# Precision determination of the $\piN$ scattering lengths and the charged $\piNN$ coupling constant

Abstract : 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 $f^2_c/4\pi= 0.0786\pm 0.0008$.
Document type :
Conference papers

http://hal.in2p3.fr/in2p3-00195705
Contributor : Dominique Girod <>
Submitted on : Tuesday, December 11, 2007 - 1:22:34 PM
Last modification on : Friday, April 10, 2020 - 5:30:57 PM

### Citation

T. E. O. Ericson, B. Loiseau, A. W. Thomas. Precision determination of the $\piN$ scattering lengths and the charged $\piNN$ coupling constant. International Conference on Particles and Nuclei 15 PANIC'99, Jun 1999, Uppsala, Sweden. pp.541-544, ⟨10.1016/S0375-9474(99)00651-X⟩. ⟨in2p3-00195705⟩