An N/D study of the S ₁₁ channel ?N scattering amplitude *

Extensive dynamical $N/D$ calculations are made in the study of $S_{11}$ channel low energy $\pi$N scatterings, based on various phenomenological model inputs left cuts at tree level. The subtleties singular behavior partial wave amplitude origin complex $s$ plane carefully analysed. Furthermore, { it is found that dispersion representation for phase shift, $\delta$, has to be modified case $\pi $N scatterings. An additional contribution from integral exists, which is, however, almost exactly cancelled two virtual poles located near end points segment cut induced by $u$ nucleon exchanges.} Relying very little details inputs, subthreshold resonance $N^*(890)$ survives.