A dispersive analysis of low energy pion photo- and electroproduction

A dispersive representation based on unitarity and analyticity is used to study the low energy $\gamma N\to \pi N\text{ and }{\gamma }^{\ast }N\to \pi N$ partial wave amplitudes. Final state interactions of the $\pi N$ system are critical to this analysis. The left-hand cut contribution is estimated by invoking baryon chiral perturbation theory results, while the right-hand cut contribution responsible for final state interaction effects is taken into account via an Omn`{e}s formalism with elastic phase shifts as input. It is found that a good numerical fit can be achieved with only one subtraction parameter, and the experimental data of the multipole amplitudes $E_{0+}, S_{0+}$intheenergyregionbelowthe$\Delta (1232)$ are well described when the photon virtuality $Q^2\le 0.1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. Furthermore, we extend the partial wave amplitudes to the second Riemann sheet to extract the couplings of the subthreshold resonance $N^{\ast }(890)$. Its couplings extracted from the multipole amplitudes $E_{0+},S_{0+}$ are comparable to those of the $N^* (1535)$ resonance.