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

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.