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.

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

References in corpus (4)

• Summing tree graphs at threshold
• Summing One-Loop Graphs at Multi-Particle Threshold
• Summing one-loop graphs in a theory with broken symmetry
• Zeros of Tree-Level Amplitudes at Multi-Boson Thresholds

Cited by in corpus (11)

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• Exploring High Multiplicity Amplitudes in Quantum Mechanics
• Some Properties of Amplitudes at Multi Boson Thresholds in Spontaneously Broken Scalar Theory
• Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken Case
• The Breakdown of Resummed Perturbation Theory at High Energies
• Exact Multiparticle Amplitudes at Threshold in Large-N Component phi^4 Theory
• On the nullification of threshold amplitudes
• Suppression exponent for multiparticle production in $\lambda {\varphi }^4$ theory
• Partial wave amplitudes and multiparticle production
• "Isochronic" dynamical systems and nullification of amplitudes
• Multiparticle tree amplitudes in scalar field theory