2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202658Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit interesting factorial and exponential behaviour at large multiplicities. As a by-product we observe that the kinematically allowed decay of one real particle into $n$ real particles of another kind, all at rest, has zero tree amplitude in this model for $n>2$.17 pages. Preprint INR-823/93High Energy Physics - Phenomenologytext