Model-independent form factor relations at large $N_c$

TL;DR

This paper proves a model-independent relation for the long-distance Fourier transform of nucleon electromagnetic form factors in the large $N_c$ and chiral limits, confirming previous conjectures through large $N_c$ chiral perturbation theory.

Contribution

It demonstrates that a previously conjectured relation is truly model-independent by deriving it directly from large $N_c$ chiral perturbation theory.

Findings

The relation holds in the combined large $N_c$ and chiral limits.

A new relation is derived when the chiral limit precedes the large $N_c$ limit.

The result confirms the universality of the form factor relation across models.

Abstract

In this paper a model-independent relation which holds for the long distance part of the Fourier transform of the electromagnetic form factors of the nucleon in the large $N_c$ and chiral limits is demonstrated. This relation was previously conjectured based on the fact that it emerged in {\it all} semiclassical chiral models independent of the details of the model. Here we show that the result is, in fact, model independent by deriving it directly in large $N_c$ chiral perturbation theory which is known to capture the long distance behavior of the form factors. The relation is valid when the large $N_c$ limit is formally taken before the chiral limit. A new relation is derived for the case where the chiral limit is taken prior to the large $N_c$ limit.