How does the $S_{11}$ $N^{\ast }(890)$ 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 $N^{\ast }(890)$ resonance exists.

arXiv comment9pages, 7 figures

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Cited by in corpus (6)

• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• The reaction $\pi N\to \omega N$ in a dynamical coupled-channel approach
• Dispersive Analysis of Low Energy $\gamma N\to \pi N$ Process and Studies on the $N^{\ast }(890)$ Resonance
• On Lowest Lying ${\frac{1}{2}}^{-}$ Octet Baryons
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson