Effects of Amplitude Nullification in the Standard Model

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.