Extraction of Electromagnetic Transition Form Factors for Nucleon Resonances within a Dynamical Coupled-Channels Model

TL;DR

This paper develops an analytic continuation method within a dynamical coupled-channels model to extract electromagnetic transition form factors of nucleon resonances at their pole positions, providing a more precise understanding of resonance structures.

Contribution

It introduces a novel analytic continuation technique for extracting resonance form factors in a coupled-channels framework, improving upon traditional Breit-Wigner approaches.

Findings

Successfully extracted $N^* ightarrow \gamma N$ transition form factors at resonance poles.

Developed a unified formula for effects of two $P_{11}$ poles near the $\pi\Delta$ threshold.

Demonstrated that a simple Laurent expansion-based formula closely reproduces exact model solutions.

Abstract

We explain the application of a recently developed analytic continuation method to extract the electromagnetic transition form factors for the nucleon resonances ($N^*$) within a dynamical coupled-channel model of meson-baryon reactions.Illustrative results of the obtained $N^*\rightarrow \gamma N$ transition form factors, defined at the resonance pole positions on the complex energy plane, for the well isolated $P_{33}$ and $D_{13}$, and the complicated $P_{11}$ resonances are presented. A formula has been developed to give an unified representation of the effects due to the first two $P_{11}$ poles, which are near the $\pi\Delta$ threshold, but are on different Riemann sheets. We also find that a simple formula, with its parameters determined in the Laurent expansions of $\pi N \rightarrow \pi N$ and $\gamma N \rightarrow\pi N$ amplitudes, can reproduce to a very large extent the exact solutions of the considered model at energies near the real parts of the extracted resonance positions. We indicate the differences between our results and those extracted from the approaches using the Breit-Wigner parametrization of resonant amplitudes to fit the data.