Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
Abstract
We present a high-accuracy calculation of the pi^- deuteron scattering length using chiral perturbation theory up to order (M_pi/m_p)^(7/2). For the first time isospin-violating corrections are included consistently. The resulting value of a_{\pi^- d} has a theoretical uncertainty of a few per cent. We use it, together with data on pionic deuterium and pionic hydrogen atoms, to extract the isoscalar and isovector pion-nucleon scattering lengths from a combined analysis, and obtain a^+=(7.9 +/- 3.2) x 10^{-3} M_pi^{-1} and a^-=(86.3 +/- 1.0) x 10^{-3} M_pi^{-1}. Via the Goldberger-Miyazawa-Oehme sum rule, this leads to a charged-pion-nucleon coupling constant g_c^2/(4 pi) = 13.76 +/- 0.17.Keywords
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