Probing Higgs portals with matrix-element based kinematic discriminants in $ZZ \to 4 \ell$ production

A Higgs portal in the form of the operator $|H|^2$ provides a minimal and theoretically motivated link between the Standard Model (SM) and new physics. While Higgs portals can be constrained well by exotic Higgs decays if the beyond-the-SM states are light, testing scenarios where these particles are kinematically inaccessible is known to be challenging. We explore the sensitivity of future hadron collider measurements of $ZZ \to 4 \ell$ production in constraining Higgs portal interactions. It is shown that by using a matrix-element based kinematic discriminant the reach of the high-luminosity option of the Large Hadron Collider (LHC) can be significantly enhanced compared to studies that are based on measurements of the four-lepton invariant mass spectrum alone. We also analyse the potential of the high-energy upgrade of the LHC and a Future Circular Collider in constraining new physics that couples to $|H|^2$. The obtained constraints are compared to the limits one expects to find from other single-Higgs probes. In addition, we provide an independent analysis of the relevant Higgs portal effects in double-Higgs production. We find that the constraints obtained from our $ZZ \to 4 \ell$ analysis turn out to be both competitive with and complementary to the projected limits obtained using other search techniques.