Pseudoscalar decay constants andη→3πin chiral and1Nperturbation theory

The normal and anomalous chiral Ward identities are reexamined from the point of view of chiral and $\frac{1}{N}$ perturbation theory. Constraints of $\psi \to \eta \gamma$ and $\psi \to {\eta }^{\prime }\gamma$ and pseudoscalar two-photon decays are imposed, yielding a system of six simultaneous equations. A solution for the pseudoscalar decay constants is found which is relatively insensitive to the quantum-chromodynamic surface term. The decay $\eta \to 3\pi$ is then calculated using these results, with good agreement with recent measurements.