On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses

TL;DR

This study investigates how the pole position of the subthreshold negative parity nucleon varies with pion mass using a linear sigma model and unitarization, revealing pole movement towards the real axis and consistency with Roy equation analysis.

Contribution

It provides a detailed analysis of the pole trajectory of the $N^*(920)$ nucleon state with changing pion masses within a linear sigma model framework, including loop effects.

Findings

Pole moves toward the real axis as pion mass increases.

At larger pion masses, the pole crosses to an adjacent Riemann sheet.

Re-examined $\sigma$ pole trajectory aligns with Roy equation results.

Abstract

We study the pole trajectory of the recently established subthreshold negative parity nucleon pole, namely the $N^*(920)$, with varying pion masses, in the scheme of linear $\sigma$ model with nucleons using the $N/D$ unitarization method. We find that as the pion mass increases, the pole moves toward the real axis. For larger pion masses, at tree level, the pole falls to a specific point on $u$-channel cut and crosses to the adjacent Riemann sheet defined by the logarithmic $u$ channel cut. At one-loop level, the pole does not meet the $u$-cut up to $m_\pi=0.36$GeV. We also re-examined the $\sigma$ pole trajectory and find it in good agreement with Roy equation analysis result.