Extracting $\sigma_{\pi N}$ from pionic atoms

Abstract

We discuss a recent extraction of the $\pi N$ $\sigma$ term $\sigma_{\pi N}$ from a large-scale fit of pionic-atom strong-interaction data across the periodic table. The value thus derived, $\sigma_{\pi N}^{\rm FG}=57\pm 7$ MeV, is directly connected via the Gell-Mann--Oakes--Renner expression to the medium-renormalized $\pi N$ isovector scattering amplitude near threshold. It compares well with the value derived recently by the Bern-Bonn-J\"{u}lich group, $\sigma_{\pi N}^{\rm RS}=58\pm 5$ MeV, using the Roy-Steiner equations to control the extrapolation of the vanishingly small near threshold $\pi N$ isoscalar scattering amplitude to zero pion mass.