Some Features of Angular-Momentum Branch Points

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Abstract
Arguments for the existence of angular-momentum branch points based on the necessity for the Gribov-Pomeranchuk singularities to be fixed poles rather than essential singularities are reviewed. Sum rules for scattering amplitudes on the second sheet are then deduced. Reasons are given for expecting two kinds of branch points to be present, namely, those described as "Regge pole plus Regge pole" and "Regge pole plus elementary particle" (called types 1 and 2, respectively). It is argued that the latter must be concealed by the former in the scattering region, and from the requirement that the branch points are suitably positioned in general, an inequality on derivatives of Regge-pole trajectories is derived. A model of the Amati-Fubini-Stanghellini type is examined to indicate why type-2 branch points may be expected to occur in a theory without elementary particles.