Pion-proton scattering and isospin breaking in the $Δ^0-Δ^{++}$ system

Abstract

We determine the mass and width of the $Δ^{++}\ (Δ^0)$ resonance from data on $π^+ p\ (π^- p)$ scattering both, in the pole of the $S$-matrix and conventional Breit-Wigner approaches to the scattering amplitude. We provide a simple formula that relates the two definitions for the parameters of the $Δ$. Isospin symmetry breaking in the $\d0-\dm$ system depends on the definition of the resonant properties: we find $M_0-M_{++} = 0.40 \pm 0.57\ {\rm MeV},\ Γ_0 -Γ_{++} = 6.89 \pm 0.95\ {\rm MeV}$ in the pole approach while $\wt{M}_0-\wt{M}_{++} = 2.25 \pm 0.68\ {\rm MeV},\ \wtΓ_0 - \wtΓ_{++} = 8.45 \pm 1.11\ {\rm MeV}$ in the conventional approach.