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

We report the first lattice QCD calculation of the complex kaon decay amplitude A0 with physical kinematics, using a 323×64 lattice volume and a single lattice spacing a, with 1/a=1.3784(68)  GeV. We find Re(A0)=4.66(1.00)(1.26)×10−7  GeV and Im(A0)=−1.90(1.23)(1.08)×10−11  GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A0)=3.3201(18)×10−7  GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ′/ϵ)=1.38(5.15)(4.59)×10−4, which is 2.1σ below the experimental value 16.6(2.3)×10−4. The real part of A0 is CP conserving and serves as a test of our method while the result for Re(ϵ′/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.