Application of dispersion relations to pion-nucleon scattering

Abstract

The generalized Kramers-Kronig dispersion relations for charged bosons are used to treat the problem of pion-nucleon scattering. The complications associated with the charge of the pions are discussed. The importance of a "bound state" corresponding to the neutron is emphasized and its constrbution to the scattering amplitude is computed rigorously, assuming only that pions are pseudoscalar and that the interaction with nucleons is charge-independent. The connection between our exact dispersion relations and the approximate equations for pion-nucleon scattering given by Low is discussed. A rigorous effective-range relation is derived.

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