The problem of the continuation to complex values of the angularmomentum of the partial wave amplitude is examined for the simplestproduction process, that of two particles → three particles. Thepresence of so-called "anomalous singularities" complicates the procedurefollowed relative to that used for quasi two-body scatteringamplitudes. The anomalous singularities are shown to lead to exchangedegenerate amplitudes with possible poles in much the same way as"normal" singularities lead to the usual signatured amplitudes. Theresulting exchange-degenerate trajectories would also be expected tooccur in two-body amplitudes.
The representation of the production amplitude in terms of thesingularities of the partial wave amplitude is then developed andapplied to the high energy region, with attention being paid to theemergence of "double Regge" terms. Certain new results are obtainedfor the behavior of the amplitude at zero momentum transfer, and somepredictions of polarization and minima in momentum transfer distributionsare made. A calculation of the polarization of the ρo meson inthe reaction π - p → π - ρop at high energy with small momentum transferto the proton is compared with data taken at 25 Gev by W. D. Walker andcollaborators. The result is favorable, although limited by the statisticsof the available data.
