Properties of perturbative multi-particle amplitudes in $ϕ^k$ and $O(N)$ theories

Abstract

Threshold amplitudes are considered for multi-particle production in $ϕ^k$ and $O(N) ~ϕ^4$ 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 $ϕ^k$ 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.