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Register a new userCalculation of $Ktopipi$ decay amplitudes from $Ktopi$ matrix elements in quenched domain-wall QCD
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We present a calculation of the $Ktopipi$ decay amplitudes from the $Ktopi$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $Delta I=1/2$ enhancement is only half of the experimental value, and $epsilon/epsilon$ is negative.
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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.
We report on the nucleon decay matrix elements with domain-wall fermions in quenched approximation. Results from direct and indirect method are compared with a focus on the process of a proton decaying to a pion and a lepton. We discuss the renormalization necessary for the matching to the continuum theory. Preliminary results for the renormalized chiral lagrangian parameters are presented.
Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with non-perturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements, as well as the indirect estimate of them from the nucleon to vacuum matrix elements, are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative value for the low energy constants from the nucleon to vacuum matrix elements are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable estimate of the physical low energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give smaller value of the form factors, compared to the indirect one, thus enhancing the proton life-time; indeed for the pi^0 final state the difference between the two methods is quite appreciable.
We present a lattice QCD calculation of the parameters alpha and beta which are necessary in the theoretical estimation of the proton lifetime in grand unified theories (GUTs) using chiral lagrangian approach. The simulation is carried out using the Wilson quark action at three gauge coupling constants in the quenched approximation. We obtain |alpha(2GeV)|=0.0091(08)(^{+10}_{-19})GeV^3 and |beta(2GeV)|=0.0098(08)(^{+10}_{-20})GeV^3 in the continuum limit where the first error is statistical and the second one is due to scale setting.
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.
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