Extraction of Resonances from Meson-Nucleon Reactions

TL;DR

This paper compares traditional methods for extracting nucleon resonance parameters, identifies their limitations, and introduces an analytic continuation approach within a coupled-channel framework, demonstrating improved accuracy in realistic models.

Contribution

It develops and verifies an analytic continuation method for resonance extraction in coupled-channel reactions, addressing limitations of traditional Speed-Plot and Time-delay techniques.

Findings

SP and TD methods locate poles on different Riemann sheets.

Traditional methods often fail to accurately extract resonance parameters.

The new analytic continuation method provides more reliable resonance extraction in complex models.

Abstract

We present a pedagogical study of the commonly employed Speed-Plot (SP) and Time-delay (TD) methods for extracting the resonance parameters from the data of two particle coupled-channels reactions. Within several exactly solvable models, it is found that these two methods find poles on different Riemann sheets and are not always valid. We then develop an analytic continuation method for extracting the nucleon resonances within a dynamical coupled-channel formulation of the $\pi N$ and $\gamma N$ reactions. The main focus is on resolving the complications due to the coupling with the unstable $\pi \Delta, \rho N, \sigma N$ channels which decay into $\pi \pi N$ states. By using the results from the considered exactly solvable models, explicit numerical procedures are presented and verified. As a first application of the developed analytic continuation method, we present the nucleon resonances in the $S_{11}$ and $S_{31}$ partial waves extracted within a recently developed coupled-channels model of $\pi N$ reactions. The results from this realistic $\pi N$ model, which includes $\pi N$, $\eta N$, $\pi\Delta$, $\rho N$, and $\sigma N$ channels, also show that the simple pole parametrization of the resonant propagator using the poles extracted from SP and TD methods works poorly.