Measurement of Pion Spectra in the DecayK20→π++π−+π0

The pion spectra of the decay ${K_2}^0\to {\pi }^{+}+{\pi }^{-}+{\pi }^0$ are presented. Results are based on 1198 ${K_{\pi 3}}^0$ decays that were recorded with a spark chamber setup. ${K_{\pi 3}}^0$ is well described by a linear matrix element of the form $M\propto 1+{{\sigma }_0}^{\prime }\left[2T\right({\pi }^0)-T{\left({\pi }^0\right)}_{max}]\frac{m_k}{{m_{\pi }}^2}$ with ${{\sigma }_0}^{\prime }=-0.21\mathrm{}\pm 0.02$. There is no observable dependence of the matrix element on the $X$ variable, $X\propto \left[T\right({\pi }^{+})-T({\pi }^{-}\left)\right]$. Our measurement is in agreement with the $\left|\Delta I\right|=\frac{1}{2}$ rule. Various models to explain the observed variation of the density of the Dalitz plot are discussed. The value for the slope parameter is in good agreement with certain speculative predictions based on equal-time current commutators. No evidence for $\mathrm{CP}$ violation is found.