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

TL;DR

This paper presents a new extraction of the $\sigma_{\pi N}$ term from pionic atom data, providing a value consistent with recent Roy-Steiner equation analyses, and clarifies its connection to the $\pi N$ scattering amplitude.

Contribution

It introduces a large-scale fit of pionic-atom data to determine $\sigma_{\pi N}$, linking experimental data with theoretical scattering amplitudes.

Findings

$\sigma_{\pi N}^{FG} = 57 \pm 7$ MeV from pionic atoms

Agreement with $\sigma_{\pi N}^{RS} = 58 \pm 5$ MeV from Roy-Steiner analysis

Validation of the connection between $\sigma_{\pi N}$ and the $\pi N$ scattering amplitude

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.