Direct CP violation in KL → π0e+e− beyond leading logarithms

We analyze the direct CP violation in the rare decay KL → 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 Q7V = (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 C7V(μ) depends only very weakly on μ, renormalization scheme and ΓMS. 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 |Vub/Vcb | and |Vcb|. We expect typically BR(KL → π0e+e−)dir ≈ 6 × 10−12, although values as high as 10−11 are not yet excluded.