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

TL;DR

This paper improves the standard-model prediction of the CP violation parameter $_K$ in the neutral kaon system by reducing uncertainties, especially from charm-quark contributions, using CKM unitarity constraints.

Contribution

It introduces a unique form of the $| S=2|$ weak effective Lagrangian that significantly reduces charm-related uncertainties in $_K$ prediction.

Findings

Charm-quark contribution uncertainty reduced to percent level.

Updated $_K$ prediction: 2.16(6)(8)(15) x 10^{-3}.

CKM unitarity enforces a specific effective Lagrangian form.

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.