Dispersive Analysis of Low Energy $\gamma N\to\pi N$ Process and Studies on the $N^*(890)$ Resonance

TL;DR

This paper develops a dispersive approach to analyze low-energy gamma-nucleon to pion-nucleon scattering, successfully fitting experimental data and extracting properties of the N*(890) resonance, revealing its strong coupling to the pi-N system.

Contribution

It introduces a dispersive representation combining unitarity, analyticity, and chiral perturbation theory to study gamma-N to pi-N scattering and extracts the N*(890) resonance parameters.

Findings

Good fit to experimental multipole amplitude data below the Delta(1232)

Extraction of N*(890) resonance coupling and width

N*(890) strongly couples to the pi-N system

Abstract

We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effect are taken into account via an Omn\'es formalism with elastic $\pi N$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data of the multipole amplitude $E_{0}^+$ in the energy region below the $\Delta(1232)$ are well described. Furthermore, we extend the $\gamma N\rightarrow \pi N$ partial-wave amplitude to the second Riemann sheet so as to extract the couplings of the $N^\ast(890)$. The modulus of the residue of the multipole amplitude $E_{0}^+$ ($S_{11pE}$) is $2.41\rm{mfm\cdot GeV^2}$ and the partial width of $N^*(890)\to\gamma N$ at the pole is about $0.369\ {\rm MeV}$, which is almost the same as the one of $N^*(1535)$, indicating that $N^\ast(890)$ strongly couples to $\pi N$ system.