Two-photon exchange corrections to elastic electron-proton scattering: Full dispersive treatment of πN states at low momentum transfers

We evaluate the pion-nucleon intermediate-state contribution to the two-photon exchange (TPE) correction in the elastic electron-nucleon scattering within a dispersive framework. We calculate the contribution from all πN partial waves using the MAID parametrization. We provide the corresponding TPE correction to the unpolarized ep scattering cross section in the region of low momentum transfer Q2≲0.064  GeV2, where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. We compare our result in the forward angular region with an alternative TPE calculation, in terms of structure functions, and find a good agreement, indicating a small contribution at low Q2 due to discontinuities beyond πN. We also compare our results with empirical fits.