Coulomb corrections in the extraction of the proton radius

TL;DR

This paper evaluates higher-order Coulomb corrections in electron-proton scattering at low Q^2 using the Effective Momentum Approximation, revealing small but Q^2-dependent effects that could impact proton radius measurements.

Contribution

It introduces a method to include all-order Coulomb interactions in radius extraction, extending beyond second-photon exchange calculations.

Findings

Small Coulomb corrections with strong Q^2 dependence at low Q^2

Higher order terms may significantly affect proton magnetic radius extraction

Effective Momentum Approximation effectively captures all-order Coulomb effects

Abstract

Multi-photon exchange contributions are important in extracting the proton charge radius from elastic electron--proton scattering. So far, only diagrams associated with the exchange of a second photon have been evaluated. At the very low $Q^2$ values relevant to the radius extraction, higher order contributions may become important. We evaluate these corrections in the Effective Momentum Approximation, which includes the Coulomb interaction to all orders, and find small corrections with a strong $Q^2$ dependence at low $Q^2$ and large scattering angles. This suggests that the higher order terms may be important in the evaluation of the proton magnetic radius.