Final-State Interaction Effects in the Algebra-of-Currents Approach to the Three-Pion Decay Modes ofηandKMesons

The current-algebra approach to $K\to 3\pi$ and $\eta \to 3\pi$ decays is simply modified to take account of final-state $\pi -\pi$ interactions. Expressions are obtained for the relevant branching ratios in terms of certain assumed analytic forms for the $I=0\mathrm{}$ $S$-wave $\pi \pi$ scattering phase shift. It is shown how this mechanism may help to explain the anomalously low $\frac{(\eta \to 3{\pi }_0)}{(\eta \to {\pi }_{+}{\pi }_{-}{\pi }_0)}$ branching ratio without disturbing the "good" current-algebra results.