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Register a new userKaon $B$-parameters for Generic $Delta S=2$ Four-Quark Operators in Quenched Domain Wall QCD
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We present a study of $B$-parameters for generic $Delta S=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3times 32times 16$ and $24^3times 32times 16$ at the lattice spacing $1/aapprox 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, which are compared with the previous results obtained with the overlap and the clover quark actions.
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We calculate one-loop renormalization factors of generic DeltaS=2 four-quark operators for domain-wall QCD with the plaquette gauge action and the Iwasaki gauge action. The renormalization factors are presented in the modified minimal subtraction (MS-bar) scheme with the naive dimensional regularization. As an important application we show how to construct the renormalization factors for the operators contributing to K^0-K^0bar mixing in the supersymmetric models with the use of our results.
We report on a calculation of $B_K$ with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at $beta=2.6$ and 2.9 corresponding to $a^{-1}approx 2$GeV and 3GeV. Effects due to finite fifth dimensional size $N_5$ and finite spatial size $N_sigma$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain $B_K(mu = 2 GeV)= 0.5746(61)(191)$, where the first error is statistical and the second error represents an estimate of scaling violation and ${cal O}(alpha^2)$ errors in the renormalization factor added in quadrature, as an estimate of the continuum value in the $msbar$ scheme with naive dimensional regularization. This value is consistent, albeit somewhat small, with $B_K(mu = 2 {GeV})= 0.628(42)$ obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for light quark masses are also reported.
We present non-perturbative renormalization factors for $Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
We calculate non-perturbative renormalization factors at hadronic scale for $Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schr{o}dinger functional method. Combining them with the non-perturbative renormalization group running by the Alpha collaboration, our result yields the fully non-perturbative renormalization factor, which converts the lattice bare $B_K$ to the renormalization group invariant (RGI) $hat{B}_K$. Applying this to the bare $B_K$ previously obtained by the CP-PACS collaboration at $a^{-1}simeq 2, 3, 4$ GeV, we obtain $hat{B}_K=0.782(5)(7)$ (equivalent to $B_K^{bar{rm MS}}({rm NDR}, 2 {rm GeV}) = 0.565(4)(5)$ by 2-loop running) in the continuum limit, where the first error is statistical and the second is systematic due to the continuum extrapolation. Except the quenching error, the total error we have achieved is less than 2%, which is much smaller than the previous ones. Taking the same procedure, we obtain $m_{u,d}^{rm RGI}=5.613(66)$ MeV and $m_s^{rm RGI}=147.1(17)$ MeV (equivalent to $m_{u,d}^{bar{rm MS}}(2 {rm GeV})=4.026(48)$ MeV and $m_{s}^{bar{rm MS}}(2 {rm GeV})=105.6(12)$ MeV by 4-loop running) in the continuum limit.
We explore application of the domain wall fermion formalism of lattice QCD to calculate the $Ktopipi$ decay amplitudes in terms of the $Ktopi$ and $Kto 0$ 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 $16^3times 32times 16$ and $24^3times 32times 16$ lattice at $beta=2.6$ 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 $Ktopi$ 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.
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