Separation ofNandΔExchanges inπNScattering and Deduction of Amplitude Zeros

Abstract

Linear combinations of $\ensuremath{\pi}N$ differential cross sections and polarizations are used to isolate the ${I}_{u}=\frac{1}{2}$ and ${I}_{u}=\frac{3}{2}$ exchange amplitudes directly from data. For ${I}_{u}=\frac{1}{2}$ exchange the cross section has a zero at $u=\ensuremath{-}0.15$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ and the polarization becomes large and negative for $|u|>0.25$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. Our phenomenological analysis indicates that in the dip region the ${I}_{u}=\frac{1}{2}$ amplitude is inconsistent with appreciable secondary trajectories or absorptive corrections. For ${I}_{u}=\frac{3}{2}$ exchange we infer that the imaginary $s$-channel helicity-flip amplitude has a zero near $u=\ensuremath{-}0.15$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, consistent with peripherality for $\ensuremath{\Delta}$ exchange. We also derive a sum rule relating the $\ensuremath{\pi}N$ differential cross sections at 180\ifmmode^\circ\else\textdegree\fi{} to the Regge-trajectory difference ${\ensuremath{\alpha}}_{\ensuremath{\Delta}}\ensuremath{-}{\ensuremath{\alpha}}_{N}$.