Precision calculation of the π−d scattering length and its impact on threshold πN scattering

We present a calculation of the π−d scattering length with an accuracy of a few percent using chiral perturbation theory. For the first time isospin-violating corrections are included consistently. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion–nucleon scattering lengths and obtain a+=(7.6±3.1)⋅10−3Mπ−1 and a−=(86.1±0.9)⋅10−3Mπ−1. Via the Goldberger–Miyazawa–Oehme sum rule, this leads to a charged-pion–nucleon coupling constant gc2/4π=13.69±0.20.