Pion cloud and the $Q^2-$dependence of ${\gamma }^{\ast }N\leftrightarrow \Delta$ transition form factors

Abstract

Recent experiment indicates that the behavior exhibited by the ratios $E_{1^{+}}/M_{1^{+}}$ and $S_{1^{+}}/M_{1^{+}}$ of the ${\gamma }^{\ast }N\leftrightarrow \Delta$ transition remain small and negative for $Q^2\le 4.0Ge{V}^2$. 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 ${\gamma }^{\ast }N\Delta$ 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 $Q^2\le 4.0Ge{V}^2$.

9 pages, 1 table, 4 figures

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