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In this article we study the phenomenological implications of multiple Higgsboson production from longitudinal vector boson scattering in the context ofeffective field theories. We find compact representations for effectivetree-level amplitudes with up to four final state Higgs bosons. Total crosssections are then computed for scenarios relevant at the LHC in which we findthe general Higgs Effective Theory (HEFT) prediction avoids the heavysuppression observed in Standard Model Effective Field Theory (SMEFT).

Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart