Multiparticle tree amplitudes in scalar field theory

TL;DR

This paper develops a method to compute tree-level scattering amplitudes in scalar field theory, revealing factorial growth in amplitudes at threshold, which is significant for understanding multiparticle production.

Contribution

It introduces a technique based on Feynman's argument to derive effective actions for summing tree diagrams, applied specifically to b4b4 theory to analyze multiparticle production.

Findings

Tree amplitudes grow factorially with the number of particles n.

The method effectively derives threshold amplitudes for multiparticle production.

Singular behavior of amplitudes at the threshold limit is characterized.

Abstract

Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory, to the derivation of the threshold amplitude for the production of $n$ scalar particles by $n$ initial particles. The leading contributions to the tree amplitude, which become singular in the threshold limit, exhibit a factorial growth with n.