Standard-model prediction of ${\epsilon }_K$ with manifest CKM unitarity

Abstract

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 CKM unitarity enforces a unique form of the $|\Delta S=2|$ 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 ${\epsilon }_K=2.16(6)(8)(15)\times 10^{-3}$, where the errors in brackets correspond to QCD short-distance and long-distance, and parametric uncertainties, respectively.

5 pages, 1 figure