Pion Exchange, Duality, and the Forward Structure of Scattering Amplitudes

Forward dips and peaks in $\pi$-exchange differential cross sections are analyzed from the $t$- and $s$-channel points of view. Simple criteria for the presence of forward structures are given. They lead, among other things, to the prediction that $\frac{d\sigma ({\pi }^{-}p\to {{\rho }_{\mathrm{tr}}}^{0}n)}{\mathrm{dt}}$, where "tr" denotes transverse polarization, does not have a forward peak with a width of ${m_{\pi }}^2$, contrary to expectations based on vector dominance.