The RMS Charge Radius of the Proton and Zemach Moments

TL;DR

This paper calculates Zemach moments from recent proton form factor measurements, revealing significant uncertainties and challenging previous hypotheses about reconciling muonic and electronic proton radius measurements.

Contribution

It provides updated Zemach moments based on recent data, demonstrating their impact on proton radius determination and testing hypotheses about discrepancies.

Findings

Zemach moments have uncertainties comparable to experimental errors

Large Zemach moments are inconsistent with experimental data

Alternative explanations for the proton radius discrepancy are discussed

Abstract

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al.. De Rujula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.