Pion Cloud and the ${\mathit{Q}}^2$ Dependence of ${\mathit{\gamma }}^{*}\mathit{N}\leftrightarrow \mathit{\Delta }$ Transition Form Factors

Recent experiments indicate that the behavior exhibited by the ratios $E_{1^{+}}/M_{1^{+}}$ and $S_{1^{+}}/M_{1^{+}}$ of the ${\gamma }^{*}N\leftrightarrow \Delta$ transition remains small and negative for $Q^2\le 4.0{\mathrm{GeV}}^2$. It implies that 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 $E2\mathrm{}$ and Coulomb $C2\mathrm{}$ quadrupole excitations of the physical $\Delta$ are nearly saturated by the pion cloud contribution in $Q^2\le 4.0{\mathrm{GeV}}^2$.