Two photon exchange amplitude with π N intermediate states: spin-1/2 and spin-3/2 channels

We calculate two-photon exchange (TPE) amplitudes for the elastic electron-proton scattering, and take into account intermediate hadronic states containing \pi N system with total angular momentum 1/2 or 3/2, which includes 8 different channels. This is the improvement of our previous calculation, where only the \pi N states with quantum numbers of \Delta(1232) resonance were included. The results show good consistency with recent experimental data. At high Q^2, newly-calculated contributions affect the correction to the measured proton form factor ratio \mu G_E/G_M. The total correction becomes somewhat smaller compared to our previous work, but is still significant and grows approximately linearly with Q^2. Comparing contributions of different channels, we found that larger contributions come from the channels with quantum numbers of lightest resonances.