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The derivative of the topological susceptibility at zero momentum and an estimate of $η'$ 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 $π, eta$ and $η'$, the derivative of correlator $chi'(0)$ is evaluated and found to be $\approx 1.82 \times 10^{-3}$ GeV$^2$. Assuming that $χ'(0)$ has no significant dependence on quark masses, the mass of $η'$ 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.