Abstract
The two-photon-exchange (TPE) effect plays a key role in extracting the form factors (FFs) of the proton. In this work, we discuss several exact properties of the TPE effect in the elastic scattering. By taking four low energy interactions as examples, we analyze kinematical singularities, asymptotic behaviors, and branch cuts of TPE amplitudes. The analytical expressions clearly indicate several exact relations between the dispersion relation (DR) and hadronic model (HM) methods. This suggests that the two methods must be modified to general forms, while novel forms yield the same results. After the modification, new DRs include a non-trivial term with two singularities. Furthermore, new DRs automatically include contributions due to the seagull interaction, meson-exchange effect, contact interactions, and off-shell effect. To analyze the elastic scattering data sets, the new forms must be used.
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