The pole structure of low energy $\pi N$ scattering amplitudes

TL;DR

This paper analyzes low-energy pion-nucleon scattering by decomposing phase shifts into pole and branch cut contributions, revealing hidden low-lying poles that explain experimental data discrepancies.

Contribution

It introduces a production representation of the S matrix and identifies previously unknown low-lying hidden poles in pion-nucleon scattering.

Findings

Known contributions do not fully explain data in certain channels

Hidden low-lying poles are identified and their positions are determined

The physics behind these hidden poles is explored

Abstract

This report presents an investigation of the pion-nucleon elastic scattering in low energy region using a production representation of the partial wave $S$ matrix. The phase shifts are separated into contributions from poles and branch cuts, where the left-hand cut term can be evaluated by tree-level covariant baryon chiral perturbation theory. A comparison between the sum of known contributions and the data in $S$- and $P$- wave channels is made. It is found that the known components in $S_{11}$ and $P_{11}$ channels are far from enough to saturate the corresponding experimental data, indicating the existence of low-lying hidden poles. The positions of those hidden poles are figured out and the physics behind them are explored.