Two-photon exchange in dispersion approach

TL;DR

This paper presents a dispersion relation approach to calculate two-photon exchange amplitudes in elastic electron-proton scattering, emphasizing unitarity and off-shell form factors, with results closely matching traditional methods up to 6 GeV^2.

Contribution

It introduces a dispersion-based method for two-photon exchange calculations that avoids off-shell form factors and compares favorably with traditional on-shell approaches.

Findings

Real part of amplitude evaluated using dispersion relations.

Minor numerical differences with traditional methods up to 6 GeV^2.

Method leverages unitarity and on-shell intermediate states.

Abstract

We calculate two-photon exchange amplitude for the elastic electron-proton scattering in the framework of dispersion relations. The imaginary part of the amplitude is determined by unitarity. Since in the unitarity relation intermediate states are on shell, off-shell form factors are not needed for the calculation. The real part is then evaluated using analytical properties of the amplitude. The expression for the elastic contribution to the amplitude, obtained in our approach, differs from the results of traditional calculations with on-shell form factors. Nevertheless, numerically the difference is minor for Q^2 up to 6 GeV^2.