The reaction at high energiesat high energies

Abstract

The process Open image in new window is studied at high energies in both the forward and backward directions. The helicity formalism is used. Contributions from ρ, ω, ϕ and π trajectories in thet-channel and from the Open image in new window and Open image in new window -trajectories in\(\bar s\)-channel are included. Polarization formulae for the final-state nucleon are given.If we may neglect cuts in the angular-momentum plane, then at high energies for momentum transfers —t ≫μπ2 the ρ trajectory should dominate charged pion photoproduction in the forward direction. A crude estimate of the cross-section yields\({{d\sigma } \mathord{\left/ {\vphantom {{d\sigma } {dt \sim s}}} \right. \kern-\nulldelimiterspace} {dt \sim s}}^{2j} \rho ^{(0)} \approx {1 \mathord{\left/ {\vphantom {1 s}} \right. \kern-\nulldelimiterspace} s}\). However, the pion trajectory is expected to be important for small momentum transfers up to very high energies. Inclusion of both the ρ and π trajectories yields the interesting result that π+ and π− photoproduction cross-sections are identical at high energies in the forward direction. For forward neutral pion photoproduction both the ρ and ω trajectories should be important. The cross-section is estimated to be dσ/dt∼1/s. If one trajectory is dominant, then the differential cross-sections for γ+p→π0+p and γ+n→π0+n should be identical. For photoproduction in the backward direction, the situation is much more complex with at least three trajectories contributing to dσ/d∼1/s. However, since the same set of trajectories is to be used in π Open image in new window scattering, backward Open image in new window scattering and backward photoproduction are expected to have the same energy-dependence. Assuming that the Open image in new window trajectory dominates with Open image in new window , we obtain Open image in new window .