Two-photon exchange corrections to elastic $e^-$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers

TL;DR

This paper calculates the two-photon exchange correction in elastic electron-proton scattering at low momentum transfers using a dispersive approach with pion-nucleon states, providing detailed results relevant for precision measurements.

Contribution

The study offers a full dispersive treatment of $ N$ states in TPE corrections, including all partial waves, at low $Q^2$, with comparisons to structure function methods and empirical fits.

Findings

Good agreement with structure function calculations at low $Q^2$

Small contribution from discontinuities beyond $ N$ states

Provides TPE correction data for low momentum transfer region

Abstract

We evaluate the pion-nucleon intermediate-state contribution to the two-photon exchange (TPE) correction in the elastic electron-nucleon scattering within a dispersive framework. We calculate the contribution from all $\pi N$ partial waves using the MAID parametrization. We provide the corresponding TPE correction to the unpolarized $e p$ scattering cross section in the region of low momentum transfer $ Q^2 \lesssim 0.064~\mathrm{GeV}^2$, where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. We compare our result in the forward angular region with an alternative TPE calculation, in terms of structure functions, and find a good agreement, indicating a small contribution at low $Q^2$ due to discontinuities beyond $ \pi N$. We also compare our results with empirical fits.