Reggeization of Some Unequal Mass Processes Involving Higher Spins: The Reactions πN → VN, πN → VΔ , and γp → π⁺n

Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model. The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – MΔ)2 are also considered. It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – MΔ)2 has been removed. The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π+n in which the data for dσ/dt indicate conspiracy, is studied in detail.