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

Abstract

The recent determination of the charged $\pi NN$ coupling constant, $g_{{\pi }^{\pm }}$, 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 ${}^1{S}_0$ scattering length, $\Delta a_{CIB}$. We find that $\Delta a_{CIB}$ depends sensitively on the difference between $g_{{\pi }^{\pm }}$ and the neutral $\pi NN$ coupling constant, $g_{{\pi }^0}$. Moreover, if $g_{{\pi }^{\pm }}^2$ is only about 3% larger than $g_{{\pi }^0}^2$, then the established theoretical explanation of $\Delta a_{CIB}$ (in terms of pion mass splitting) is completely wiped out.

Comments: 9 pages, fbs styles, 1 figure; dedicated to Walter Glöckle on the occasion of his 60th birthday