Direct CP violation in K_L → π⁰e⁺e^- beyond leading logarithms

We analyze the direct CP violation in the rare decay K_L → π⁰e⁺e^- with QCD effects taken into account consistently in the next-to-leading order. We calculate the two-loop mixing between the four-quark ΔS = 1 operators and the operator Q_7V = (sd)_{V - A}(ee)_V in the NDR and HV renormalization schemes. Using the known two-loop anomalous dimension matrix of the four-quark operators, we find that the coefficient C_7V(μ) depends only very weakly on μ, renormalization scheme and Γ_MS. The next-to-leading QCD corrections enhance the direct CP violating contribution over its leading order estimate so that it remains dominant in spite of the recent decrease of |V_ub/V_cb | and |V_cb|. We expect typically BR(K_L → π⁰e⁺e^-)_dir ≈ 6 × 10^-12, although values as high as 10^-11 are not yet excluded.