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

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 and speed-plot and regularization method. For all four-star resonances except the $S_{11}(1535)$, we find very good 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.

Figure 1

The pole positions for the $S$ waves in the complex energy plane. The (red) stars show the results found by analytic continuation; the (green) solid circles and the (blue) open circles are determined by the SP and the RM, respectively. The rectangular regions show the range of the pole positions listed by the Particle Data Group (PDG08) [13]. The sizes of the (red) stars are proportional to $\left|r_p\right|/{\Gamma }_p$ and therefore a measure for the strength of the resonance poles in the $\pi N$ channel.

Figure 2

The pole positions for the $P$ waves in the complex energy plane. The notation is the same as in Fig. 1.

Figure 3

The pole positions for the $D$ waves in the complex energy plane. The notation is the same as in Fig. 1.

Figure 4

The pole positions for the $F$ waves in the complex energy plane. The notation is the same as in Fig. 1.