How sensitive are various NN observables to changes in the $\pi NN$ coupling constant?

Abstract

The deuteron, NN analyzing powers A_y, and the singlet scattering length show great sensitivity to the $\pi NN$ coupling constant $g_\pi$. While the pp A_y data favor $g^2_\pi/4\pi\leq 13.6$, the np A_y data and the deuteron quadrupole moment imply $g^2_\pi/4\pi\geq 14.0$. The two diverging values could be reconciled by the assumption of (substantial) charge-splitting of $g_\pi$. However, the established theoretical explanation of the charge-dependence of the $^1S_0$ scattering length (based upon pion mass splitting) is very sensitive to a difference between $g_{\pi^0}$ and $g_{\pi^\pm}$ and rules out any substantial charge-splitting of $g_\pi$. Thus, there are real and large discrepancies between the values for $g_\pi$ extracted from different NN observables. Future work that could resolve the problems is suggested.