Nucleon resonances in $\pi N$ scattering up to energies $\sqrt{s}⩽2.0$ GeV

A meson-exchange model for pion-nucleon scattering was previously constructed using a three-dimensional reduction scheme of the Bethe-Salpeter equation for a model Lagrangian involving $\pi ,\eta ,N,\Delta ,\rho$, and σ fields. We thereby extend our previous work by including the $\eta N$ channel and all the $\pi N$ resonances with masses $~2$ GeV, up to the $F$ waves. The effects of the $\pi \pi N$ channels are taken into account by introducing an effective width in the resonance propagators. The extended model gives an excellent fit to both $\pi N$ phase shifts and inelasticity parameters in all channels, except $F_{17}$, up to the $F$ waves and for energies below 2 GeV. We present a new scheme for extracting the properties of overlapping resonances. The predicted values for the resonance masses and widths as well as resonance pole positions and residues are compared with the listing of the Particle Data Group.

Figure 1

Dressed and bare $\pi NR$ vertex.

Figure 2

Resonance self-energy.

Figure 3

Real and imaginary parts of $t_{\pi N}$ in the $S$ waves as function of the total c.m. energy $W$. The solid (red) lines are the best fits of our meson-exchange model, the dashed (blue) lines correspond to the contributions of the nonresonant background ${\tilde{t}}_{\pi N}^B$ of Eq. (22). The open circles are the results of the partial wave analysis of Ref. [34].

Figure 4

Same as Fig. 3, but for $P$ waves.

Figure 5

Same as Fig. 3, but for $D$ waves.

Figure 6

Same as Fig. 3, but for $F$ waves.