Violation of Time Reversal Invariance in the Decays $K_L\to {\pi }^{+}{\pi }^{-}\gamma$ and $K_L\to {\pi }^{+}{\pi }^{-}{\mathit{e}}^{+}{\mathit{e}}^{-}$

The origin of the large $\mathrm{CP}$-odd and $T$-odd asymmetry observed in the decay $K_L\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ is traced to the polarization properties of the photon in the decay $K_L\to {\pi }^{+}{\pi }^{-}\gamma$. The Stokes vector of the photon $\overrightarrow{S}=\left(S_1{,S}_2{,S}_3\right)$ is studied as a function of the photon energy and found to possess $\mathrm{CP}$-violating components $S_1$ and $S_2$ which are large, despite being proportional to the $\epsilon$ parameter of the $K_L$ wave function. The component $S_2$ is $T$-even and manifests itself as a circular polarization of the photon, while $S_1$ is $T$-odd and gives rise to the asymmetry observed in $K_L\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$. The latter survives in the limit in which all unitarity phases are absent, and represents a genuine example of time reversal symmetry breaking in a $\mathrm{CPT}$ invariant theory.