Abstract
The sheet properties of Regge cuts are investigated by examining the singularity properties of the relevant perturbation-theory model integrals. A complete geometrical and hierarchical structure satisfying the Froissart bound is first established for the n-Reggeon cut generalizing recent work on the 2-Reggeon cut. It is found that all Regge cuts possess, in general, cusps in the physical region; this is established assuming only that Regge trajectories have positive slope below threshold. The essential features of these cusps are examined for different models for Regge-trajectory functions. A fully consistent picture in the l-plane is obtained showing that there are only real l-plane branch points of the Regge amplitude for real physical momentum transfer. A new feature is that each given n-Reggeon-exchange process (n⩾2) in two-body scattering will contribute in general more than one such branch point when the momentum transfer is fixed at a suitable real negative value. It is shown how the full amplitude need not have the cusp singularities which occur in the Regge amplitude.
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