Sidewise Dispersion Relations and the Axial-Vector Coupling Constant

Abstract

The axial-vector renormalization constant is related to low-energy pion-nucleon scattering amplitude by dispersing the axial-vector vertex in the nucleon mass and using the idea of threshold dominance. The low-energy pion-nucleon amplitude, in turn, can be related to the axial-vector renormalization, giving rise to a consistency condition involving $\frac{g_A}{g_V}$ and the pion-nucleon coupling constant. The solution to this consistency condition is in rough agreement with the observed value.