Precision determination of the pi-N scattering lengths and the charged pi-NN coupling constant

Abstract

We critically evaluate the isovector GMO sumrule for the charged $\pi NN$ coupling constant using recent precision data from ${\pi }^{-}$p and ${\pi }^{-}$d atoms and with careful attention to systematic errors. From the ${\pi }^{-}$d scattering length we deduce the pion-proton scattering lengths $1/2(a_{{\pi }^{-}p}+a_{{\pi }^{-}n})=(-20\pm 6$(statistic)$\pm 10$ (systematic))~$\cdot 10^{-4}{m}_{{\pi }_c}^{-1}$ and $1/2(a_{{\pi }^{-}p}-a_{{\pi }^{-}n})=(903\pm 14)\cdot 10^{-4}{m}_{{\pi }_c}^{-1}$. From this a direct evaluation gives $g_c^2(GMO)/4\pi =14.20\pm 0.07$(statistic)$\pm 0.13$(systematic) or $f_c^2/4\pi =0.0786\pm 0.0008$.

Comments: 4 pages, 1 figure, latex and postscript; invited talk at PANIC99; to appear in Nucl. Phys. A; changed notation: g^2 and f^2 replaced by conventional g^2/4\pi and f^2/4\pi