Two-Photon Exchange Calculations Versus Data

In view of the proton form-factor problem and proton radius puzzle, the two-photon exchange (TPE) corrections require a model-independent investigation as the largest source of the hadronic uncertainty in modern experiments. I present the dispersion relation approach, which is based on unitarity and analyticity, to evaluate the TPE in the elastic electron-proton scattering. The leading elastic and first inelastic pion-nucleon intermediate state contributions are fully accounted for in the region of small momentum transfer below 1 GeV. A novel method of analytical continuation allowed to perform a calculation without a restriction to a particular form of the input. For the numerical evaluation, the elastic form factor fit of A1 Collaboration and the pion electroproduction amplitudes from MAID were exploited. The results are compared to the recent CLAS, VEPP-3 and OLYMPUS data as well as the full TPE correction in the near-forward approximation, which is based on the Christy and Bosted unpolarized structure functions fit. Additionally, predictions are given for a forthcoming muon-proton scattering experiment (MUSE) within the hadronic model and near-forward approximation. The obtained knowledge of TPE is going to be applied for the reanalysis of the electron-proton scattering data. The unambiguous knowledge of the proton form factors and radii, which enter the evaluation of the TPE correction, is relevant in view of the forthcoming ground state hyperfine splitting (HFS) measurements by CREMA and FAMU collaborations as well as at J-PARC. The current theoretical knowledge of TPE exceeds by two orders of magnitude the expected ppm accuracy level. In the ordinary hydrogen, the theory is even six orders of magnitude behind the experiment. The expansion of the proton form factors in terms of charge and magnetic radii sizably reduces the theoretical error when evaluating the leading Zemach contribution to HFS. I also discuss how the precise measurements in electronic hydrogen may further reduce the proton structure uncertainty in muonic hydrogen HFS.