$K_L\to {\pi }^0\gamma e^{+}{e}^{-}$ and its relation to $\mathrm{CP}$ and chiral tests

The decay $K_L\to {\pi }^0\gamma e^{+}{e}^{-}$ occurs at a higher rate than the nonradiative process $K_L\to {\pi }^0{e}^{+}{e}^{-}$, and hence can be a background to $\mathrm{CP}$ violation studies using the latter reaction. It also has interest in its own right in the context of chiral perturbation theory, through its relation to the decay $K_L\to {\pi }^0\gamma \gamma$. The leading order chiral loop contribution to $K_L\to {\pi }^0\gamma e^{+}{e}^{-}$, including the ${(q}_{e^{+}}{+q}_{e^{-}}{)}^2{/m}_{\pi }^2$ dependence, is completely calculable. We present this result and also include the higher order modifications which are required in the analysis of $K_L\to {\pi }^0\gamma \gamma$.