Are the Muonic Hydrogen and Electron Scattering Experiments Measuring the Same Observable?

TL;DR

This paper develops a model to correct relativistic recoil effects in electron scattering experiments, aligning measurements of the proton's charge radius with those from muonic hydrogen and improving consistency across methods.

Contribution

It introduces a correction model for relativistic recoil effects in form factor measurements, enabling more accurate comparisons between electron scattering and muonic hydrogen results.

Findings

Corrected form factors suggest similar charge and magnetization distributions.

Applying recoil corrections aligns electron scattering charge radius with muonic hydrogen measurements.

Predicted corrections improve consistency for deuteron, triton, and helium isotopes.

Abstract

Elastic scattering of relativistic electrons from the nucleon yields Lorentz invariant form factors that describe the fundamental distribution of charge and magnetism. The spatial dependence of the nucleon's charge and magnetism is typically interpreted in the Breit reference frame which is related by a Lorentz boost from the laboratory frame, where the nucleon is at rest. We construct a model to estimate how the Sachs electric and magnetic form factors can be corrected for the effects of relativistic recoil. When the corrections are applied, the ratio of the proton's Sachs form factors is approximately flat with $Q^2$, i.e. the spatial distributions of the proton's intrinsic charge and magnetization are similar. Further, we estimate the correction due to recoil that must be applied to the determination of the proton charge radius from elastic electron scattering before it can be compared to the value determined using the Lamb shift in hydrogen. Application of the correction brings the two values of the proton charge radius into significantly closer agreement. Predicted corrections based on the model are provided for the rms charge radii of the deuteron, the triton, and the helium isotopes.