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A production representation of partial-wave $S$ matrix is utilized toconstruct low-energy elastic pion-nucleon scattering amplitudes from cuts andpoles on complex Riemann sheets. Among them, the contribution of left-hand cutsis estimated using the $\mathcal{O}(p^3)$ results obtained in covariant baryonchiral perturbation theory within the extended-on-nass-shell scheme. By fittingto data on partial-wave phase shifts, it is indicated that the existences ofhidden poles in $S_{11}$ and $P_{11}$ channels, as conjectured in our previouspaper~\citep{Wang:2017agd}, are firmly established. Specifically, the pole massof the $S_{11}$ hidden resonance is determined to be $(895\pm81)-(164\pm23)i$MeV, whereas, the virtual pole in the $P_{11}$ channel locates at $(966\pm18)$MeV. It is found that analyses at the $\mathcal{O}(p^3)$ level improvessignificantly the fit quality, comparing with the previous $\mathcal{O}(p^2)$one. Quantitative studies with cautious physical discussions are also conductedfor the other $S$- and $P$-wave channels.

New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level