Sum rule for the double virtual Compton scattering

TL;DR

This paper derives a sum rule connecting elastic and inelastic electron-proton scattering cross sections, incorporating nucleon-antinucleon pair production, based on the analytic properties of the virtual Compton scattering amplitude.

Contribution

It introduces a novel sum rule relating different scattering processes using analyticity arguments and models nucleon-pion interactions for the pair production contribution.

Findings

Derived a sum rule linking elastic and inelastic scattering cross sections.

Calculated nucleon-antinucleon pair production contribution using a simple nucleon-pion interaction model.

Provided insights into the analytic structure of the virtual Compton scattering amplitude.

Abstract

The two photon exchange amplitude is investigated in frame of analytic properties of the virtual Compton scattering amplitude as a function of the invariant mass squared of the intermediate hadronic state. A sum rule is built, based on arguments from analyticity. It relates the differential cross section of elastic electron-proton scattering including form factors, and the cross section of inelastic scattering channel, with a contribution of nucleon anti-nucleon pair production arising from the Fermi statistics. The last term is calculated in frame of a simple model of nucleon-pion interaction.