Comment on "Summing One-Loop Graphs at Multi-Particle Threshold"

Details Comment on "Summing One-Loop Graphs at Multi-Particle Threshold" Comment on "Summing One-Loop Graphs at Multi-Particle Threshold"

1992-09-23

arxiv.org/abs/hep-ph/9209270v1

Phys.Rev. D47 (1993) 1712-1714

Physics

High Energy Physics

High Energy Physics - Phenomenology

7 pages, LaTeX, TPI-MINN-92/46-T

Scientific paper

10.1103/PhysRevD.47.1712

The propagator of a virtual $\phi$-field with emission of $n$ on-mass-shell particles all being exactly at rest is calculated at the tree-level in $\lambda \phi^4$ theory by directly solving recursion equations for the sum of Feynman graphs. It is shown that the generating function for these propagators is equivalent to a Fourier transform of the recently found Green's function within the background-field technique for summing graphs at threshold suggested by Lowell Brown. Also the derivation of the result that the tree-level on-mass-shell scattering amplitudes of the processes $2 \to n$ are exactly vanishing at threshold for $n > 4$ is thus given in the more conventional Feynman diagram technique.

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