We critically evaluate the isovector GMO sumrule for the charged $\pi N N$ 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 $g^2_c(GMO)/4\pi =14.20\pm 0.07$(statistic)$\pm 0.13$(systematic) or $f^2_c/4\pi= 0.0786\pm 0.0008$.
Categories: hep-ph