Singularities in Complex Angular Momentum and Helicity

Simple representations of multiparticle amplitudes are proposed which we hope will be useful in working out the implications of Regge asymptotic behavior in practical applications. These generalized Sommerfeld-Watson transforms are integrals over complex angular momentum and helicity. We discuss the various types of singularities in complex angular momentum and helicity and the asymptotic limits of multiparticle amplitudes which they will determine. We discuss Regge-pole and Regge-cut singularities in the angular momentum plane and generalize the concept of wrong-signature---nonsense fixed poles to multiparticle amplitudes. We find that the absence of simultaneous discontinuities in overlapping channel invariants in the physical region requires that the relevant singularities in complex helicity be completely determined by the singularities in complex angular momentum. Therefore the only truly dynamical singularities are those in complex angular momentum.