Standard-Model Prediction of epsilon(K) with Manifest Quark-Mixing Unitarity

The parameter epsilon(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 epsilon(K) have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the vertical bar Delta S = 2 vertical bar 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 epsilon(K)=2.16(6)(8)(15) x 10(-3), where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.