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arXiv · hep-ph/9211242

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

M. B. Voloshin
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Abstract

It is shown that in a $λϕ^4$ theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of production by a virtual field $ϕ$ 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.

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M. B. Voloshin. 1992-11-13. Some Properties of Amplitudes at Multi Boson Thresholds in Spontaneously Broken Scalar Theory. https://doi.org/10.1103/physrevd.47.3525

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