  Delicate cancellations among diagrams can result in the vanishing of
threshold amplitudes in the standard model. This phenomenon is investigated for
multi-Higgs production by scalar, vector, and fermionic fields. A surprising
gap is found where although the tree-level amplitude for $2$ incoming gauge
bosons to produce $N_v$ particle may vanish, the amplitude for the production
of $N_{v}+1$ particles is nonzero.
