%0 Journal Article
%T Properties of perturbative multi-particle amplitudes in $¦Õ^k$ and $O(N)$ theories
%A B. H. Smith
%J Physics
%D 1992
%I arXiv
%R 10.1103/PhysRevD.47.3521
%X Threshold amplitudes are considered for multi-particle production in $\phi^k$ and $O(N) ~\phi^4$ theories. It is found that the disappearance of tree-level threshold amplitudes of $2$ on-shell particles producing a large number of particles occurs in $\phi^k$ theory only for $k=3$ and $k=4$. The one-loop correction to the threshold amplitude for a highly virtual scalar particle decaying into $n$ particles in an $O(N)$ model is derived.
%U http://arxiv.org/abs/hep-ph/9211238v1