Two-photon exchange corrections in elastic lepton-proton scattering

Abstract

Elastic electron-proton scattering has been a time-honored tool to provide basic information on general properties of the proton, such as its charge distribution. At leading order, this process is described by the exchange of one photon. In recent years, two experimental approaches, with and without polarized protons, gave strikingly different results for the ratio of the electric to magnetic proton form factors. Even more recently, a mysterious discrepancy ("the proton radius puzzle") has been observed in the extraction of the proton charge radius from the muonic hydrogen versus hydrogen spectroscopy and elastic electron-proton scattering. In these experiments, two-photon exchange (TPE) contributions are the largest source of the hadronic uncertainty. In the present work, the forward virtual Compton scattering is calculated within a dispersive formalism to determine TPE corrections. One of the amplitudes requires a subtraction function, which is estimated based on experimental data. Exploiting these results, the TPE correction to the Lamb shift for the 2S level in muonic hydrogen is evaluated. Within a dispersion relation approach for the lepton-proton amplitudes, the hadronic TPE correction to the hyperfine splitting of the S energy levels is also determined. The TPE correction in the elastic lepton-proton scattering is given by a sum of diagrams with proton and with inelastic intermediate states. At low energies, the former yields the main TPE correction. Comparing a box graph model with the dispersion relations at fixed momentum transfer, we find agreement when performing one subtraction. Fixing the subtraction point to the TPE fit of data performed by the MAMI/A1 Collaboration, the contribution from the inelastic intermediate states in the electron-proton scattering is estimated. Additionally, a new method of analytical continuation of the elastic contribution to TPE amplitudes is developed. At low momentum transfer, the inelastic intermediate states are included approximating the hadronic part of the TPE box graph by the near-forward unpolarized virtual Compton scattering which has the proton structure functions as input. The resulting TPE are compared with the empirical fit. Subsequently, the study is extended to larger momentum transfer. For this purpose, the pion-nucleon intermediate state in the dispersion relation approach is studied. A further part of this work is devoted to the muon-proton scattering experiment (MUSE), which was proposed to compare the elastic scattering of electrons and muons on the proton target and to measure the proton charge radius in the muon-proton scattering. The sub-percent level of the experimental accuracy requires an account of TPE corrections. In this work, the proton TPE box graph for the muon-proton process is evaluated for the kinematics of the proposed experiment. Approximating the doubly virtual Compton tensor by the near-forward form, the inelastic TPE correction is quantified. Additionally, the contribution of the subtraction function, relevant because of the muon mass as compared to the beam energy, is studied in detail. The evaluated TPE correction provides the necessary input for the forthcoming MUSE experiment.