A dispersive analysis of low energy pion photo- and electroproduction

TL;DR

This paper employs a dispersive approach based on unitarity and analyticity to analyze low energy pion photo- and electroproduction, successfully fitting experimental data and extracting resonance couplings, including the subthreshold $N^*(890)$.

Contribution

It introduces a dispersive analysis framework incorporating final state interactions and estimates left-hand cuts using baryon chiral perturbation theory, extending amplitudes to identify subthreshold resonances.

Findings

Good fit to experimental multipole data below the $ riangle(1232)$

Extraction of couplings for the subthreshold $N^*(890)$ resonance

Comparable couplings of $N^*(890)$ and $N^*(1535)$ resonances

Abstract

A dispersive representation based on unitarity and analyticity is used to study the low energy $\gamma N \to \pi N\ \text{and}\ \gamma^* N \to \pi N$ 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 $E_{0+}, S_{0+}$ in the energy region below the $\Delta (1232)$ are well described when the photon virtuality $Q^2 \leq 0.1 \mathrm{GeV}^2$. Furthermore, we extend the partial wave amplitudes to the second Riemann sheet to extract the couplings of the subthreshold resonance $N^*(890)$. Its couplings extracted from the multipole amplitudes $E_{0+}, S_{0+}$ are comparable to those of the $N^* (1535)$ resonance.