Standard-Model Prediction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ε</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:math> with Manifest Quark-Mixing Unitarity
Joachim Brod, Martin Gorbahn, Emmanuel Stamou
Abstract
The parameter ${\ensuremath{\epsilon}}_{K}$ 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 ${\ensuremath{\epsilon}}_{K}$ have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the $|\mathrm{\ensuremath{\Delta}}S=2|$ 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 ${\ensuremath{\epsilon}}_{K}=2.16(6)(8)(15)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.