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

Abstract

We determine the mass and width of the ${\Delta }^{++}({\Delta }^0)$ resonance from data on ${\pi }^{+}p({\pi }^{-}p)$ 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 $\Delta$. Isospin symmetry breaking in the $\text{d}0-\text{dm}$ system depends on the definition of the resonant properties: we find $M_0-M_{++}=0.40\pm 0.57\mathrm{MeV},{\Gamma }_0-{\Gamma }_{++}=6.89\pm 0.95\mathrm{MeV}$ in the pole approach while $\text{wt}{M}_0-\text{wt}{M}_{++}=2.25\pm 0.68\mathrm{MeV},\text{wt}{\Gamma }_0-\text{wt}{\Gamma }_{++}=8.45\pm 1.11\mathrm{MeV}$ in the conventional approach.

Comments: Latex, 23 pages, two figures upon request