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

TL;DR

This paper precisely evaluates the pion-nucleon scattering lengths and the charged pion-nucleon-nucleon coupling constant using recent experimental data and systematic error analysis, providing updated fundamental constants in hadronic physics.

Contribution

It offers a new, precise determination of the pion-nucleon scattering lengths and the charged pion-nucleon-nucleon coupling constant based on recent atomic data and careful error analysis.

Findings

Determined the pion-proton scattering lengths with high precision.

Calculated the charged pion-nucleon-nucleon coupling constant from sumrule analysis.

Provided updated values for fundamental hadronic interaction constants.

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 $f^2_c/4\pi= 0.0786\pm 0.0008$.