Zeros of tree amplitudes at rest and symmetries of mechanical systems

Abstract

We consider the tree amplitudes of production of $n_2$ scalar particles by $n_1$ particles of another kind, where both initial and final particles are at rest and on mass shell, in a model of two scalar fields with $O(2)$ symmetric interaction and unequal masses. We find that these amplitudes are zero except for the lowest possible $n_1$ and $n_2$, and that the cancellation of the corresponding Feynman graphs occurs due to a special symmetry of the classical mechanical counterpart of this theory. This feature is rather general and is inherent in various other scalar field theories.

11 pages Preprint INR-830/93, August 1993

References in corpus (3)

• Summing tree graphs at threshold
• Summing One-Loop Graphs at Multi-Particle Threshold
• Zeros of Tree-Level Amplitudes at Multi-Boson Thresholds

Cited by in corpus (8)

• Exponentiation of Multiparticle Amplitudes in Scalar Theories
• Exact Multiparticle Amplitudes at Threshold in Large-N Component phi^4 Theory
• On the nullification of threshold amplitudes
• Exact Multiparticle Amplitudes at Threshold in ${\varphi }^4$ Theories with Softly Broken $O(\infty )$ Symmetry
• "Isochronic" dynamical systems and nullification of amplitudes
• Multiparticle tree amplitudes in scalar field theory
• On threshold amplitudes II: Amplitudes nullification via classical symmetries
• Multiboson threshold production by fermion-antifermion pair and hidden symmetry