Complex Regge Poles in the Cut<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>j</mml:mi></mml:math>Plane: Pion-Nucleon Charge-Exchange Scattering

Abstract

The structure of the pole-cut combination in $\ensuremath{\pi}N$ charge-exchange scattering for $t&lt;~0$ is represented by a pair of complex poles. Excellent fits to the $\ensuremath{\pi}N$ charge-exchange differential cross section, polarization, and total cross-section difference ${\ensuremath{\sigma}}_{t}({\ensuremath{\pi}}^{\ensuremath{-}}p)\ensuremath{-}{\ensuremath{\sigma}}_{t}({\ensuremath{\pi}}^{+}p)$ are obtained for the two examples considered, $\mathrm{Im}\ensuremath{\alpha}=g\sqrt{\ensuremath{-}t}$ and $\mathrm{Im}\ensuremath{\alpha}=g$. The phases of the residues are allowed to vary and a zero in $\mathrm{Im}{A}^{{\ensuremath{'}}^{(\ensuremath{-})}}$ (the "crossover" zero) is obtained.