# How much two-photon exchange is needed to resolve the proton form factor discrepancy?

## TL;DR

This paper estimates the size of two-photon exchange contributions needed to explain the proton form factor discrepancy, using global fits and recent experimental data, highlighting uncertainties in the magnitude of TPE effects.

## Contribution

It provides a model-independent estimate of the TPE correction magnitude required to resolve the form factor discrepancy, based on global scattering data and recent measurements.

## Key findings

- Wide variation in TPE estimates depending on global fit used
- Recent TPE measurements are consistent with TPE explaining the discrepancy
- Magnitude of the discrepancy is not well-constrained by current data

## Abstract

One possible explanation for the proton form factor discrepancy is a contribution to the elastic electron-proton cross section from hard two-photon exchange (TPE), a typically neglected radiative correction. Hard TPE cannot be calculated in a model-independent way, but it can be determined experimentally by looking for deviations from unity in the ratio of positron-proton to electron-proton cross sections. Three recent experiments have measured this cross section ratio to quantify hard TPE. To interpret the results of these experiments, it is germane to ask: 'How large of a deviation from unity is necessary to fully resolve the form factor discrepancy?' With a minimal set of assumptions and using global fits to unpolarized and polarized elastic scattering data, I estimate the necessary size of the TPE correction in the kinematics of the three recent experiments and compare to their measurements. I find wide variation when using different global fits, implying that the magnitude of the form factor discrepancy is not well-constrained. The recent hard TPE measurements can easily accommodate the hypothesis that TPE underlies the proton form factor discrepancy.