Calculation of nonleptonic kaon decay amplitudes from [Formula Presented] matrix elements in quenched domain-wall QCD

Abstract

We explore the application of the domain wall fermion formalism of lattice QCD to calculate the [Formula Presented] decay amplitudes in terms of the [Formula Presented] and [Formula Presented] 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 [Formula Presented] and [Formula Presented] lattice at [Formula Presented] corresponding to the lattice spacing [Formula Presented] Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the [Formula Presented] 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 [Formula Presented] matrix elements. Matching the lattice matrix elements to those in the continuum at [Formula Presented] using the perturbative renormalization factor to one loop order, and running to the scale [Formula Presented] with the renormalization group for [Formula Presented] flavors, we calculate all the matrix elements needed for the decay amplitudes. With these matrix elements, the [Formula Presented] decay amplitude [Formula Presented] shows a good agreement with experiment after an extrapolation to the chiral limit. The [Formula Presented] amplitude [Formula Presented] on the other hand, is about 50–60 % of the experimental one even after chiral extrapolation. In view of the insufficient enhancement of the [Formula Presented] contribution, we employ the experimental values for the real parts of the decay amplitudes in our calculation of [Formula Presented] The central values of our result indicate that the [Formula Presented] contribution is larger than the [Formula Presented] contribution so that [Formula Presented] is negative and has a magnitude of order [Formula Presented] We discuss in detail possible systematic uncertainties, which seem too large for a definite conclusion on the value of [Formula Presented] © 2003 The American Physical Society.