Proposal for Determining the Pion-Nucleon Coupling Constant from the Angular Distribution for Nucleon-Nucleon Scattering

Abstract

A plausibility argument is made that the real and imaginary parts of the nucleon-nucleon scattering amplitude as a function of the cosine of the barycentric system scattering angle, for fixed energy, are analytic in the complex plane, with singularities confined to the real axis. It is conjectured that in the real part there are poles at $cos\ensuremath{\theta}=\ifmmode\pm\else\textpm\fi{}(1+\frac{{\ensuremath{\mu}}^{2}}{2{k}^{2}})$, where $\ensuremath{\mu}$ is the pion rest mass and $k$ the barycentric momentum, branch points at $cos\ensuremath{\theta}=\ifmmode\pm\else\textpm\fi{}(1+\frac{2{\ensuremath{\mu}}^{2}}{{k}^{2}}), \ifmmode\pm\else\textpm\fi{}(1+\frac{9{\ensuremath{\mu}}^{2}}{2{k}^{2}})$, etc. The residues of the poles are related directly to ${g}^{2}$, the pion nucleon coupling constant, and a procedure is outlined for determining ${g}^{2}$ by an extrapolation of experimental data on either backward or forward nucleon-nucleon scattering.