The derivative of the topological susceptibility at zero momentum and an estimate of ${\eta }^{\prime }$ mass in the chiral limit

Abstract

The anomaly-anomaly correlator is studied using QCD sum rules. Using the matrix elements of anomaly between vacuum and pseudoscalars $\pi ,eta$ and ${\eta }^{\prime }$, the derivative of correlator $ch{i}^{\prime }(0)$ is evaluated and found to be $\approx 1.82\times 10^{-3}$ GeV${}^2$. Assuming that ${\chi }^{\prime }(0)$ has no significant dependence on quark masses, the mass of ${\eta }^{\prime }$ 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.

Comments: LaTeX, 7 pages, 2 figures, uses cernrep.cls (included)