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Calculation of Non-Leptonic Kaon Decay Amplitudes from $K opi$ Matrix Elements in Quenched Domain-Wall QCD | | CP-PACS Collaboration: J.Noaki
; S.Aoki
; Y.Aoki
; R.Burkhalter
; S.Ejiri
; M.Fukugita
; S.Hashimoto
; N.Ishizuka
; Y.Iwasaki
; T.Izubuchi
; K.Kanaya
; T.Kaneko
; Y.Kuramashi
; V.Lesk
; K.I.Nagai
; M.Okawa
; Y.Taniguchi
; A.Ukawa
; T.Yoshie
; | | Date: |
11 Aug 2001 | | Journal: | Phys.Rev. D68 (2003) 014501 | | Subject: | hep-lat | | Abstract: | We explore application of the domain wall fermion formalism of lattice QCD to calculate the $K opipi$ decay amplitudes in terms of the $K opi$ and $K o 0$ hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using domain-wall fermion action for quarks and an RG-improved gauge action for gluons on a $16^3 imes 32 imes 16$ and $24^3 imes 32 imes 16$ lattice at $eta=2.6$ corresponding to the lattice spacing $1/aapprox 2$GeV. Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the $Delta I=1/2$ matrix elements which require subtractions with the quark loop contractions are obtained with a statistical accuracy of about 10%. We confirm the chiral properties required of the $K opi$ matrix elements. Matching the lattice matrix elements to those in the continuum at $mu=1/a$ using the perturbative renormalization factor to one loop order, and running to the scale $mu=m_c=1.3$ GeV with the renormalization group for $N_f=3$ flavors, we calculate all the matrix elements needed for the decay amplitudes. With these matrix elements, the $Delta I=3/2$ decay amplitude shows a good agreement with experiment in the chiral limit. The $Delta I=1/2$ amplitude, on the other hand, is about 50--60% of the experimental one even after chiral extrapolation. In view ofthe insufficient enhancement of the $Delta I=1/2$ contribution, we employ the experimental values for the real parts of the decay amplitudes in our calculation of $epsilon’/epsilon$. We find that the $Delta I=3/2$ contribution is larger than the $Delta I=1/2$ contribution so that $epsilon’/epsilon$ is negative and has a magnitude of order $10^{-4}$. Possible reasons for these unsatisfactory results are discussed. | | Source: | arXiv, hep-lat/0108013 | | Services: | Forum | Review | PDF | Favorites | |
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