Unstable particles, gauge invariance and the Delta⁺⁺ resonance parameters

The elastic and radiative pion(+)-proton scattering are studied in the framework of an effective Lagrangian model for the Delta^{++} resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole (Delta^{++}) and background contributions (rho^0, sigma, Delta and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the \Delta^{++} obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative pion-proton scattering is mu_Delta^{++}=(6.14 +/- 0.51) nuclear magnetons.