Non-decoupling scalars at future colliders

We consider a class of BSM models where a generic scalar electroweak multiplet obtains a significant fraction of its mass from a coupling to the Higgs. Such models are non-decoupling: their new states are necessarily at the TeV scale or below, they can significantly alter the electroweak phase transition, and they have a pattern of low energy effects that are distinct from those predicted by SMEFT. Using their minimal gauge and Higgs couplings, we show that a future precision lepton collider (such as FCC-ee, CEPC, ILC, or CLIC) can probe all the non-decoupling parameter space of scalar electroweak multiplets, providing fundamental information on the mechanism of electroweak symmetry breaking.