Fermion Regge-Pole Model for the Structure of Pion-Nucleon Elastic Scattering in the Backward Hemisphere

The $Y=+1$ fermion resonances that show up strongly in total-cross-section data are classified as Regge recurrences on three straight-line trajectories (namely, Δ_δ, N_γ, N_α) in a Chew-Frautschi plot. From extrapolations of the trajectories, resonance doublets are predicted in the vicinity of 2200 MeV (with JP=7/2^- and 9/2⁺) and 2630 MeV (with JP=112^- and 132⁺), due to recurrences of the N_γ and N_α trajectories at similar mass values. A model is constructed for π^-p elastic scattering near the backward direction based on interference of the direct-channel resonance amplitude (Δ_δ, Δ_γ, N_α) with the amplitude due to fermion Regge exchange (Δ_δ) in the crossed channel. The predictions of the model compare favorably with existing data on the energy dependence of the π^-p differential cross section at 180^∘{} center-of-mass scattering angle and the general shape of the π^-p angular distributions near 180^∘{}. The results confirm the consistency of the Regge-recurrence parity assignments with the scattering data. The resonance elasticities used in the calculations are roughly the same as the elasticities determined from total-cross-section data. The model is extended to π⁺p elastic scattering at backward angles. In the π⁺p process, the direct-channel Δ_δ resonance contribution alone saturates the experimental differential cross section in the backward cone at momenta below 4 BeV/c. Comparison with the π⁺p backward-scattering data gives additional confirmation for the proposed Δ_δ Regge-recurrence parity assignments. In addition, the model supports the existence of an I=3/2 s-wave resonance at 1690 MeV. Finally, the polarization is predicted for π^±p elastic scattering in the backward cone.