On the Goldberger-Miyazawa-Oehme sum rule

Abstract

We show that the Goldberg-Miyazawa-Oehme sum rule provides a relatively model-independent way of predicting a value for the pion-nucleon coupling constant, which we find to be below the canonical value of ${\mathit{f}}^2$/4π=0.079. The connections between this result, the low-energy theorem (LET) for pion photoproduction, and the pion-nucleon scattering lengths are discussed. We show that a value of ${\mathit{f}}^2$/4π near 0.073 results in consistency between the LET, the Goldberger-Miyazawa-Oehme sum rule, and a Fubini-Furlan prediction for the difference between the isospin 1/2 and 3/2 pion-nucleon scattering lengths.