Reanalysis of the decay Kₗ -> pi0 e+ e-

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The decay Kₗ -> pi0 e+ e- is being searched for as a signal of direct Delta S = 1 CP violation. We provide a thorough updating of the analysis of the three components of the decay: 1) Direct CP violation, 2) CP violation through the mass matrix and 3) CP-conserving (two-photon) contributions. First the chiral calculation of the Kₛ -> pi0 e+ e- rate, due to Ecker, Pich and de Rafael (EPR), is updated to include recent results on the nonleptonic amplitude. Then we systematically explore the uncertainties in this method. These appear to be so large that they will obscure the direct CP violation unless it is possible to measure the Kₛ -> pi0 e+ e- rate. The CP-conserving amplitude remains somewhat uncertain, but present indications are such that there may be a sizable CP-violating asymmetry in the e+, e- energies from the interference of the CP-conserving and CP-violating amplitudes and this may potentially be useful in determining whether direct CP violation is present.