Shape of Higgs Potential at Future Colliders

Although the Higgs boson has been discovered, its self-couplings are poorly constrained, which leaves the nature of the Higgs boson undetermined. Motivated more from the difference potential than Landau-Ginzburg type, we systematically organize various new physics scenarios, psuedo-Goldstone Higgs, Coleman-Weinberg Higgs and Tadpole-induced Higgs, etc. We find that di-Higgs production at 27 TeV HE-LHC have the ability to discriminate different Higgs scenarios, while it is necessary to use three Higgs production at 100 TeV collider to fully determine the shape of Higgs potential.