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arXiv · 2102.00977

An $N/D$ study of the $S_{11}$ channel $\pi N$ scattering amplitude

Qu-Zhi Li·Yao Ma·Wen-Qi Niu·Yu-Fei Wang·Han-Qing Zheng
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Abstract

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

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Qu-Zhi Li, Yao Ma, Wen-Qi Niu, Yu-Fei Wang, Han-Qing Zheng. 2021-02-01. An $N/D$ study of the $S_{11}$ channel $\pi N$ scattering amplitude. https://doi.org/10.1088/1674-1137/ac31a4

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