Search

The K-matrix approach with effective Lagrangians is used to describe the S and P pion-nucleon partial-wave amplitudes in the energy range E lab≤ 1 GeV. It is demonstrated, that treating the resonance as K-matrix a pole gives the natural way to separate the resonance and non-resonance parts of the πN amplitude. The model includes all the four-star πN resonances, the non-resonance contributions are calculated from relevant Feynman graphs without any phenomenological form factors. Different contributions to the inelastic π− p→ηn amplitude are estimated.

The recently proposed model for the pion-nucleon interaction, based on σ, ρ, N and Δ-isobar exchanges, is investigated further. We demonstrate the validity of the unitarity prescription. We prove that the inclusion of the higher resonances has a very small effect, only on the parameters of the model. The coupling constants g π NN and g π N Δ , as deduced with the model, are found to be very close to the literature values. This is interpreted as an indication that the model should provide an excellent description of the pion-nucleon interaction at low energies. Our prediction for the π N Σ -term is found to be independent of the only free parameter of our model ( G ( V ) ρ ). A number of applications, both for the pion-nucleon and pion-nucleus interactions, are discussed.