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 $\chi^{\prime}(0)= (2.3 \pm 0.6) \times 10^{-3} ~ GeV^2$. 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 $g^8_A = 0.65 \pm 0.15$ are also determined.