Invisible Higgs Decay Width vs. Dark Matter Direct Detection Cross Section in Higgs Portal Dark Matter Models

TL;DR

This paper derives explicit correlations between invisible Higgs decay and dark matter detection in UV-complete Higgs portal models, revealing limitations of the effective field theory approach and introducing additional parameters affecting collider bounds.

Contribution

It provides explicit formulas for the Higgs-portal dark matter correlation in UV completions, highlighting extra parameters and limitations of EFT assumptions.

Findings

Additional parameters influence direct detection cross sections.

Collider bounds are weaker in certain mass regimes.

EFT approach may not be reliable for specific models.

Abstract

The correlation between the invisible Higgs branching ratio ($B_h^{\rm inv} $) vs. dark matter (DM) direct detection ($\sigma_p^{\rm SI}$) in Higgs portal DM models is usually presented in the effective field theory (EFT) framework. This is fine for singlet scalar DM, but not in the singlet fermion DM (SFDM) or vector DM (VDM) models. In this paper, we derive the explicit expressions for this correlation within UV completions of SFDM and VDM models with Higgs portals, and discuss the limitation of the EFT approach. We show that there are at least two additional hidden parameter in $\sigma_p^{\rm SI}$ in the UV completions: the singlet-like scalar mass $m_2$ and its mixing angle $\alpha$ with the SM Higgs boson ($h$). In particular, if the singlet-like scalar is lighter than the SM Higgs boson ($m_2 < m_h \cos \alpha / \sqrt{1 + \cos^2 \alpha}$), the collider bound becomes weaker than the one based on EFT.