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We consider extended scalar sectors of the Standard Model asultraviolet-complete motivations for studying the effective Higgsself-interaction operators of the Standard Model effective field theory. Weinvestigate all motivated heavy scalar models which generate the dimension-6effective operator, $|H|^6$, at tree level and proceed to identify the full setof tree-level dimension-six operators by integrating out the heavy scalars. Ofseven models which generate $|H|^6$ at tree level only two, quadruplets ofhypercharge $Y=3Y_H$ and $Y=Y_H$, generate only this operator. Next we performglobal fits to constrain relevant Wilson coefficients from the LHC single Higgsmeasurements as well as the electroweak oblique parameters $S$ and $T$. We findthat the $T$ parameter puts very strong constraints on the Wilson coefficientof the $|H|^6$ operator in the triplet and quadruplet models, while the singletand doublet models could still have Higgs self-couplings which deviatesignificantly from the standard model prediction. To determine the extent towhich the $|H|^6$ operator could be constrained, we study the dihiggssignatures at the future 100 TeV collider and explore future sensitivity ofthis operator. Projected onto the Higgs potential parameters of the extendedscalar sectors, with $3$ ab$^{-1}$ luminosity data we will be able to explorethe Higgs potential parameters in all seven models.

Exploring Extended Scalar Sectors with Di-Higgs Signals: A Higgs EFT Perspective