We examine the large-$N_c$ relations which express the electromagnetic $N$-to-$\Delta$ transition quantities in terms of the electromagnetic properties of the nucleon. These relations are based on the known large-$N_c$ relation between the $N\to \Delta$ electric quadrupole moment and the neutron charge radius, and a newly derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Extending these relations to finite, but small, momentum transfer, we find that the description of the electromagnetic $N\to \Delta$ ratios ($R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$) in terms of the nucleon form factors predicts a structure which may be ascribed to the effect of the “pion cloud.” These relations also provide useful constraints for the $N\to \Delta$ generalized parton distributions.

• Received 3 November 2006

DOI:https://doi.org/10.1103/PhysRevD.76.111501