π-Exchange in a Partial Wave Analysis of πN → Nππ: I. Partial Wave Analysis Including π-Exchange for πN → Nππ in the Center of Mass Energy Range 1.65 - 1.97 GeV. II. Resonance Parameter Analyses of πN → Δπ + ρN + εN

I. Partial Wave Analysis Including π-Exchange for πN → Nππ in the center of mass Energy Range 1.65 - 1.97 GeV We study the inelastic scattering processes πN → Nππ from c.m. energies 1.65 - 1.97 GeV using an isobar model. The effect of including a non-zero high partial wave contribution on the determination of low partial wave scattering amplitudes is analysed in detail. The proper formulation of a high partial wave input due to the π-exchange process πN → ρN is presented. The major improvements due to including the π-exchange high partial wave input in the analysis of low energy πN → Nππ scattering are found to be the elimination of the overall phase ambiguity in the scattering matrix, and improvement in the representation of the angular scattering distribution by the fit parameterization, for c.m. energies above 1.8 GeV. The previous major isobar model analysis of these reactions at these energies is found to have serious deficiencies, as well as having many areas of agreement with our analysis. II. Resonance Parameter Analyses of πN → Δπ + ρN + εN Couplings of πN resonances with masses between 1.65 and 1.97 GeV/c2 to Δπ and ρN channels are determined using the scattering matrix elements resulting from inelastic partial wave analyses of πN → Nππ. The inelastic amplitudes were derived using an isobar model with a π-exchange based high partial wave input. These couplings are compared to those derived from an analysis of πN → Nππ without a high partial wave input. Evidence for coupling of the ρN channel to the P31(1910) resonance is found.