Two-photon exchange corrections in elastic electron-proton scattering. Dispersion theory

The recent measurements of the proton charge radius from the Lamb shift of energy levels in muonic hydrogen are in strong contradiction, by 5-7 standard deviations, with the value obtained with electronic hydrogen and the value extracted from the unpolarized electron-proton scattering data. The precise determination of the proton radius from scattering experiments can be taken only with account of the higher order corrections, like two photon exchange diagram and 2-loops QED corrections. Two photon exchange correction was studied with the fixed momentum transfer dispersion relations. It was shown that the dispersion relations calculation of the two- photon exchange processes in elastic electron-proton scattering requires one subtraction. Theoretical predictions of elastic contribution of TPE corrections to the unpolarized elastic electron-proton scattering and polarization transfer were made.