Multi-Higgs boson production and unitarity in vector-boson fusion at future hadron colliders

We study multi-Higgs final states in vector boson fusion (VBF) processes at the LHC and at future proton-proton colliders, focusing on the prospects for measurements at 27 and 100 TeV. We use an effective Lagrangian which includes higher-dimensional operators in the mass eigenstates which are relevant to VBF processes and relate this to specific parametrizations and models for new physics in the Higgs sector. We derive theoretical constraints on the parameter space from the unitarity of 2→n scattering amplitudes and apply the results to VV→hh and hhh processes, where V=W, Z. As a result, we present constraints on differential distributions as appropriate to the study of VV→hh and hhh processes.