Review on recent progress in the study of the $N^*(920)$ subthreshold singularity and the $\sigma/f_0(500)$ meson

TL;DR

This paper reviews recent model-independent dispersion analyses of the $N^*(920)$ and $\sigma/f_0(500)$ meson, highlighting their pole structures, trajectories, and thermal properties in pion and nucleon scattering studies.

Contribution

It provides a comprehensive summary of recent advances in understanding the subthreshold singularity and the $\sigma/f_0(500)$ meson through dispersion analysis and thermal studies.

Findings

Identification of a negative-parity nucleon pole below the nucleon mass.

Observation of the $f_0(500)$ pole trajectory with changing pion mass.

Analysis of the thermal behavior of $f_0(500)$ using the $O(N)$ $\sigma$ model.

Abstract

We summarize recent results on studies of $\pi\pi$ and $\pi N$ scatterings. They include the finding of a negative-parity nucleon pole with a mass lower than the nucleon mass, and the pole trajectory of $f_0(500)$ as the pion mass varies. The results are obtained from model-independent dispersion analyses. We also study the thermal properties of $f_0(500)$ based on the $O(N)$ $\sigma$ model and $N/D$ method.