Two-photon exchange corrections to elastic electron-proton scattering at large momentum transfer within the SCET approach

We calculate the two-photon exchange (TPE) corrections in the region where the kinematical variables describing the elastic ep scattering are moderately large momentum scales relative to the soft hadronic scale. For such kinematics we use the QCD factorization approach formulated in the framework of the soft-collinear effective theory (SCET). Such technique allows us to develop a description for the soft-spectator scattering contribution which is found to be important in the region of moderately large scales. Together with the hard-spectator contribution we present the complete factorization formulas for the TPE amplitudes at the leading power and leading logarithmic accuracy. The momentum region where both photons are hard is described by only one new nonperturbative SCET form factor. It turns out that the same form factor also arises for wide-angle Compton scattering which is also described in the framework of the SCET approach. This allows us to estimate the soft-spectator contribution associated with the hard photons in a model independent way. The main unknown in our description of the TPE contribution is related with the configuration where one photon is soft. The nonperturbative dynamics in this case is described by two unknown SCET amplitudes. We use a simple model in order to estimate their contribution. The formalism is then applied to a phenomenological analysis of existing data for the reduced cross section as well as for the transverse and longitudinal polarization observables.