Calculation of nonleptonic kaon decay amplitudes from K→π matrix elements in quenched domain-wall QCD

We explore the application of the domain wall fermion formalism of lattice QCD to calculate the K→ππ decay amplitudes in terms of the K+→π+ and K0→0 hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using the domain-wall fermion action for quarks and a renormalization group-improved gauge action for gluons on a 163×32×16 and 243×32×16 lattice at β=2.6 corresponding to the lattice spacing 1/a≈2 GeV. Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the ΔI=1/2 matrix elements which require subtractions with the quark loop contractions are obtained with a statistical accuracy of about 10%. We investigate the chiral properties required of the K+→π+ matrix elements. Matching the lattice matrix elements to those in the continuum at μ=1/a using the perturbative renormalization factor to one loop order, and running to the scale μ=mc=1.3 GeV with the renormalization group for Nf=3 flavors, we calculate all the matrix elements needed for the decay amplitudes. With these matrix elements, the ΔI=3/2 decay amplitude Re A2 shows a good agreement with experiment after an extrapolation to the chiral limit. The ΔI=1/2 amplitude Re A0, on the other hand, is about 50–60 % of the experimental one even after chiral extrapolation. In view of the insufficient enhancement of the ΔI=1/2 contribution, we employ the experimental values for the real parts of the decay amplitudes in our calculation of ɛ′/ɛ. The central values of our result indicate that the ΔI=3/2 contribution is larger than the ΔI=1/2 contribution so that ɛ′/ɛ is negative and has a magnitude of order 10-4. We discuss in detail possible systematic uncertainties, which seem too large for a definite conclusion on the value of ɛ′/ɛ