In the present review, we discuss different aspects of the two-photon exchange (TPE) physics in elastic ep scattering at high Q2, as well as at low Q2. The imaginary part of the TPE amplitude gives rise to beam and target single-spin asymmetries. Different theoretical approaches to the calculation of these observables are considered. The real part of the TPE amplitude influences the unpolarized cross-section and double-spin observables and is, most likely, responsible for the discrepancy between two methods of measurements of the proton form factors. We review different methods of calculations of the TPE amplitudes in the framework of the “hadron” and “quark-gluon” approaches. We discuss the dispersion approach suitable for low and intermediate Q2, which includes elastic and inelastic intermediate hadronic states, as well as the connection of TPE with the proton radius puzzle. The present situation with direct experimental searches for the TPE amplitude in the e+p/e−p charge asymmetry is also discussed, as well as attempts to extract the TPE amplitudes from existing experimental data obtained by the Rosenbluth and double polarization techniques. The TPE physics in other processes such as elastic мp, e-nucleus, and еп scattering is also reviewed.
Two-photon exchange contribution to proton form factors in the time-like region
