Decayη→2π+2γand Current Algebra

The decay $\eta \to 2\pi +2\mathrm{}\gamma$ is studied with the use of current-algebra techniques. The possibility that this mode simulates the $3\pi$-decay mode of the $\eta$ meson and thereby resolves the discrepancy between the experimental and theoretical values of the branching ratio $\frac{\Gamma (\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)}{\Gamma (\eta \to 3{\pi }^0)}$ is considered. Although the digamma spectrum in the decay $\eta \to 2\pi +2\mathrm{}\gamma$ simulates the digamma spectrum in the decay of ${\pi }^0$ (involved in the final state of the decay $\eta \to 3\pi$) very well, the predicted rate for $\eta \to 2\pi +2\mathrm{}\gamma$ is too small to resolve the discrepancy. The definite prediction for the decay rate for $\eta \to 2\pi +2\mathrm{}\gamma$ is offered as a test of current algebra, as this mode does not involve some of the ambiguities contained in other applications.