Pionic hydrogen

Abstract

Strong-interaction shift ε1s and broadening Γ1s in the pionic hydrogen atom are determined from the energies and line widths of X-ray transitions to the 1s ground state. They are directly connected to the πN scattering lengths which are related to the πN coupling constant and the πN sigma term being a measure of chiral symmetry breaking. Therefore, the measurement of the pion-nucleon s-wave scattering lengths constitutes a high-precision test of the methods of chiral perturbation theory (XPT), which is the low-energy approach of QCD. Additional constraints for the πN scattering lengths are obtained from the measurement of the ground-state shift in pionic deuterium. The hadronic width is linked to s-wave pion production in nucleon-nucleon collisions. A new experiment, set up at the Paul Scherrer Institut (PSI), has finished taking data recently and will allow the determination of the scattering lengths at the few per cent level. © 2008 Springer-Verlag Berlin Heidelberg.