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

Abstract

We study the pole trajectory of the recently established subthreshold negative parity nucleon pole, namely the $N^{\ast }(920)$, 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.

arXiv comment15 pages, 6 figures; v3, changed to revtex style; v2 Discussions substantially improved, main conclusion not changed

References in corpus (22)

• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• The $\kappa$ resonance in s wave $\pi K$ scatterings
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• Left Hand Singularities, Hadron Form Factors and the Properties of the Sigma Meson
• An improved study of the kappa resonance and the non-exotic $s$ wave $\pi K$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data
• Partial waves and large $N_C$ resonance sum rules
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Nucleon resonance parameters from Roy-Steiner equations
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• $O(p^6)$ extension of the large--$N_C$ partial wave dispersion relations
• The [1,2] Padé Amplitudes for $\pi \pi$ Scatterings in Chiral Perturbation Theory
• Is the $f_0(600)$ meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond
• Determination of crossing-symmetric $\pi \pi$ scattering amplitudes and the quark mass evolution of the $\sigma$ constrained by lattice QCD
• New Insights on Low Energy $\pi N$ Scattering Amplitudes
• Scrutinizing $\pi \pi$ scattering in light of recent lattice phase shifts
• New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level
• A possible subthreshold pole in $S_{11}$ channel from $\pi N$ Roy-Steiner equation analyses
• How does the $S_{11}$ $N^{\ast }(890)$ state emerge from a naive $K$ matrix fit?
• Dispersive Analysis of Low Energy $\gamma N\to \pi N$ Process and Studies on the $N^{\ast }(890)$ Resonance
• Singularities and Accumulation of Singularities of $\pi$N Scattering amplitudes
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal $\sigma$ pole trajectory with cross-channel improvements

Cited by in corpus (1)

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