AbstractAn 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.
Towards consistent Electroweak Precision Data constraints in the SMEFT