Proton spin content 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, $Σ\ga 0.05,~~ χ^{\prime} (0) \ga 1.6 \times 10^{-3} ~ GeV^2$. The values of $g_A=1.37\pm 0.10$ and $g_A^8=0.65\pm 0.15$ are also determined.

8 pages, 2 figures (eps), RevTex