The derivative of the topological susceptibility at zero momentum and an   estimate of $\eta'$ mass in the chiral limit
  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. 
J. Pasupathy, J. P. Singh, R. K. Singh and A. Upadhyay