Pion-Nucleon Spin-Flip Sum Rule

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Abstract
Current algebra and the hypothesis of partially conserved axial-vector current are used to derive a sum rule for the spin-flip pion-nucleon scattering amplitude analogous to the Weisberger-Adler (W-A) sum rule for the non-spin-flip amplitude. We find that such a sum rule requires information about the weak amplitude for axial-vector-nucleon scattering, in contrast to the W-A relation, which requires no such information. As a byproduct we give a decomposition of this weak amplitude into tensor covariants which is more useful than those previously appearing in the literature. This expansion applies to polar-vector-nucleon scattering as well, and hence is relevant to Compton scattering.