The K-matrix approach to the Δ-resonance mass splitting and isospin violation in low-energy πN scattering

Experimental data on pi N scattering in the elastic energy region T-pi <= 250 MeV are analyzed within the multichannel K-matrix approach with effective Lagrangians. Isospin invariance is not assumed in this analysis and the physical values for masses of the involved particles are used. The corrections due to pi(+)-pi(0) and p-n mass differences are calculated and found to be in a reasonable agreement with the NORDITA results. The results of our analysis describe the experimental observables very well. New values for mass and width of the Delta(o) and Delta(++) resonances were obtained from the data. The isospin-symmetric version yields phase-shift values similar to the new Solution, FA02, for the pi N elastic scattering amplitude by the GW group based on the latest experimental data. While our analysis leads to a considerably smaller (<= 1%) isospin violation in the energy interval T-pi similar to 30-70 MeV as compared to 7% in works by W.R. Gibbs et al. and E. Matsinos, it confirms calculations based on chiral perturbation theory.