Note on the electromagnetic radius of proton

TL;DR

This paper analyzes proton form factor data across a wide range of momentum transfer to determine the proton's electric and magnetic radii, highlighting model-dependent variations and suggesting future experimental focus near $Q^2=0.2$ GeV$^2$.

Contribution

It provides a comprehensive global fit to form factor data using various models, revealing model-dependent structures and their impact on proton radius extraction.

Findings

Different models show varying structures near $Q^2=0.2$ GeV$^2$.

Proton radii vary depending on the model used.

Most extracted radii align with muonic hydrogen measurements.

Abstract

We have analyzed the proton form factor data by using a number of phenomenological parameterizations (models) and extracting the proton electric and magnetic radii. To this end we performed a global fit to all available form factor data, with the virtual photon momentum squared $Q^2$ from $0.0002$ to nearly 10 GeV$^2$ for electric form factor and from $0.015$ to 31 GeV$^2$ for magnetic one. Special attention was given to the small structure shown by the form factor data near $Q^2 = 0.2$ GeV$^2$. It was found that different models yield different structures with different numbers of minimum at this kinematics. Since the slope of form factor in the limit of $Q^2\to 0$ is influenced by this structure, the extracted proton radii are consequently different for different models. Our finding recommends that future experiments should focus on this kinematics instead of low $Q^2$. Experimental data with accuracies comparable to those of the latest data at low $Q^2$ would clearly help to clarify the effect of this structure on the proton charge radius. Interestingly, most of the extracted proton charge radii were found to be closer to the value obtained from the muonic hydrogen atom spectroscopy.