Classifying Extended Higgs Models through the Trilinear Higgs Boson Coupling Measurement at Future Colliders

Abstract We investigate the trilinear Higgs boson coupling derived from the functional forms of various extended Higgs potentials. In light of experimental constraints on Higgs boson couplings, we focus on extended Higgs models in which the trilinear Higgs boson coupling is predominantly determined by the Standard Model Higgs field. Such models include the nearly aligned Higgs Effective Field Theory, classically scale-invariant models, pseudo-Nambu–Goldstone boson scenarios, tadpole-induced models, and others. We also consider higher-order corrections, including top quark and new particle contributions that are often neglected, and discuss their impact on the trilinear Higgs boson coupling. Finally, we show to what extent the functional forms of the Higgs potentials can be probed at future colliders.