Complex Regge Poles in the CutjPlane: Pion-Nucleon Charge-Exchange Scattering

The structure of the pole-cut combination in $\pi N$ charge-exchange scattering for $t<~0$ is represented by a pair of complex poles. Excellent fits to the $\pi N$ charge-exchange differential cross section, polarization, and total cross-section difference ${\sigma }_t\left({\pi }^{-}p\right)-{\sigma }_t\left({\pi }^{+}p\right)$ are obtained for the two examples considered, $\mathrm{Im}\alpha =g\sqrt{-t}$ and $\mathrm{Im}\alpha =g$. The phases of the residues are allowed to vary and a zero in $\mathrm{Im}{A}^{{\prime }^{\mathrm{}(-)\mathrm{}}}$ (the "crossover" zero) is obtained.