Charge radii of the nucleon from its flavor dependent Dirac form factors

TL;DR

This paper presents a model-independent analysis of nucleon form factors to precisely determine proton and neutron charge radii, confirming previous proton measurements and providing the first neutron radius extraction from form factor data.

Contribution

The study introduces a novel, model-independent method to extract nucleon charge radii from form factors, improving precision and consistency over previous techniques.

Findings

Proton charge radius: 0.852 ± 0.002 (stat) ± 0.009 (syst) fm.

First neutron charge radius extraction from form factor data: -0.122 ± 0.004 (stat) ± 0.010 (syst) fm².

Method aligns with the smallest electron scattering measurements for the proton.

Abstract

We have determined the proton and the neutron charge radii from a global analysis of the proton and the neutron elastic form factors, after first performing a flavor decomposition of these form factors under charge symmetry in the light cone frame formulation. We then extracted the transverse mean-square radii of the flavor dependent quark distributions. In turn, these are related in a model-independent way to the proton and neutron charge radii but allow us to take into account motion effects of the recoiling nucleon for data at finite but high momentum transfer. In the proton case we find $\langle r_p \rangle = 0.852 \pm0.002_{\rm (stat.)} \pm0.009_{\rm (syst.)}~({\rm fm})$, consistent with the proton charge radius obtained from muonic hydrogen spectroscopy \cite{pohl:2010,antog2013}. The current method improves on the precision of the $\langle r_p \rangle$ extraction based on the form factor measurements. Furthermore, we find no discrepancy in the $\langle r_p \rangle$ determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a value that is consistent with the smallest $\langle r_p \rangle$ extraction from the electron scattering measurements \cite{Xiong:2019umf}. Concerning the neutron case, past results relied solely on the neutron-electron scattering length measurements, which suffer from an underestimation of underlying systematic uncertainties inherent to the extraction technique. Utilizing the present method we have performed the first extraction of the neutron charge radius based on nucleon form factor data, and we find $\langle r_n^2 \rangle = -0.122 \pm0.004_{\rm (stat.)} \pm0.010_{\rm (syst.)}~({\rm fm}^2)$.