Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering

TL;DR

This paper accurately calculates the pi^- deuteron scattering length using chiral perturbation theory, including isospin-violating corrections, and extracts pion-nucleon scattering lengths impacting the pion-nucleon coupling constant.

Contribution

First comprehensive calculation of pi^- d scattering length with isospin-violation effects included using chiral perturbation theory.

Findings

Determined isoscalar and isovector pion-nucleon scattering lengths.

Extracted the charged-pion-nucleon coupling constant g_c^2/4 pi.

Achieved a few percent accuracy in the scattering length calculation.

Abstract

We present a calculation of the pi^- 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) x 10^{-3} mpi^{-1} and a^-=(86.1 +/- 0.9) x 10^{-3} mpi^{-1}. Via the Goldberger-Miyazawa-Oehme sum rule, this leads to a charged-pion-nucleon coupling constant g_c^2/4 pi = 13.69 +/- 0.20.