The structure of the pole-cut combination in $\pi N$ backward scattering is represented by a complex $N_{\alpha }$ and ${\Delta }_{\delta }$ pair. For negative $u$, these are not complex conjugate but rather each pair splits into a steep (normal) and a flat trajectory. There are no MacDowell partners and each steep trajectory would produce the usual baryon spectrum at positive $u$ and the steep $N_{\alpha }$ is mainly responsible for the dips at $u\approx -0.2\mathrm{}$ through wrong-signature nonsense zeros. The trajectories are generated by a $D$ function which has a fixed cut with squareroot singularity at the branch point. Excellent fits have been obtained for $\pi N$ elastic and charge-exchange differential cross sections in the backward direction.

• Received 29 April 1971

DOI:https://doi.org/10.1103/PhysRevD.4.834