Standard-model prediction of $\epsilon_K$ with manifest CKM unitarity

Understand

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.