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, $$\lambda _{hhh}/\lambda _{\mathrm {SM}}$$ λ hhh / λ SM , can range between $$\sim -0.5$$ ∼ - 0.5 and $$\sim 1.5$$ ∼ 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 $$\lambda _{hhH}$$ λ hhH between $$\sim -1.5$$ ∼ - 1.5 and $$\sim 1.5$$ ∼ 1.5 . Triple Higgs couplings involving two heavy Higgs bosons, $$\lambda _{hHH}$$ λ hHH , $$\lambda _{hAA}$$ λ hAA and $$\lambda _{hH^+H^-}$$ λ h H + H - can reach values up to $${{\mathcal {O}}}(10)$$ 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 $$e^+e^-$$ e + e - colliders.

An important task at future colliders is the investigation of the Higgs-boson sector. Here the measurement of the triple Higgs coupling(s) plays a special role. Based on previous analyses, within the framework of Two Higgs Doublet Models (2HDM) type I and II, we define and analyze several two-dimensional benchmark planes, that are over large parts in agreement with all theoretical and experimental constraints. For these planes we evaluate di-Higgs production cross sections at future high-energy $$e^+e^-$$ e + e - colliders, such as ILC or CLIC. We consider two different channels for the neutral di-Higgs pairs $$h_i h_j=hh,hH,HH,AA$$ h i h j = h h , h H , H H , A A : $$e^+e^- \rightarrow h_i h_j Z$$ e + e - → h i h j Z and $$e^+e^- \rightarrow h_i h_j \nu {{\bar{\nu }}}$$ e + e - → h i h j ν ν ¯ . In both channels the various triple Higgs-boson couplings contribute substantially. We find regions with a strong enhancement of the production channel of two SM-like light Higgs bosons and/or with very large production cross sections involving one light and one heavy or two heavy 2HDM Higgs bosons, offering interesting prospects for the ILC or CLIC. The mechanisms leading to these enhanced production cross sections are analyzed in detail. We propose the use of cross section distributions with the invariant mass of the two final Higgs bosons where the contributions from intermediate resonant and non-resonant BSM Higgs bosons play a crucial role. We outline which process at which center-of-mass energy would be best suited to probe the corresponding triple Higgs-boson couplings.

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The measurement of the triple Higgs coupling is one of the main tasks of the (HL-)LHC and future lepton colliders. Similarly, triple Higgs couplings involving BSM Higgs bosons are of high interest. Within the framework of Two Higgs Doublet Models (2HDM) we investigate the allowed ranges for all triple Higgs couplings involving at least one light, SM-like Higgs boson. We present newly the allowed ranges for 2HDM type III and IV and update the results within the type I and II. We take into account theoretical constraints from unitarity and stability, experimental constraints from direct BSM Higgs-boson searches, measurements of the rates of the SM-like Higgs-boson at the LHC, as well as flavor observables and electroweak precision data. For the SM-type triple Higgs coupling w.r.t. its SM value, $$\lambda _{hhh}/\lambda _{\mathrm{SM}}$$ λ hhh / λ SM , we find allowed intervals of $$\sim [{-0.5}, {1.3}]$$ ∼ [ - 0.5 , 1.3 ] in type I and $$\sim [{0.5}, {1.0}]$$ ∼ [ 0.5 , 1.0 ] in the other Yukawa types. These allowed ranges have important implications for the experimental determination of this coupling at future collider experiments. We find the coupling $$\lambda _{hhH}$$ λ hhH between $$\sim -1.5$$ ∼ - 1.5 and $$\sim +1.5$$ ∼ + 1.5 in the four Yukawa types. For the triple Higgs couplings involving two heavy neutral Higgs bosons, $$\lambda _{hHH}$$ λ hHH and $$\lambda _{hAA}$$ λ hAA we find values between $$\sim -0.5$$ ∼ - 0.5 and $$\sim 16$$ ∼ 16 , and between $$\sim -1$$ ∼ - 1 and $$\sim 32$$ ∼ 32 for $$\lambda _{hH^+H^-}$$ λ h H + H - . These potentially large values could lead to strongly enhanced production of two Higgs-bosons at the HL-LHC or high-energy lepton colliders.