On the Existence of $N^*(890)$ Resonance in $S_{11}$ Channel of $\pi N$ Scatterings

TL;DR

This paper reexamines low-energy $cba0N$ scattering data using a detailed $S$ matrix approach, revealing a new $N^*(890)$ resonance in the $S_{11}$ channel supported by improved theoretical analysis.

Contribution

The study introduces a refined analysis method incorporating systematic error estimates and finds evidence for a new $N^*(890)$ resonance in the $S_{11}$ channel of $cba0N$ scattering.

Findings

Identification of an $N^*(890)$ resonance pole at $\,0.895-i0.164$ GeV.

Discovery of a $P_{11}$ virtual pole near the nucleon mass.

Improved fit quality with $cba0p^3$ chiral amplitudes over $cba0p^2$.

Abstract

Low-energy partial-wave $\pi N$ scattering data is reexamined with the help of the production representation of partial-wave $S$ matrix, where branch cuts and poles are thoroughly under consideration. The left-hand cut contribution to the phase shift is determined, with controlled systematic error estimates, by using the results of $\mathcal{O}(p^3)$ chiral perturbative amplitudes obtained in the extended-on-mass-shell scheme. In $S_{11}$ and $P_{11}$ channels, severe discrepancies are observed between the phase shift data and the sum of all known contributions. Statistically satisfactory fits to the data can only be achieved by adding extra poles in the two channels. We find that a $S_{11}$ resonance pole locates at $\sqrt{z_{r}}=(0.895\pm0.081)-(0.164\pm0.023)i$ GeV, on the complex $s$-plane. On the other hand, a $P_{11}$ virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at $\sqrt{z_{v}}=(0.966\pm0.018)$ GeV, slightly above the nucleon pole on the real axis below threshold. Physical origin of the two newly established poles is explored to the best of our knowledge. It is emphasized that the $\mathcal{O}(p^3)$ calculation greatly improves the fit quality comparing with the previous $\mathcal{O}(p^2)$ one.