Exact Relations for Two-Photon-Exchange Effect in Elastic $ep$ Scattering by Dispersion Relation and Hadronic Model

Abstract

The two-photon-exchange (TPE) effect plays a key role to extract the form factors (FFs) of the proton. In this work, we present some exact properties on the TPE effect in the elastic $ep$ scattering based on four types of typical and general interactions. The possible kinematical singularities, the asymptotic behaviors and the branch cuts of the TPE amplitudes are analyzed. The analytic expressions clearly indicate some exact relations between the dispersion relation (DR) method and the hadronic model (HM) method. It suggests that the two methods should be modified to general forms, respectively. After the modifications the new forms give the same results. Furthermore, they automatically and correctly include the contributions due to the seagull interaction, the meson-exchange effect, the contact interactions and the off-shell effect. To analyze the elastic $e^{\pm }p$ scattering data sets, the new forms should be used.

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References in corpus (19)

• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Measurement of the two-photon exchange contribution to the elastic $e^{\pm }p$ scattering cross sections at the VEPP-3 storage ring
• Towards a resolution of the proton form factor problem: new electron and positron scattering data
• Search for effects beyond the Born approximation in polarization transfer observables in $\vec{e}p$ elastic scattering
• Two-photon exchange in elastic electron-proton scattering : QCD factorization approach
• Box diagram in the elastic electron-proton scattering
• Is there model-independent evidence of the two-photon-exchange effect in the electron-proton elastic scattering cross section?
• On Delta resonance contribution to two-photon exchange amplitude
• Phenomenological analysis of two-photon exchange effects in proton form factor measurements
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• Technical Design Report for the Paul Scherrer Institute Experiment R-12-01.1: Studying the Proton "Radius" Puzzle with μp Elastic Scattering
• The contribution of axial-vector mesons to hyperfine structure of muonic hydrogen
• Solving three-body scattering problem in the momentum lattice representation
• Lepton-Proton Two-Photon Exchange in Chiral Perturbation Theory
• Model-independent extraction of two-photon effects in elastic electron-proton scattering
• Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model
• Contribution of σ-meson exchange to elastic lepton-proton scattering
• Meson exchange in lepton-nucleon scattering and proton radius puzzle
• Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range