Are Electron Scattering Data Consistent with a Small Proton Radius?

TL;DR

This paper analyzes low momentum transfer electron-proton scattering data to determine the proton charge radius, finding results consistent with muonic atom measurements and addressing convergence issues in form factor expansions.

Contribution

It demonstrates that polynomial expansions of the form factor converge below a specific momentum transfer and provides a proton radius estimate aligning with muonic atom results.

Findings

Proton radius estimated at 0.840(16) fm.

Polynomial expansions converge below 4m_pi^2.

Results are consistent with muonic atom measurements.

Abstract

We determine the charge radius of the proton by analyzing the published low momentum transfer electron-proton scattering data from Mainz. We note that polynomial expansions of the form factor converge for momentum transfers squared below $4m_\pi^2$, where $m_\pi$ is the pion mass. Expansions with enough terms to fit the data, but few enough not to overfit, yield proton radii smaller than the CODATA or Mainz values and in accord with the muonic atom results. We also comment on analyses using a wider range of data, and overall obtain a proton radius $R_E=0.840(16$) fm.