Two-photon exchange from intermediate state resonances in elastic electron-proton scattering

TL;DR

This paper calculates the two-photon exchange correction in elastic electron-proton scattering, incorporating resonant intermediate states using dispersive methods and new electroproduction data, which helps resolve discrepancies in proton form factor measurements.

Contribution

It introduces a dispersive approach including multiple resonant states and uses new electroproduction data to improve TPE correction calculations in electron-proton scattering.

Findings

Resonant states significantly affect TPE corrections at higher Q^2.

The N(1520) resonance dominates for Q^2 > 2 GeV^2.

Results align with recent experimental measurements and help resolve form factor ratio discrepancies.

Abstract

We use a recently developed dispersive approach to compute the two-photon exchange (TPE) correction to elastic electron-proton scattering, including contributions from hadronic $J^P=1/2^\pm$ and $3/2^\pm$ resonant intermediate states below~1.8~GeV. For the transition amplitudes from the proton ground state to the resonant excited states we employ new exclusive meson electroproduction data from CLAS at $Q^2 \lesssim 5$~GeV$^2$, and we explore the effects of both fixed and dynamic widths for the resonances. Among the resonant states, the $N(1520)~\!3/2^-$ becomes dominant for $Q^2 \gtrsim 2$~GeV$^2$, with a sign opposite to the comparably sized $\Delta(1232)~\!3/2^+$ contribution, leading to an overall increase in the size of the TPE correction to the cross section relative to the nucleon only contribution at higher $Q^2$ values. The results are in good overall agreement with recent $e^+ p$ to $e^- p$ cross section ratio and polarization transfer measurements, and provide compelling evidence for a resolution of the electric to magnetic form factor ratio discrepancy.