Strong anomaly andη→3πdecay

Abstract

The amplitude for $\eta \to 3\pi$ is calculated in terms of the amplitude for ${\eta }^{\prime }\to \eta \pi \pi$ using the strong anomaly and the partial conservation of the U(1) current. The isospin violation, an $\frac{(m_u-m_d)}{(m_u+m_d)}$ effect, is large. The ${\eta }^{\prime }$ decay constant is estimated from $\psi \to {\eta }^{\prime }\gamma$. The result for $\eta \to 3\pi$ is in good agreement with experiment.