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.

arXiv comment4 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

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• Total cross sections
• Dispersion Relation Constrained Partial Wave Analysis of piN Elastic and piN\to\etaN Scattering Data: The Baryon Spectrum
• Ground-state energy of pionic hydrogen to one loop
• Determination of the pion-nucleon coupling constant and scattering lengths
• Complete analysis of pion-nucleon scattering in chiral perturbation theory to third order
• Phase-shift analysis of low-energy ${\pi }^{\pm }p$ elastic-scattering data
• Low-energy Pion-nucleon Scattering
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Cited by in corpus (9)

• Roy-Steiner-equation analysis of pion-nucleon scattering
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Pionic deuterium
• Tests of non-standard electroweak couplings of right-handed quarks
• Effective Field Theory calculations of $NN\to NN\pi$
• Hadronic Atoms
• Forward analysis of $\pi$N scattering with an expansion method
• Chiral corrections to the Adler-Weisberger sum rule