Constraints on the $πNN$ Coupling Constant from the $NN$ System

Abstract

The sensitivity of the deuteron and of $pp$ scattering to the $πNN$ and $ρNN$ coupling constants is investigated systematically. We find that the deuteron can be described about equally well with either {\it large $π$ and $ρ$} or {\it small $π$ and $ρ$} coupling constants. However, $pp$ scattering clearly {\it requires} the strong $ρ$, but favors the weak $π$ (particularly, in $^3P_0$ at low energies). This apparent contradiction between bound-state and scattering can be resolved by either assuming charge-dependent $πNN$ coupling constants or by adding a heavy pion to the NN model. In both cases, the neutral-pion coupling constant is small ($g^2_{π^0}/4π= 13.5$).