regions of stability/metastability/instability are denoted in blue/purple/red respectively. The solid lines indicate central values while the dotted lines indicate $\pm 2 \sigma$ error bars on the experimental measurement of the top quark mass.
• Figure 2: Metastability bands for SM + singlet/doublet and triplet/doublet fermion, shown as a function of the Higgs mass. Regions above/below each band are stable/unstable. Each band is labeled with the corresponding value of the Yukawa coupling, $y_{S,T} = y_{S,T}^c$. The dashed lines correspond to the value of $m_H$ suggested by ATLASCMS.
• Figure 3: Higgs mass bounds as a function of the cutoff, for the SM + singlet scalar. The left panel depicts metastability bands and the right panel depicts the scale at which the largest coupling in the theory becomes non-perturbative. Each label denotes the corresponding value of the cross-quartic coupling, $\kappa_S$, and we have fixed the self-quartic coupling, $\lambda_S=0$.
• Figure 4: Same as Fig. (\ref{['fig:S_mh_scalar']}) but for SM + triplet scalar and varying $\kappa_T$ with $\lambda_T$=0.
• Figure 5: Same as Fig. (\ref{['fig:S_mh_scalar']}) but for SM + doublet scalar and varying $\kappa_D$ with $\lambda_D = \lambda_{D}' = \kappa_{D}'$=0.