Exchange of Even- and Odd-Parity Baryon-Meson Resonances and Backward Elastic Scattering

If there are two meson-baryon resonances or bound states with opposite parities but with the same remaining internal quantum numbers including signature, one at c.m. energy $W_1$ with $l=J-\frac{1}{2}$ and the other at $W_2$ with $l=J+\frac{1}{2}$, then the residue of the Regge trajectory on which they lie must change sign between $W_1$ and $-W_2$. Consequences of the exchange of such a trajectory to backward elastic scattering are discussed.