Extracting $\ddot{I}{ƒ}_{\ddot{I}€N}$ from pionic atoms

Abstract

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

10 pages, 3 figures; presented at the 15th International Conference on Meson-Nucleon (MENU) Physics and the Structure of the Nucleon, Pittsburgh, and in a slightly different form at the 3rd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Kraków, both in June 2019; v2: typos corrected