Large-$N_c$ relations for the electromagnetic N to Delta(1232) transition

TL;DR

This paper explores large-N_c relations linking the electromagnetic N to Delta(1232) transition properties to nucleon characteristics, revealing insights into pion cloud effects and constraining generalized parton distributions.

Contribution

It derives new large-N_c relations connecting N to Delta transition form factors with nucleon properties, extending understanding of these transitions at finite momentum transfer.

Findings

Relations predict pion cloud contributions to N to Delta transitions.

Constraints on N to Delta generalized parton distributions.

Extension of large-N_c relations to finite momentum transfer.

Abstract

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 ($R_{EM}$ and $R_{SM}$) 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.