Proton spin content, axial coupling constant and QCD topological susceptibility

Abstract

The part of the proton spin $\Sigma$ carried by $u,d,s$ quarks is calculated in the framework of the QCD sum rules in the external fields. The operators up to dimension 9 are accounted. An important contribution comes from the operator of dimension 3, which in the limit of massless $u,d,s$ quarks is equal to the derivative of QCD topological susceptibility ${\chi }^{\prime }(0)$. The comparison with the experimental data on $\Sigma$ gives ${\chi }^{\prime }(0)=(2.3\pm 0.6)\times 10^{-3}Ge{V}^2$. The limits on $\Sigma$ and ${\chi }^{\prime }(0)$ are found from selfconsistency of the sum rule, $\Sigma =0.33\pm 0.20$, ${\chi }^{\prime }(0)=(2.4\pm 0.5)\cdot 10^{-3}GeV.$ The values of $g_A=1.37\pm 0.10$ and $g_A^8=0.65\pm 0.15$ are also determined.

Invited talk at the Conference Baryon 98, Bonn, Sept. 22-26, 1998, to be published in Proceedings, 5 pages, LaTeX 2e, b98proc.sty, (style is enclosed) 1 eps figures included using epsf.sty