Extracting the sigma-term from low-energy pion-nucleon scattering

Abstract

We present an extraction of the pion-nucleon ($\pi N$) scattering lengths from low-energy $\pi N$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $\pi N$ $\sigma$-term, ${\sigma }_{\pi N}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.

17 pages, 3 figures; journal version

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• Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles
• Flavor decomposition of the pion-nucleon $\sigma$-term