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.

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

References in corpus (7)

• High-precision determination of the electric and magnetic form factors of the proton
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Two-photon exchange in dispersion approach
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Two-photon exchange at low Q^2
• Two-photon exchange corrections in elastic muon-proton scattering
• Dispersive contributions to $e^{+}p/e^{-}p$ cross section ratio in forward regime

Cited by in corpus (5)

• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• 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
• Precision Measurement of the Beam-Normal Single-Spin Asymmetry in Forward-Angle Elastic Electron-Proton Scattering
• Hadronic weak charges and parity-violating forward Compton scattering