Crossing Matrices for Helicity Amplitudes, Application to Crossed Channel Partial-Wave Analysis, and Reggeization

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Abstract
The crossing relations of two-body scattering amplitudes for reactions involving particles with spin are derived for the helicity amplitudes of Jacob and Wick. From the crossing relations, the differential cross section and polarization of the direct channel are related to the analytic continuation of the crossed channel helicity amplitude. The differential cross section is then expressed in terms of the crossed channel partial waves, and rules are given for treating the exchange of fixed angular momentum poles and Regge poles for two-body processes involving particles with higher spin.