Regge-Pole Model for High-Energy Backwardπ±pScattering

It is well known by now that both the ${\pi }^{+}p$ and ${\pi }^{-}p$ elastic-scattering reactions show peaks near the backward direction at high energy. The most striking difference between the two distributions in the backward region is the dip in $\frac{d\sigma }{\mathrm{du}}$ which appears in ${\pi }^{+}p$ but not ${\pi }^{-}p$. We show in this paper that the present experimental situation in high-energy ${\pi }^{\pm }p$ scattering can be readily understood in terms of the exchange of the $N$ and $\Delta$ Regge trajectories. The interpretation of the dip is that $N$ trajectory exchange, which contributes only to ${\pi }^{+}p$, becomes numerically very small when the $N$ pole moves near $J=-\frac{1}{2}$.