Higgs characterisation in the presence of theoretical uncertainties and invisible decays

While the Higgs characterisation programme is well underway, direct signs for new physics beyond the Standard Model remain elusive. Performing a fit of fully differential Higgs production cross sections at the LHC to a subset of Higgs-relevant effective operators, we discuss the extent to which theoretical uncertainties can limit the sensitivity in such a new physics search programme. Extending the dimension-6 Higgs Effective Field Theory framework by introducing new light degrees of freedom that can contribute to an invisible (or undetectable) Higgs decay width $h \to \phi\phi$, we show how differential coupling fits can disentangle effects from non-Standard Model couplings and an invisible decay width, as present in many new physics scenarios, such as Higgs-portal dark matter. Including the so-called off-shell measurement that has been advocated as a sensitive determination of the Higgs width in the $\kappa$ framework, we show explicitly that this method does not provide complementary sensitivity for scale-separated new physics $\Lambda\gg m_h \gg m_\phi$, which is favoured in beyond the Standard Model scenarios that relate astrophysics and collider phenomenology in light of non-observation of new physics during run 1 of the LHC.