Pauli radius of the proton

TL;DR

This paper introduces a novel interpolation method using continued fractions and statistical sampling to accurately determine the proton's magnetic radius from scattering data without assuming specific functional forms.

Contribution

It presents a new approach for extracting the proton magnetic radius that avoids model assumptions, providing a more direct analysis of scattering data.

Findings

Proton magnetic radius found to be 0.817(27) fm.

Data are compatible with the magnetic and electric radii difference.

The slopes of the proton form factors may not be independent.

Abstract

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyse proton magnetic form factor data obtained via electron+proton scattering on $Q^2 \in [0.027,0.55]\,$GeV$^2$ with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we find $r_M = 0.817(27)\,$fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, $F_{1,2}(Q^2)$, are not truly independent observables; to wit, the difference $F_1^\prime(0)-F_2^\prime(0)/\kappa_p = [1+\kappa_p]/[4 m_p^2]$, viz. the proton Foldy term.