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 $\d0-\dm$ 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 $\wt{M}_0-\wt{M}_{++} = 2.25 \pm 0.68\ {\rm MeV},\ \wtΓ_0 - \wtΓ_{++} = 8.45 \pm 1.11\ {\rm MeV}$ in the conventional approach.

Latex, 23 pages, two figures upon request

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