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