Dispersion Relations for Virtual Pion-Nucleon Scattering

In connection with a proposed calculation of single pion production in nucleon-nucleon collisions, the process of pion-nucleon scattering in which the incoming pion is virtual is investigated by means of the dispersion theoretic method developed by Chew, Goldberger, Low and Nambu. The static limit is studied in detail and the Chew-Low amplitude for virtual scattering is shown to result for small virtual pion masses. More generally, it is proposed that the Blankenbecler-Gantenhaus solution, which is recorded, may provide a useful approach in applications in which large virtual pion masses play an essential role. (auth)