Construction of Invariant Scalar Amplitudes without Kinematical Singularities for Arbitrary-Spin Nonzero-Mass Two-Body Scattering Processes

The relativistic transition amplitude for any two-body reaction involving only particles of nonzero mass but arbitrary spin is decomposed in terms of scalar amplitudes that are regular functions in the space of scalar invariants at points corresponding to regular points of the transition matrix elements in momentum space, on the mass shell. Detailed formulas for the scalar amplitudes in terms of the original scattering matrix elements are given. The development is in the framework of analytic S-matrix theory, and is based on a partial generalization of the Hall-Wightman Theorem. The results hold on the complete (multisheeted) domain of regularity of the scattering amplitude.