Pion cloud and the $Q^2-$dependence of $γ^* N \leftrightarrow Δ$ transition form factors

Recent experiment indicates that the behavior exhibited by the ratios $E_{1^+}/M_{1^+}$ and $S_{1^+}/M_{1^+}$ of the $\gamma^* N \leftrightarrow \Delta$ transition remain small and negative for $Q^2 \le 4.0 GeV^2$. It implies that the perturbative QCD is still not applicable at these momentum transfers. We show that these data can be explained in a dynamical model for electromagnetic production of pions, together with a simple scaling assumption for the bare $\gamma^* N \Delta$ form factors. Within our model we find that the bare $\Delta$ is almost spherical and the electric E2 and Coulomb C2 quardrupole excitations of the physical $\Delta$ are nearly saturated by pion cloud contribution in $Q^2 \le 4.0 GeV^2$.