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

Abstract

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, ${\ensuremath{\Delta}}_{\ensuremath{\delta}}$, ${N}_{\ensuremath{\gamma}}$, ${N}_{\ensuremath{\alpha}}$) in a Chew-Frautschi plot. From extrapolations of the trajectories, resonance doublets are predicted in the vicinity of 2200 MeV (with ${J}^{P}={\frac{7}{2}}^{\ensuremath{-}} \mathrm{and} {\frac{9}{2}}^{+}$) and 2630 MeV (with ${J}^{P}=\frac{11}{{2}^{\ensuremath{-}}} \mathrm{and} \frac{13}{{2}^{+}}$), due to recurrences of the ${N}_{\ensuremath{\gamma}}$ and ${N}_{\ensuremath{\alpha}}$ trajectories at similar mass values. A model is constructed for ${\ensuremath{\pi}}^{\ensuremath{-}}p$ elastic scattering near the backward direction based on interference of the direct-channel resonance amplitude (${\ensuremath{\Delta}}_{\ensuremath{\delta}}$, ${\ensuremath{\Delta}}_{\ensuremath{\gamma}}$, ${N}_{\ensuremath{\alpha}}$) with the amplitude due to fermion Regge exchange (${\ensuremath{\Delta}}_{\ensuremath{\delta}}$) in the crossed channel. The predictions of the model compare favorably with existing data on the energy dependence of the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ differential cross section at 180\ifmmode^\circ\else\textdegree\fi{} center-of-mass scattering angle and the general shape of the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ angular distributions near 180\ifmmode^\circ\else\textdegree\fi{}. 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 ${\ensuremath{\pi}}^{+}p$ elastic scattering at backward angles. In the ${\ensuremath{\pi}}^{+}p$ process, the direct-channel ${\ensuremath{\Delta}}_{\ensuremath{\delta}}$ resonance contribution alone saturates the experimental differential cross section in the backward cone at momenta below 4 $\frac{\mathrm{BeV}}{c}$. Comparison with the ${\ensuremath{\pi}}^{+}p$ backward-scattering data gives additional confirmation for the proposed ${\ensuremath{\Delta}}_{\ensuremath{\delta}}$ Regge-recurrence parity assignments. In addition, the model supports the existence of an $I=\frac{3}{2} s$-wave resonance at 1690 MeV. Finally, the polarization is predicted for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ elastic scattering in the backward cone.