The Goldberger-Miyazawa-Oehme sum rule revisited

Abstract

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.

Comments: 4 pages, 1 figure. v2: Revised the second last paragraph of 5th section and clarified the electromagnetic corrections (Tromborg vs. $\chi$PT). Also removed the KH80 slope from the fig. 1