KL → π0γγ and the bound on the CP-conserving KL → π0e+e-

It has been known for many years that there is a CP-conserving component for the decay mode K_L → π⁰e⁺e^- and that its magnitude can be obtained from a measurement of the amplitudes in the K_L → π⁰γγ 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 → π⁰γγ 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.