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arXiv · 1811.09748

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

Yu-Fei Wang·De-Liang Yao·Han-Qing Zheng
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Abstract

A production representation of partial-wave $S$ matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the $\mathcal{O}(p^3)$ results obtained in covariant baryon chiral perturbation theory within the extended-on-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in $S_{11}$ and $P_{11}$ channels, as conjectured in our previous paper~\citep{Wang:2017agd}, are firmly established. Specifically, the pole mass of 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 improves significantly the fit quality, comparing with the previous $\mathcal{O}(p^2)$ one. Quantitative studies with cautious physical discussions are also conducted for the other $S$- and $P$-wave channels.

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Yu-Fei Wang, De-Liang Yao, Han-Qing Zheng. 2019-05-27. New Insights on Low Energy $πN$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level. https://doi.org/10.1088/1674-1137%2F43%2F6%2F064110

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