Multiparticle tree amplitudes in scalar field theory

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 λϕ^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.

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References in corpus (8)

• Summing One-Loop Graphs at Multi-Particle Threshold
• Zeros of Tree-Level Amplitudes at Multi-Boson Thresholds
• Multiscalar amplitudes to all orders in perturbation theory
• Nullification of multi-Higgs threshold amplitudes in the Standard Model
• Properties of perturbative multi-particle amplitudes in ${\varphi }^k$ and $O(N)$ theories
• Tree amplitudes at multiparticle threshold in a model with softly broken $O(2)$ symmetry
• 2 \to n threshold production at tree level
• Zeros of tree amplitudes at rest and symmetries of mechanical systems