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Low-energy partial-wave $\pi N$ scattering data is reexamined with the helpof the production representation of partial-wave $S$ matrix, where branch cutsand poles are thoroughly under consideration. The left-hand cut contribution tothe phase shift is determined, with controlled systematic error estimates, byusing the results of $\mathcal{O}(p^3)$ chiral perturbative amplitudes obtainedin the extended-on-mass-shell scheme. In $S_{11}$ and $P_{11}$ channels, severediscrepancies are observed between the phase shift data and the sum of allknown contributions. Statistically satisfactory fits to the data can only beachieved by adding extra poles in the two channels. We find that a $S_{11}$resonance pole locates at $\sqrt{z_{r}}=(0.895\pm0.081)-(0.164\pm0.023)i$ GeV,on the complex $s$-plane. On the other hand, a $P_{11}$ virtual pole, as anaccompanying partner of the nucleon bound-state pole, locates at$\sqrt{z_{v}}=(0.966\pm0.018)$ GeV, slightly above the nucleon pole on the realaxis below threshold. Physical origin of the two newly established poles isexplored to the best of our knowledge. It is emphasized that the$\mathcal{O}(p^3)$ calculation greatly improves the fit quality comparing withthe previous $\mathcal{O}(p^2)$ one.

On the Existence of $N^*(890)$ Resonance in $S_{11}$ Channel of $\pi N$ Scatterings