Standard-Model Prediction of ε_{K} with Manifest Quark-Mixing Unitarity

Area of Science:

• Particle Physics
• Quantum Chromodynamics
• Flavor Physics

Background:

• The parameter epsilon_K (ε_{K}) quantifies CP violation in the neutral kaon system.
• It serves as a sensitive probe for physics beyond the Standard Model.
• Previous predictions were limited by large uncertainties in the charm-quark contribution.

Purpose of the Study:

• To reduce theoretical uncertainties in the Standard Model prediction of ε_{K}.
• To investigate the impact of Cabibbo-Kobayashi-Maskawa (CKM) unitarity on the |ΔS=2| weak effective Lagrangian.
• To provide an updated, more precise Standard Model prediction for ε_{K}.

Main Methods:

• Applying the principle of Cabibbo-Kobayashi-Maskawa (CKM) unitarity.
• Analyzing the |ΔS=2| weak effective Lagrangian.
• Reducing short-distance and long-distance theoretical uncertainties, particularly those related to charm-quark contributions.

Main Results:

• CKM unitarity enforces a unique form of the |ΔS=2| weak effective Lagrangian.
• Short-distance theoretical uncertainties in the imaginary part of ε_{K} are dramatically reduced.
• Uncertainties from the charm-quark contribution are now at the percent level.
• An updated Standard Model prediction for ε_{K} is presented: 2.16(6)(8)(15)×10^{-3}.

Conclusions:

• The study provides a significantly improved Standard Model prediction for ε_{K}.
• Reduced uncertainties enhance ε_{K} as a probe for new physics.
• The findings highlight the importance of CKM unitarity in precision flavor physics.