New Insights on Low Energy $\pi N$ Scattering Amplitudes

TL;DR

This paper analyzes low-energy pion-nucleon scattering phase shifts using a novel representation, revealing the need for previously undiscovered low-lying poles to explain experimental data.

Contribution

It introduces a decomposition method for phase shifts and suggests the existence of new low-lying poles in certain channels based on analysis.

Findings

Known resonances and cuts do not fully explain data in $S_{11}$ and $P_{11}$ channels

Evidence suggests existence of undiscovered low-lying poles

Other channels show no significant discrepancies

Abstract

The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.