Exploring sizable triple Higgs couplings in the 2HDM

An important task at future colliders is the measurement of the triple Higgs coupling. Depending on its size relative to the Standard Model (SM) value, certain collider options result in a higher experimental accuracy. Within the framework of Two Higgs Doublet Models (2HDM) types I and II we investigate the allowed ranges for all triple Higgs couplings involving at least one light, SM-like Higgs boson. We take into account theoretical constraints (unitarity, stability), experimental constraints from direct Higgs-boson searches, measurements of the SM-like Higgs-boson properties, flavor observables and electroweak precision data. We find that the SM-type triple Higgs coupling w.r.t. its SM value, $$\lambda _{hhh}/\lambda _{\mathrm {SM}}$$, can range between $$\sim -0.5$$ and $$\sim 1.5$$. Depending on which value is realized, the HL-LHC can compete with, or is clearly inferior to the ILC. We find the coupling $$\lambda _{hhH}$$ between $$\sim -1.5$$ and $$\sim 1.5$$. Triple Higgs couplings involving two heavy Higgs bosons, $$\lambda _{hHH}$$, $$\lambda _{hAA}$$ and $$\lambda _{hH^+H^-}$$ can reach values up to $${{\mathcal {O}}}(10)$$, roughly independent of the 2HDM type. This can lead to potentially strongly enhanced production of two Higgs-bosons at the HL-LHC or high-energy $$e^+e^-$$ colliders