We analyze LHC processes involving interactions of two electroweak bosons and two Higgs bosons, VVHH, where V is a W or Z boson, in terms of their sensitivity to Standard Model Effective Field Theory (SMEFT) effects.

We examine the current experimental results of the CMS collaboration in the context of an 8-dimensional SMEFT. We show that the constraints arising from producing vector-boson-fusion Higgs pairs on the operators that modify the quartic gauge-Higgs interactions are already comparable to or more stringent than those published in the analysis of the vector-boson scattering processes using CMS. We study changes to such constraints when introducing perturbative unitarity bounds and investigate the potential for new experimental final states, such as associated production of ZHH. Finally, we show the prospects for the high-luminosity phase of the LHC.