CPInvariance and the Radiative Decay of the Long-Lived NeutralKMeson into Two Pions

As a possible test to observe the effects of $\mathrm{CP}$ nonconservation, the radiative decay process ${K_L}^0\to {\pi }^{+}+{\pi }^{+}+\gamma$ is discussed in detail. A method to find the effects is given by observing the dependences of the transition rate on the energy difference of the two pions and on the polarization of the $\gamma$ ray. If $\mathrm{CP}$ non-conservation in the decay ${K_L}^0\to 2\pi$ is due to the electromagnetic interaction of hadrons, the effects of the $\mathrm{CP}$ nonconservation on the rediative decay will be expected to be quite large. A rough estimate of the magnitude of the branching ratio of this process is also made. The arguments given here are easily adapted to the decays $K_L\to 2{\pi }^0+\gamma$, ${K_S}^0\to 2{\pi }^0+\gamma$, and ${K_S}^0\to {\pi }^{+}+{\pi }^{-}+\gamma$.