How does the $S_{11}$ $N^*(890)$ state emerge from a naive $K$ matrix fit?

Abstract

We give a pedagogical analysis on $K$ matrix models describing the $\pi N$ scattering amplitude, in $S_{11}$ channel at low energies. We show how the correct use of analyticity in the $s$ channel and crossing symmetry in $t$ and $u$ channels leads to a much improved analytic behavior in the negative $s$ region, in agreement with the prediction from chiral perturbation amplitudes in its validity region. The analysis leads again to the conclusion that a genuine $N^*(890)$ resonance exists.