The Goldberger-Miyazawa-Oehme sum rule revisited

Understand

The Goldberger-Miyazawa-Oehme sum rule is used to extract the pion-nucleon coupling constant from experimental $\pi$N information.

• Chiral perturbation theory is exploited in relating the pionic hydrogen s-wave level shift and width results to the appropriate scattering lengths.
• The deduced value for the coupling is $f^2 = 0.075 \pm 0.002$, where the largest source of uncertainty is the determination of the s-wave $\pi^- p$ scattering length from the atomic level shift measurement.