Two-photon exchange contribution to elastic $e^-$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data

TL;DR

This paper calculates the two-photon exchange correction to elastic electron-proton scattering using a dispersive approach, including $ ext{π}N$ states, and compares results with experimental data across a range of momentum transfers.

Contribution

It introduces a novel analytical continuation method for two-photon exchange amplitudes and extends previous work to a broader momentum transfer region.

Findings

Results agree with recent experimental data in the forward angular region.

The dispersive framework effectively incorporates $ ext{π}N$ intermediate states.

The method improves understanding of two-photon exchange effects in elastic scattering.

Abstract

We evaluate the two-photon exchange correction to the elastic electron-proton scattering cross section within a dispersive framework. Besides the elastic contribution, we account for all $\pi N$ intermediate state contributions using the phenomenological MAID fit as an input. We develop a novel method for the analytical continuation of the two-photon exchange amplitudes into the unphysical region and generalize our previous work to the momentum transfer region $ 0.064~\mathrm{GeV}^2 \lesssim Q^2 \lesssim 1~\mathrm{GeV}^2$. We compare our results with recent OLYMPUS, CLAS and VEPP-3 data as well as with empirical fits and estimates in the forward angular region.