Zeros of tree-level amplitudes at multiboson thresholds

Propagation of particles with the emission of an arbitrary number of identical bosons all being at rest is considered. It is shown that in certain models the tree-level amplitudes for production of n scalar bosons by two incoming particles are all equal to zero at the threshold starting from some small number n. In particular, this nullification occurs for production of massive scalars by two Goldstone bosons in the linear model for n>1 and also for production of Higgs bosons in the standard model by gauge bosons and/or by fermions, provided that the ratios of their masses to that of the Higgs boson take special discrete values.