Unitarity Analyses of $\pi N$ Elastic Scattering Amplitudes

TL;DR

This paper analyzes pion-nucleon elastic scattering phase shifts using a unitarization approach, revealing significant missing contributions in certain channels likely due to shadow poles of known resonances.

Contribution

It introduces a unitarization method that separates phase shift contributions from poles and cuts, highlighting potential shadow pole effects in $ ext{S}_{11}$ and $ ext{P}_{11}$ channels.

Findings

Large positive missing contributions in $S_{11}$ and $P_{11}$ channels.

Indication of sizable effects from $N^*(1535)$ and $N^*(1440)$ shadow poles.

Results based on tree level $ ext{π}N$ amplitudes.

Abstract

The pion - nucleon scattering phase shifts in $s$ and $p$ waves are analyzed using PKU unitarization approach that can separate the phase shifts into different contributions from poles and branch cuts. It is found that in $S_{11}$ and $P_{11}$ channels, there exist large and positive missing contributions when one compares the phase shift from known resonances plus branch cuts with the experimental data, which indicates that those two channels may contain sizable effects from $N^*(1535)$ and $N^*(1440)$ shadow poles. Those results are obtained using tree level results of the $\pi N$ amplitude.