Chiral Dynamics of Deeply Bound Pionic Atoms

We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear [Formula presented]-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the [Formula presented] and [Formula presented] levels in pionic [Formula presented] and [Formula presented] are well reproduced without need for a notorious “missing repulsion” in the pion-nuclear [Formula presented]-wave optical potential. The connection with the in-medium change of the pion decay constant is clarified.