Description
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,
$\lambda_{hhh}/\lambda_{hhh}^{\rm SM}$, 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 also derive limits on the triple Higgs couplings involving heavy Higgs bosons.