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 − 3 M π − 1 and a − = ( 86.1 ± 0.9 ) ⋅ 10 − 3 M π − 1 . Via the Goldberger–Miyazawa–Oehme sum rule, this leads to a charged-pion–nucleon coupling constant g c 2 / 4 π = 13.69 ± 0.20 .