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

Noaki J.

Aoki S.

Aoki Y.

Burkhalter R.

Ejiri S.

Fukugita M.

Hashimoto S.

Ishizuka N.

Iwasaki Y.

Izubuchi T.

Kanaya K.

Kaneko T.

Kuramashi Y.

Lesk V.

Nagai K.I.

Okawa Masanori

Taniguchi Y.

Ukawa A.

Yoshie T.

CP-PACS Collaboration

Physical Review D

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%.0 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=m c=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 ReA2 shows a good agreement with experiment after an extrapolation to the chiral limit. The ΔI =1/2 amplitude ReA0, on the other hand, is about 50-600f 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 ε′/ε. The central values of our result indicate that the ΔI=3/2 contribution is larger than the ΔI=1/2 contribution so that ε′/ε 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 ε′/ε.

lattice QCD

domain-wall fermion action

Physics [ 420 ]

eng

American Physical Soceity

Copyright (c) 2003 American Physical Soceity

[ISSN] 1550-7998

[DOI] 10.1103/PhysRevD.68.014501

[DOI] http://dx.doi.org/10.1103/PhysRevD.68.014501