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We evaluate the two-photon exchange correction to the elastic electron-protonscattering cross section within a dispersive framework. Besides the elasticcontribution, we account for all $\pi N$ intermediate state contributions usingthe phenomenological MAID fit as an input. We develop a novel method for theanalytical continuation of the two-photon exchange amplitudes into theunphysical region and generalize our previous work to the momentum transferregion $ 0.064~\mathrm{GeV}^2 \lesssim Q^2 \lesssim 1~\mathrm{GeV}^2$. Wecompare our results with recent OLYMPUS, CLAS and VEPP-3 data as well as withempirical fits and estimates in the forward angular region.

Two-photon exchange contribution to elastic $e^-$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data