A coupling of a scalar, charged under an unbroken global U(1) symmetry, to the Standard Model via the Higgs portal is one of the simplest gateways to a dark sector. Yet, for masses $m_{S}\geq m_{H}/2$ there are few probes of such an interaction. In this note we evaluate the sensitivity to the Higgs portal coupling of di-Higgs boson production at the LHC as well as at a future high energy hadron collider, FCC-hh, taking into account the full momentum dependence of the process. This significantly impacts the sensitivity compared to estimates of changes in the Higgs-coupling based on the effective potential. We also compare our findings to precision single Higgs boson probes such as the cross section for vector boson associated Higgs production at a future lepton collider, e.g. FCC-ee, as well as searches for missing energy based signatures.

8 pages, 8 figures, v2: references added, version accepted for publication in PRD