Precision calculation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>d</mml:mi></mml:math> scattering length and its impact on threshold πN scattering

Abstract

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.