New Insights on Low Energy $\pi N$ Scattering Amplitudes

Abstract

The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.

slightly chnaged version, a few more figures added. Physical conclusions unchanged

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Cited by in corpus (13)

• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Nucleon resonance parameters from Roy-Steiner equations
• The reaction $\pi N\to \omega N$ in a dynamical coupled-channel approach
• New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level
• Scrutinizing $\pi \pi$ scattering in light of recent lattice phase shifts
• A possible subthreshold pole in $S_{11}$ channel from $\pi N$ Roy-Steiner equation analyses
• Dispersive Analysis of Low Energy $\gamma N\to \pi N$ Process and Studies on the $N^{\ast }(890)$ Resonance
• How does the $S_{11}$ $N^{\ast }(890)$ state emerge from a naive $K$ matrix fit?
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• On Lowest Lying ${\frac{1}{2}}^{-}$ Octet Baryons
• The pseudoscalar meson and baryon octet interaction with strangeness zero in the unitary coupled-channel approximation
• 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