Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa-model framework for NN forces, a simple relation between the charged and neutral pion–nucleon coupling constants is derived. The relation implies that the charged pion–nucleon constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion–nucleon constant shows a very good agreement with one of the recent measurements. In relative units, the splitting between the charged and neutral pion–nucleon constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.