Complex Singularities in Production Amplitudes

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Abstract
It is shown for a simple model of production that Watson's scheme for final-state interaction may be good even though the amplitude has complex singularities. The method used consists in continuing analytically partial-wave dispersion relations. Stress is put upon the necessity of correctly choosing the cuts starting at the complex singularities. The safest choice in this approach is to take the cut along the line on which the series of partial waves diverges. A simple geometrical recipe is given to see the evolution of this line, the appearance of an anomalous threshold and a complex singularity.