Two-photon-exchange amplitude with $\pi$N intermediate states: P$_{33}$ channel
We consider two-photon exchange (TPE) in the elastic electron-proton scattering and evaluate the effect of \pi N (pion + nucleon) intermediate hadronic states. Among different \pi N states, we concentrate on the P33 channel; thus we effectively include Delta(1232) resonance with realistic width and shape and corresponding background as well. In agreement with the previous result, obtained for the zero-width resonance, we observe that the TPE correction to the electric form factor is the largest one; it grows with Q^2 and at Q^2 > 2.5 GeV^2 exceeds the corresponding elastic contribution.