Proton Electromagnetic Form Factor Ratios at Low Q^2

TL;DR

This paper investigates the proton's electromagnetic form factor ratio at low momentum transfer, clarifies the interpretation of form factors as two-dimensional Fourier transforms of densities, and compares experimental data with theoretical expectations.

Contribution

It demonstrates that the form factor $F_2$ can be interpreted as the Fourier transform of a magnetization density and derives relationships between measurable ratios and true charge and magnetization densities.

Findings

Magnetization density extends further than charge density.

Existing measurements show a decreasing ratio $R$ with increasing $Q^2$.

Form factor $F_2$ is correctly interpretable as a two-dimensional Fourier transform.

Abstract

We study the ratio $R\equiv\mu G_E(Q^2)/G_M(Q^2)$ of the proton at very small values of $Q^2$. Radii commonly associated with these form factors are not moments of charge or magnetization densities. We show that the form factor $F_2$ is correctly interpretable as the two-dimensional Fourier transformation of a magnetization density. A relationship between the measurable ratio and moments of true charge and magnetization densities is derived. We find that existing measurements show that the magnetization density extends further than the charge density, in contrast with expectations based on the measured reduction of $R$ as $Q^2$ increases.