Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1992-11-13
Phys.Rev. D47 (1993) 3525-3529
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages including 3 figures, LaTeX, TPI-MINN-92/61-T
Scientific paper
10.1103/PhysRevD.47.3525
It is shown that in a $\lambda \phi^4$ theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of production by a virtual field $\phi$ 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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