Role of complex poles in a field-theoretical model for πN scattering

The "uncrossed meson line" approximation for the nucleon propagator is appled to the pion-nucleon S matrix. The resulting simplification resembles the Born approximation, but with the dressed nucleon propagator of Brown, Puff, and Wilets (BPW), which contains a pair of conjugate complex poles. The complex poles appear naturally in the consistent solution of the factorized BPW equations, and are interpreted according to Lee and Wick as states of indefinite metric. Inclusion of these poles produces considerably closer agreement with experimental results. The Adler-Weinberg consistency condition on pion-nucleon scattering is now satisfied to within 20%, and this is reflected in the near-threshold suppression of the cross sections and amplitudes (nucleon-antinucleon pair suppression). The (3, 3⁺) resonance is absent in the model. The model is most appropriate for calculating the two-pion contribution to the nucleon-nucleon potential, where subthreshold behavior is more important than the scattering resonances.