Two-photon exchange amplitude with $\pi N$ intermediate states: Spin-1/2 and spin-3/2 channels

We calculate two-photon exchange amplitudes for the elastic electron-proton scattering, and take into account intermediate hadronic states containing a $\pi N$ system with total angular momentum 1/2 or 3/2, which includes eight different channels. This is the improvement of our previous calculation, where only the $\pi N$ states with quantum numbers of $\mathrm{\Delta }$ 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.

Figure 1

Comparison of VEPP-3 results [5] and our calculations. $E=1.0\mathrm{GeV}$ (a), $E=1.6\mathrm{GeV}$ (b).

Figure 2

Comparison of CLAS results [6] and our calculations. $Q^2=1.45{\mathrm{GeV}}^2$ (a), $\epsilon =0.88$ (b).

Figure 3

Comparison with $\mathrm{GEp}2\gamma$ experiment [11]. Thin lines: ${R|}_{\epsilon =1}$ fixed, thick lines: ${R|}_{\epsilon =1}$ fitted.

Figure 4

Full TPE correction to measured proton form factor ratio at high $Q^2$, fixed $\epsilon =0.5$.

Figure 5

TPE contributions of different channels compared, fixed $Q^2$ as indicated on the plots.

Figure 6

TPE contributions of different channels compared, fixed $\epsilon =0.5$.