Combined parametrization of G_En and $\gamma^{\ast} N \rightarrow \Delta (1232)$ quadrupole form factors

Abstract.

Models based on SU(6) symmetry breaking and large N_c limit provide relations between the pion cloud contributions to the $\gamma^{\ast} N \rightarrow \Delta (1232)$ quadrupole form factors, electric (G_E) and Coulomb (G_C), and the neutron electric form factor G_En, suggesting that those form factors are dominated by the same physical processes. Those relations are improved in order to satisfy a fundamental constraint between the electric and Coulomb quadrupole form factors in the long wavelength limit, when the photon three-momentum vanishes (Siegert’s theorem). Inspired by those relations, we study alternative parametrizations for the neutron electric form factor. The parameters of the new form are then determined by a combined fit to the G_En and the $\gamma^{\ast} N \rightarrow \Delta (1232)$ quadrupole form factor data. We obtain a very good description of the G_E and G_C data when we combine the pion cloud contributions with small valence quark contributions to the $\gamma^{\ast} N \rightarrow \Delta (1232)$ quadrupole form factors. The best description of the data is obtained when the second momentum of G_En is $r_{n}^{4} \simeq -0.4$ fm⁴. We conclude that the square radii associated with G_E and G_C, $r_{E}^{2}$ and $r_{C}^{2}$, respectively, are large, revealing the long extension of the pion cloud. We conclude also that those square radii are related by $r_{E}^{2} - r_{C}^{2} = 0.6 \pm 0.2$ fm². The last result is mainly the consequence of the pion cloud effects and Siegert’s theorem.