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

TL;DR

The paper reviews recent nonperturbative studies of low-energy QCD in ππ and πN scattering, focusing on a negative-parity nucleon pole N*(920) below the physical nucleon mass and the pole trajectory of f0(500)/σ as the pion mass varies. The authors rely on model-independent dispersion analyses (Roy-Steiner/Steiner equations) and unitarization schemes (N/D) within the O(N) σ model to map the analytic structure of these resonances, including the existence of subthreshold poles on the second Riemann sheet. They report that N*(920) is robustly required by πN data and lattice-consistent analyses, and that the σ pole exhibits rich behavior under varying m_pi and finite temperature, including transitions to bound and virtual states and the emergence of subthreshold poles. The results shed light on how chiral symmetry breaking and its restoration may be reflected in hadron spectra, and they outline implications for lattice QCD and future experimental tests.

Abstract

We summarize recent results on studies of $ππ$ and $πN$ 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 $O(N)$ $σ$ model and $N/D$ method.

Figures (7)

• Figure 1: The different contributions to the $S_{11}$ phase shift Wang:2017agd.
• Figure 2: The pole position of $N^*(920)$ obtained by solving Roy-Steiner equation. Cao:2022zhn
• Figure 3: Nucleon Regge trajectories.
• Figure 4: $N^*(920)$ pole trajectories on the $W\equiv \sqrt s$ plane at tree level with $m_\pi$ ranging from $0.138\mathrm{GeV}$ to $0.270\mathrm{GeV}$ for two different scenarios. The solid circles and inverse triangles below the real axis represent the $N(920)$ pole trajectories that move through the $u$-cut onto the unphysical sheet defined by the logarithmic branch points of the this cut. See Ref. Li:2025fvg for details.
• Figure 5: Validity domain of extended Roy equation for $m_\pi=391$ MeV. The dashed red boundary represents the validity domain by dropping the effects of the bound state $\sigma$, and the blue boundary corresponds to the complete validity domain within uncertainty from the location of the $\sigma$. The $\sigma$ pole now becomes a bound state pole represented by a cross. Discussions on other poles can be found in Ref. Cao:2023ntr.