On the Connection Between the Charged and Neutral Pion-Nucleon Coupling Constants in the Yukawa Model

TL;DR

This paper derives a simple relation between charged and neutral pion-nucleon coupling constants within the Yukawa model, showing the charged constant is larger and aligns well with recent experiments, and analyzes charge dependence in NN scattering.

Contribution

It introduces a new relation linking charged and neutral pion-nucleon coupling constants and predicts their relative splitting based on pion mass differences.

Findings

Charged pion-nucleon coupling constant exceeds the neutral one.

The predicted splitting matches the pion mass difference.

Charge dependence in NN scattering length is analyzed.

Abstract

In the Yukawa model for nuclear forces, a simple relation between the charged and neutral pion-nucleon coupling constants is derived. The relation implies that the charged pion-nucleon coupling 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 experimental values. The relative splitting between the charged and neutral pion-nucleon coupling 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.