Forward sum rule for the $2\gamma$-exchange correction to the charge radius extraction from elastic electron scattering

TL;DR

This paper derives a forward sum rule for two-photon exchange corrections in elastic electron-proton scattering, providing a model-independent way to improve charge radius measurements by relating the TPE amplitude to photo absorption data.

Contribution

The paper introduces a new forward sum rule for TPE corrections, enabling precise, model-independent estimates of the real part of the TPE amplitude relevant for charge radius extraction.

Findings

The dispersion relation for TPE converges without subtraction.

Numerical estimates of TPE corrections are comparable to experimental uncertainties.

The sum rule improves the accuracy of charge radius extraction from scattering data.

Abstract

Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime and in leading log $\sim t\ln|t|$ approximation in the momentum transfer $|t|$ are considered. The imaginary part of TPE amplitude in these kinematics is related to the total photo absorption cross section. The real part of the TPE amplitude is obtained from the imaginary part by means of a fixed-$t$ dispersion relation. The dispersion integrals for the relevant elastic $ep$-scattering amplitude converge and do not need subtraction. This allows us to make clean a prediction for the real part of the TPE amplitude at forward angles with the leading term $\sim t\ln|t|$. Numerical estimates are comparable to the experimental precision in extracting the charge radius from experimental data.