Power meets Precision to explore the Symmetric Higgs Portal

We perform a comprehensive study of collider aspects of a Higgs portal scenario that is protected by an unbroken ${\mathbb{Z}}_2$ symmetry. If the mass of the Higgs portal scalar is larger than half the Higgs mass, this scenario becomes very difficult to detect. We provide a detailed investigation of the model's parameter space based on analyses of the direct collider sensitivity at the LHC as well as at future lepton and hadron collider concepts and analyse the importance of these searches for this scenario in the context of expected precision Higgs and electroweak measurements. In particular we also consider the associated electroweak oblique corrections that we obtain in a first dedicated two-loop calculation for comparisons with the potential of, e.g., GigaZ. The currently available collider projections corroborate an FCC-hh 100 TeV as a very sensitive tool to search for such a weakly-coupled Higgs sector extension, driven by small statistical uncertainties over a large range of energy coverage. Crucially, however, this requires good theoretical control. Alternatively, Higgs signal-strength measurements at an optimal FCC-ee sensitivity level could yield comparable constraints.