Charge-dependence of the $πNN$ coupling constant and charge-dependence of the NN interaction

Abstract

The recent determination of the charged $πNN$ coupling constant, $g_{π^\pm}$, by the Uppsala Neutron Research Group implies that there may be considerable charge-splitting of the pion coupling constant. We investigate the consequences of this for the charge-independence breaking (CIB) of the $^1S_0$ scattering length, $Δa_{CIB}$. We find that $Δa_{CIB}$ depends sensitively on the difference between $g_{π^\pm}$ and the neutral $πNN$ coupling constant, $g_{π^0}$. Moreover, if $g^2_{π^\pm}$ is only about 3% larger than $g^2_{π^0}$, then the established theoretical explanation of $Δa_{CIB}$ (in terms of pion mass splitting) is completely wiped out.