The measurement of the pion–nucleon scattering lengths constitutes a high–precision test of the methods of Chiral Pertubation Theory (χPT), which is the low–energy approach of QCD. The πN s–wave scattering lengths and the pion–nucleon coupling constant are related to the strong–interaction shift ∊1s and width Γ1s of the s–states in the pionic hydrogen atom. ∊1s and Γ1s are determined from the measured energies and line widths of X–ray transitions to the 1s ground state when compared to the calculated electromagnetic values. A new experiment, set up at the Paul–Scherrer–Institut (PSI), has completed a first series of measurements.
s-wave pion nucleon scattering lengths fromπN, pionic hydrogen, and deuteron data