Regge-Pole Eikonal Theory of Small-Angle Pion-Nucleon Scattering

Abstract

A quantitative model for high-energy, small-momentum-transfer pion-proton elastic scattering and charge-exchange data (both differential cross sections and polarizations) is presented. The model is based on $P^{\prime }$ and $\rho$ Regge poles in the optical potential, together with a Pomeranchon whose residue is proportional to the product of electromagnetic form factors of pion and proton. Features not present in the Regge-pole approach, such as the crossover effect and nonzero charge-exchange polarization, appear automatically in this model. Specific properties of our $\rho$ and $P^{\prime }$ poles are: (a) both choose nonsense; (b) constant reduced residues; (c) linear trajectories; (d) zero helicity flip for $P^{\prime }$; and (e) helicity-nonflip $P^{\prime }$ residue given by exchange degeneracy (and symmetry, e.g., from quark model) in terms of $\rho$ residue. The elastic scattering fit is satisfactory for all momenta greater than 6 GeV/c and all squared momentum transfers less than 0.5 Ge${\mathrm{V}}^2$/${\mathit{c}}^2$. All available charge-exchange data above 5 GeV/c are fitted well, as are total cross sections and real parts of amplitudes in the forward direction.