Upper Limit on the Decay RateKL0→π+π−γ

We undertook a search for the decay mode ${K_L}^0\to {\pi }^{+}{\pi }^{-}\gamma$. The charged decay products were momentum-analyzed in a magnet and identified in a set of range-shower spark chambers. The position of the $\gamma$-ray conversion point in these chambers was compared with the position predicted on the hypothesis of ${K_L}^0\to {\pi }^{+}{\pi }^{-}\gamma$. The $K_{\pi 3}$ provided almost the sole background as well as the normalization of our rate measurement. In 962 events with good $\gamma$-ray showers we found that one event fitted the $\pi \pi \gamma$ hypothesis within our spatial resolution. However, the expected background was one event. This result corresponds to an upper limit on the decay rate $R({K_L}^0\to {\pi }^{+}{\pi }^{-}\gamma )\le 7.5\times {10}^3$ ${\sec }^{-1\mathrm{}}$ at a confidence level of 90%. The result is compared with the predictions of various theoretical models. The possible connections to other decay processes ($K^{\pm }\to {\pi }^{\pm }{\pi }^0\gamma$, ${K_L}^0\to {\pi }^0{\pi }^0\gamma$, ${K_S}^0\to {\pi }^{+}{\pi }^{-}\gamma$) and tests of $\mathrm{CP}$ in variance are discussed.