Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors

TL;DR

This paper calculates two-photon exchange corrections in electron-proton scattering, demonstrating their impact on form factor extraction and proton radius determination, and ensuring consistency with muonic hydrogen Lamb shift data.

Contribution

It provides a systematic analysis of two-photon exchange effects with nucleon and Δ intermediate states, highlighting their influence on form factor extraction and physical constraints.

Findings

Two-photon exchange corrections significantly affect form factor extraction.

Proton charge radius from scattering aligns with muonic hydrogen measurements.

Physical constraints and spectral functions are crucial for accurate radius determination.

Abstract

We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $\Delta$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$\Delta$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination of the proton charge radius from scattering data is shown to be dominated by the enforcement of a realistic spectral function. Additionally, the third Zemach moment from the resulting form factors is calculated. The obtained radius and Zemach moment are shown to be consistent with Lamb shift measurements in muonic hydrogen.