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

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^2/4πand f^2/4π