The Standard Model Prediction for ε′/ε

We present a detailed analysis of ε/ε within the Standard Model, taking into account the strong enhancement through final–state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/NC expansion, through a matching procedure between the effective short–distance Lagrangian and its corresponding low–energy description in Chiral Perturbation Theory. All large logarithms are summed up, both at short and long distances. Two different numerical analyses are performed, using either the experimental or the theoretical value for ε, with compatible results. We obtain Re (ε/ε) = (1.7±0.9) ·10−3 . The error is dominated by the uncertainty in the value of the strange quark mass and the estimated corrections from unknown 1/NC–suppressed local contributions. A better estimate of the strange quark mass would reduce the uncertainty to about 30%. The Standard Model prediction agrees with the present experimental world average Re (ε/ε) = (1.93 ± 0.24) · 10−3 .