Standard-Model Prediction of ε K with Manifest Quark-Mixing Unitarity

The parameter εK describes CP violation in the neutral kaon system and is one of the most sensitive probes of new physics. The large uncertainties related to the charm-quark contribution to εK have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the |ΔS = 2| weak effective Lagrangian in which the short-distance theory uncertainty of the imaginary part is dramatically reduced. The uncertainty related to the charm-quark contribution is now at the percent level. We present the updated standard-model prediction εK = 2.16 (6) (8) (15) × 10−3, where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.