Coupling Constant andP-Wave Phase Shifts in Low-Energy Pion-Nucleon Scattering

Abstract

By means of a model for low-energy pion-nucleon scattering, it is shown that analyticity, unitarity, and the crossing properties are sufficiently strong conditions to determine the pi N coupling constant, the P-wave phase shifts STAincluding the position and width of the (3/2,3/2) resonance! and to give restrictions on the pi pi cut. In addition, the solution for the (1/2,1/2) scattering amplitude turns out to be of the form describing the nucleon as a bound state of the pi N system in close analogy to a bound state in potential theory. In the model, the pi pi cut is represented by a pair of conjugate poles, and crossing is approximated by the static crossing relations. No cutoff parameter has to be introduced, and the crossing relations are fulfilled to a high degree. (auth)