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

TL;DR

This paper solves a hyperbolic Roy-Steiner equation for low energy πN scattering, revealing a subthreshold pole in the S11 channel near 918 MeV, consistent with previous phase shift analyses.

Contribution

It introduces a hyperbolic Roy-Steiner approach with an expanded analyticity domain to analyze πN scattering and identifies a subthreshold pole in the S11 channel.

Findings

Phase shifts agree with previous studies.

Identification of a subthreshold pole at approximately 918 MeV.

Supports the validity of the hyperbolic Roy-Steiner method.

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.