$γ^{*}NΔ$ Form Factors from a Relativistic Dynamical Model of Pion Electroproduction

Abstract

We obtain the electromagnetic form factors of the ${\hat{I}}^{3}N\hat{I}”$ transition by analyzing recent pion-electroproduction data using a fully relativistic dynamical model. Special care is taken to satisfy Ward-Takahashi identities for the Born term in the presence of form factors thereby allowing the use of realistic electromagnetic form factors of the nucleon and pion. We parametrize the $Q^2$ dependence of the {\it bare} ${\hat{I}}^{3}N\hat{I}”$ form factors by a three-parameter form which is consistent with the asymptotic behavior inferred from QCD. The parameters of the bare ${\hat{I}}^{3}N\hat{I}”$ form factors are the only free parameters of the model and are fitted to the differential cross-section and multipole-analysis data up to $Q^2=4$ (GeV/c)${}^2$ in the $\hat{I}”(1232)$-resonance region. This analysis emphasizes the significance of the pion-cloud effects in the extraction of the resonance parameters.

9 pages, 5 figures, several small corrections, to be published in Phys. Rev. C