Direct CP Violation in KL → π0e+e− Beyond

We analyze the direct CP violation in the rare decay KL → �0e+e− with QCD effects taken into account consistently in the next-to-leading order. We calculate the two-loop mixing between the four-quarkS = 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 coefficientC7V (µ) depends only very weakly on µ, renormalization scheme andMS. The next-to-leading QCD corrections enhance the direct CP violating contribution over its leading order estimate so that it remains domi- nant in spite of the recent decrease of |Vub/Vcb| and |Vcb|. We expect typically BR(KL → �0e+e−)dir ≈ 6 � 10−12, although values as high as 10−11 are not yet excluded.