A possible subthreshold pole in $S_{11}$ channel from $\pi N$ Roy-Steiner equation analyses

Abstract

The hyperbolic version of Roy-Steiner equation describing low energy $\pi N$ scatterings, with larger analyticity domain in the complex $s$ plane is solved. The numerical results on phase shifts of low partial waves are in agreement with that of Hoferichter et al. [Phys. Rept. 625 (2016) 1]. A subthreshold pole in $S_{11}$ channel is found located at $\sqrt{s}=(918\pm 3)-i(163\pm 9)$~MeV.

12 pages, 4 figures; Minor improvements in numerical results and discussions, conclusions unchanged, final version to appear in JHEP

References in corpus (9)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Roy-Steiner equations for pion-nucleon scattering
• Dispersive analysis of the scalar form factor of the nucleon
• An improved study of the kappa resonance and the non-exotic $s$ wave $\pi K$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data
• On Lowest Lying ${\frac{1}{2}}^{-}$ Octet Baryons

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