Standard-Model Prediction of ε_{K} with Manifest Quark-Mixing Unitarity.

The parameter ε_{K} 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 ε_{K} 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 ε_{K}=2.16(6)(8)(15)×10^{-3}, where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.