Nucleon spin structure,topological susceptibility and the $η^\prime$ singlet axial vector coupling

Abstract

The observed small value of the first moment of the polarized nucleon spin structure function $g_1$ may be interpreted, in the Veneziano--Shore approach, as a suppression of the first moment $χ^\prime(0)$ of the QCD topological susceptibility. I give an extension of the Witten--Veneziano argument for the $U(1)$ problem, which yields the $O(1/N)$ correction to the $N = \infty$ relation $χ^\prime(0)/F^2_0 = 1$ (where $F_0$ is the $η^\prime$ axial vector coupling).The correction, although negative, seems too small to account for the data. I further argue that the $(η,η^\prime)\rightarrowγγ$ and $J/ψ\rightarrow (η, η^\prime)γ$ decays indicate an enhancement rather than a suppression of $F_0$. A substantial gluon-like contribution in $\langle 0\vert\partial^μj^{(0)}_{μ_5} \vertγγ\rangle \vert_{q^2=0}$,which could parallel a similar one in the corresponding nucleon matrix element,is suggested.