Combined parametrization of the neutron electric form factor and the ${\gamma }^{\ast }N\to \Delta (1232)$ 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 ${\gamma }^{\ast }N\to \Delta (1232)$ 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 ${\gamma }^{\ast }N\to \Delta (1232)$ 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 ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors. The best description of the data is obtained when the second momentum of $G_{En}$ is $r_n^4\simeq -0.4$ fm${}^4$. 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 $r_E^2-r_C^2=0.6\pm 0.2$ fm${}^2$. The last result is mainly the consequence of the pion cloud effects and Siegert's theorem.

Comments: Published in European Physics Journal A. Extended version. New format. 14 pages, 7 figures