We explore the phenomenological consequences of non-minimal hidden sector interactions on observable correlations in the Higgs sector, mediated through the Z₂-symmetric Higgs portal. Particular attention is given to non-standard momentum dependencies of the hidden sector scalar, which arise naturally in an effective field theory (EFT) framework. We demonstrate that perturbatively reliable constraints can be derived from four-top quark production data and precision measurements of Higgs couplings. These constraints are especially relevant in parameter regions where destructive interference suppresses invisible Higgs decays to light exotic scalars, keeping them within experimentally allowed limits. Finally, we discuss the implications of such hidden sector interactions for the thermal history of the universe. We show that non-standard momentum dependencies open up the Higgs portal to account for the observed dark matter relic abundance whilst evading current direct detection constraints. They can also be probed at the (HL-) LHC and, ultimately, at future lepton colliders such as a FCC-ee.
Anisha et al. (Wed,) studied this question.