Some Properties of Amplitudes at Multi Boson Thresholds in Spontaneously Broken Scalar Theory

Abstract

It is shown that in a $\lambda {\varphi }^4$ theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of production by a virtual field $\varphi$ of $n$ on-mass-shell bosons all being exactly at rest is equivalent in any order of the loop expansion to a Euclidean space calculation of the mean field of a kink-type configuration. Using this equivalence it is found that all the $1\to n$ amplitudes have no absorptive part at the thresholds to any order of perturbation theory. This implies non-trivial relations between multi-boson threshold production amplitudes. In particular the on-mass-shell amplitude of the process $2\to 3$ should vanish at the threshold in all loops. It is also shown that the factor $n!$ in the $1\to n$ amplitudes at the threshold is not eliminated by loop effects.

11 pages including 3 figures, LaTeX, TPI-MINN-92/61-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
• Properties of perturbative multi-particle amplitudes in ${\varphi }^k$ and $O(N)$ theories

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