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