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.Comment: 9 pages, 3 figures. Updated to match published versio