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 ${\chi }^{\prime }(0)/F_0^2=1$ (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 $(\eta ,{\eta }^{\prime })\to \gamma \gamma$ and $J/\psi \to (\eta ,{\eta }^{\prime })\gamma$ decays indicate an enhancement rather than a suppression of $F_0$. A substantial gluon-like contribution in $⟨0|{\partial }^{\mu }{j}_{{\mu }_5}^{(0)}|\gamma \gamma ⟩{|}_{q^2=0}$,which could parallel a similar one in the corresponding nucleon matrix element,is suggested.

Comments: Latex 209,10 pages,no figures