Properties of perturbative multi-particle amplitudes in ${\varphi }^k$ and $O(N)$ theories

Abstract

Threshold amplitudes are considered for multi-particle production in ${\varphi }^k$ and $O(N){\varphi }^4$ 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 ${\varphi }^k$ 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.

Comments: 7 pages, LaTex, TPI-MINN-92/60-T