$K_L\to {\pi }^0\gamma \gamma$ and the bound on the $\mathrm{CP}$-conserving $K_L\to {\pi }^0{e}^{+}{e}^{-}$

It has been known for many years that there is a CP-conserving component for the decay mode $K_L\to {\pi }^0{e}^{+}{e}^{-}$ and that its magnitude can be obtained from a measurement of the amplitudes in the $K_L\to {\pi }^0\gamma \gamma$ decay mode. We point out that the usual description of the latter in terms of a single parameter $a_V$ is not sufficient to extract the former in a model independent manner. We further show that there exist known physics contributions to $K_L\to {\pi }^0\gamma \gamma$ that cannot be described in terms of the single parameter $a_V.$ We conclude that a model independent analysis requires the experimental extraction of three parameters.