Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV

TL;DR

This paper investigates the singularity structure of pi N scattering amplitudes within a meson-exchange model up to 2 GeV, identifying resonance poles using multiple techniques and comparing their effectiveness.

Contribution

It provides a detailed analysis of the resonance pole structure in pi N scattering amplitudes using three different methods within a meson-exchange framework, highlighting their agreements and discrepancies.

Findings

Perfect agreement between analytic continuation and regularization for well-established resonances.

Identification of resonance poles for less well-known resonances.

Differences in pole positions and residues among methods for certain resonances.

Abstract

Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.