Dispersive analysis of low energy $\gamma^* N\rightarrow\pi N$ process

TL;DR

This paper employs dispersion relations and chiral perturbation theory to analyze low-energy gamma* N to pi N processes, accurately fitting experimental data below the Delta resonance with minimal parameters.

Contribution

It introduces a dispersive approach combining unitarity, analyticity, and chiral perturbation theory to model the process with high precision at low energies.

Findings

Successful fit to experimental multipole amplitudes below Delta(1232)

Accurate description of electroproduction data for Q^2 ≤ 0.1 GeV^2

Minimal parameter model with only one subtraction parameter

Abstract

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