Dispersive analysis of low energy γ*N→πN process

We use a dispersion representation based on unitarity and analyticity to study the low energy $\gamma^* N\rightarrow \pi N$ process in $S_{11}$ channel. Final state interactions among $\pi system are critical this analysis. The left-hand part of partial wave amplitude is imported from $\mathcal{O}(p^2)$ chiral perturbation theory result. On right-hand part, final interaction calculated through Omn\`es formula $S$ wave. It found that good numerical fit can be achieved with only one subtraction parameter, eletroproduction experimental data multipole amplitudes $E_{0+},\ S_{0+}$ region below $\Delta(1232)$ well described when photon virtuality $Q^2 \leq 0.1 \mathrm{GeV}^2$.