Exploring sizable triple Higgs couplings in the 2HDM

Abstract: 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) type 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, $\lambda_{hhh}/\lambda_{\rm SM}$, 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 ${\cal O}(10)$, 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.