  Triplet extensions are attractive alternatives to the standard model (SM) of
particle physics. While models with only one triplet are highly constrained by
electroweak precision observables, this is not necessarily the case once
several triplets are present as in the Georgi-Machacek model. As in all other
BSM models, the parameter space of triplet extensions is constrained by the
condition that perturbative unitarity is not violated. For this purpose, limits
on the eigenvalues of the scalar $2 \to 2$ scattering matrix are set. It is
very common in the BSM literature that the scattering matrix is calculated
under one crucial assumption: the scattering energy s is so large that only
point interactions involving quartic couplings provide non-negligible
contributions. However, it is not given that this approximation is always valid
- in fact, diagrams involving propagators can play an important role. We
discuss at the examples of (i) the SM model extended by a real triplet, (ii)
the Y = 1 triplet extension of the SM, and (iii) the Georgi-Machacek model, how
the tree-level unitarity constraints are affected once the large s
approximation is given up. For all models we find that the impact of
(effective) cubic couplings can be crucial.
