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

We obtain the electromagnetic form factors of the $γNΔ$ 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} $γN Δ$ form factors by a three-parameter form which is consistent with the asymptotic behavior inferred from QCD. The parameters of the bare $γN Δ$ 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 $Δ(1232)$-resonance region. This analysis emphasizes the significance of the pion-cloud effects in the extraction of the resonance parameters.