Standard Model Prediction for Direct CP Violation in K→ππ Decay

Area of Science:

• * Theoretical Particle Physics
• * Quantum Chromodynamics (QCD)
• * Hadron Spectroscopy

Background:

• * Kaon decays are crucial for understanding CP violation in the Standard Model.
• * Lattice QCD provides a non-perturbative approach to calculating fundamental particle physics quantities.
• * Previous calculations of kaon decay amplitudes have faced limitations in precision and physical kinematics.

Purpose of the Study:

• * To perform the first lattice QCD calculation of the complex kaon decay amplitude A₀ with physical kinematics.
• * To determine the real and imaginary parts of A₀.
• * To compute the direct CP-violating ratio Re(ϵ'/ϵ) and test the Standard Model's predictions.

Main Methods:

• * Utilized lattice QCD with a 32³×64 lattice volume and a single lattice spacing (1/a=1.3784(68) GeV).
• * Employed physical kinematics for the kaon decay amplitude calculation.
• * Calculated statistical and systematic errors for the obtained amplitudes.

Main Results:

• * Obtained Re(A₀)=4.66(1.00)(1.26)×10⁻⁷ GeV and Im(A₀)=-1.90(1.23)(1.08)×10⁻¹¹ GeV.
• * The real part of A₀ is in approximate agreement with experimental values.
• * Calculated Re(ϵ'/ϵ)=1.38(5.15)(4.59)×10⁻⁴, which is 2.1σ below the experimental value.

Conclusions:

• * The real part of A₀ serves as a validation of the lattice QCD methodology.
• * The calculated Re(ϵ'/ϵ) provides a new, precise test of the Standard Model's CP violation theory.
• * Future improvements in computational power will enhance the accuracy of these predictions.