  The anomaly-anomaly correlator is studied using QCD sum rules. Using the
matrix elements of anomaly between vacuum and pseudoscalars $\pi, eta$ and
$\eta'$, the derivative of correlator $chi'(0)$ is evaluated and found to be
$\approx 1.82 \times 10^{-3}$ GeV$^2$. Assuming that $\chi'(0)$ has no
significant dependence on quark masses, the mass of $\eta'$ in the chiral limit
is found to be $\approx$723 MeV. The same calculation also yields for the
singlet pseudoscalar decay constant in the chiral limit a value of $\approx
178$ MeV.
