Invisible Higgs decay width versus dark matter direct detection cross section in Higgs portal dark matter models

The correlation between the invisible Higgs branching ratio (B-h(inv)) versus dark matter (DM) direct detection cross section (sigma(SI)(p)) in Higgs portal singlet fermion DM (SFDM) or vector DM (VDM) models is usually presented in the effective field theory (EFT) framework. In this paper, we derive the explicit expressions for this correlation within UV completions of SFDM and VDM models with Higgs portals, and we discuss the limitations of the EFT approach. We show that there are at least two additional hidden parameters in sigma(SI)(p) in the UV completions: the singletlike scalar mass m(2) and its mixing angle alpha with the SM Higgs boson (h). In particular, if the singletlike scalar is lighter than the SM Higgs boson (m(2) < m(h) cos alpha/root 1+cos(2)alpha) the collider bound becomes weaker than the one based on EFT.