Finite-Energy Sum Rules forπNScattering atu=(1236 MeV)2

Abstract

To test the assumptions which underlie them, four finite-energy sum rules are evaluated for $\pi N$ scattering. Results are obtained for three choices of end point: ${\mathrm{}\left(1356\mathrm{M}\mathrm{e}\mathrm{V}\right)\mathrm{}}^2$, ${\mathrm{}\left(1808\mathrm{M}\mathrm{e}\mathrm{V}\right)\mathrm{}}^2$, and ${\mathrm{}\left(2313\mathrm{M}\mathrm{e}\mathrm{V}\right)\mathrm{}}^2$. For the intermediate end point all four sum rules work. However, for the highest one they all fail. The results are interpreted as confirming the assumptions of analyticity and Regge behavior, but pointing to the limitations of the resonances-dominance approximation.