New insights on low energy $$\pi N$$ πN scattering amplitudes

Abstract

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 $$\mathcal {O}(p^2)$$ O(p2) . It is found that in $$S_{11}$$ S11 and $$P_{11}$$ P11 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.