Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters

The elastic and radiative π+p scattering are studied in the framework of an effective Lagrangian model for the Δ++ 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 (Δ++) and background contributions (ρ0, σ, Δ, and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the Δ++ 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 π+p scattering is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mu _{\Delta ^{ + + } } = (6.14 \pm 0.51)$$ \end{document} nuclear magnetons.