New large-$N_c$ relations among the nucleon and nucleon-to-Delta GPDs

We establish relations which express the generalized parton distributions (GPDs) describing the $N\to \Delta$ transition in terms of the nucleon GPDs. 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. Namely, in the large-$N_c$ limit we find $C2=E2$. The resulting relations among the nucleon and $N\to\Delta$ GPDs provide predictions for the $N\to\Delta$ electromagnetic form factors which are found to be in very good agreement with experiment for moderate momentum transfers.