Singularities and Accumulation of Singularities of $\pi$N Scattering amplitudes

Abstract

It is demonstrated that for the isospin $I=1/2$ $\pi$N scattering amplitude, $T^{I=1/2}(s,t)$, $s=(m_N^2-m_{\pi }^2{)}^2/m_N^2$ and $s=m_N^2+2m_{\pi }^2$ are two accumulation points of poles on the second sheet of complex $s$ plane, and are hence accumulation of singularities of $T^{I=1/2}(s,t)$. For $T^{I=3/2}(s,t)$, $s=(m_N^2-m_{\pi }^2{)}^2/m_N^2$ is the accumulation point of poles on the second sheet of complex $s$ plane. The proof is valid up to all orders of chiral expansions.

arXiv comment6 pages, one reference added, a bug removed, major conclusions remain unchanged

References in corpus (5)

• The $\kappa$ resonance in s wave $\pi K$ scatterings
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• 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
• New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level

Cited by in corpus (3)

• A possible subthreshold pole in $S_{11}$ channel from $\pi N$ Roy-Steiner equation analyses
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson