On the physics behind the form factor ratio $\mu_p G_E^p (Q^2) / G_M^p (Q^2)$

TL;DR

This paper explores the theoretical relationship between different definitions of nucleon magnetization densities and evaluates their implications using the chiral quark soliton model, revealing qualitative differences consistent with empirical data.

Contribution

It derives an explicit relation between two nucleon magnetization densities and compares their behavior within a specific theoretical framework.

Findings

Noticeable qualitative difference between charge density and Kelly's magnetization density.

Theoretical relation aligns with empirical observations of form factors.

Evaluation within the chiral quark soliton model supports the physical relevance of the densities.

Abstract

We point out that there exist two natural definitions of the nucleon magnetization densities : the density $\rho_M^K (r)$ introduced in Kelly's phenomenological analysis and theoretically more standard one $\rho_M (r)$. We can derive an explicit analytical relation between them, although Kelly's density is more useful to disentangle the physical origin of the different $Q^2$ dependence of the Sachs electric and magnetic form factors of the nucleon. We evaluate both of $\rho_M (r)$ and $\rho_M^K (r)$ as well as the charge density $\rho_{ch}(r)$ of the proton within the framework of the chiral quark soliton model, to find a noticeable qualitative difference between $\rho_{ch}(r)$ and $\rho_M^K (r)$, which is just consistent with Kelly's result obtained from the empirical information on the Sachs electric and magnetic form factors of the proton.