Forward sum rule for the $2\gamma$-exchange correction to the charge radius extraction from elastic electron scattering

Abstract

Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime and in leading log $\sim t\ln |t|$ approximation in the momentum transfer $|t|$ are considered. The imaginary part of TPE amplitude in these kinematics is related to the total photo absorption cross section. The real part of the TPE amplitude is obtained from the imaginary part by means of a fixed-$t$ dispersion relation. The dispersion integrals for the relevant elastic $ep$-scattering amplitude converge and do not need subtraction. This allows us to make clean a prediction for the real part of the TPE amplitude at forward angles with the leading term $\sim t\ln |t|$. Numerical estimates are comparable to the experimental precision in extracting the charge radius from experimental data.

arXiv comment6 pages, 4 figures; a reviewed version accepted to publication in PRC rapid communications

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• Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: comparison with data
• Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• The proton radius (puzzle?) and its relatives
• Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
• Two-photon exchange corrections to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers
• Two-photon exchange correction in elastic lepton-proton scattering
• Beam-normal single-spin asymmetry in elastic scattering of electrons from a spin-0 nucleus
• 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
• Precision Measurement of the Beam-Normal Single-Spin Asymmetry in Forward-Angle Elastic Electron-Proton Scattering
• Lepton mass effects for beam-normal single-spin asymmetry in elastic muon-proton scattering
• Hadronic weak charges and parity-violating forward Compton scattering
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Radiative corrections to elastic proton-electron scattering measured in coincidence