Nucleon spin structure,topological susceptibility and the $\eta^\prime$ 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 $\chi^\prime(0)$ 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 $\chi^\prime(0)/F^2_0 = 1$ (where $F_0$ is the $\eta^\prime$ axial vector coupling).The correction, although negative, seems too small to account for the data. I further argue that the $(\eta,\eta^\prime)\rightarrow\gamma\gamma$ and $J/\psi\rightarrow (\eta , \eta^\prime)\gamma$ decays indicate an enhancement rather than a suppression of $F_0$. A substantial gluon-like contribution in $\langle 0\vert\partial^\mu j^{(0)}_{\mu_5} \vert\gamma\gamma \rangle \vert_{q^2=0}$,which could parallel a similar one in the corresponding nucleon matrix element,is suggested.