Direct CP Violation in K_L --> \pi^0 e^+e^- Beyond Leading Logarithms

Abstract

We analyze the direct CP violation in the rare decay K_L --> Pi^0 e+e- with QCD effects taken into account consistently in the next-to-leading order. We calculate the two-loop mixing between the four-quark \Delta S=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(\mu) depends only very weakly on \mu, renormalization scheme and \Lambda_MSbar. 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 --> \pi^0 e^+ e^-)_dir ~ 6*10^(-12), although values as high as 10^(-11) are not yet excluded.