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Register a new userLattice QCD Calculation of the Kaon B-parameter with the Wilson Quark Action
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The kaon B parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the Delta s=2 four-quark operators is solved non-perturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find B_K(NDR, 2GeV)=0.562(64) in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.
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A lattice QCD calculation of the kaon $B$ parameter $B_K$ is carried out with the Wilson quark action in the quenched approximation at $beta=6/g^2=5.9-6.5$. The mixing problem of the $Delta s=2$ four-quark operators is solved non-perturbatively with full use of chiral Ward identities employing four external quarks with an equal off-shell momentum in the Landau gauge. This method, without invoking any effective theory, enables us to construct the weak four-quark operators exhibiting good chiral behavior. Our results for $B_K$ with the non-perturbative mixing coefficients show small scaling violation beyond the lattice cut-off $a^{-1}sim 2.5 $GeV. Our estimate concludes $B_K(NDR, 2 GeV)=0.69(7)$ at $a^{-1}=2.7-4.3$GeV, which agrees with the value obtained with the Kogut-Susskind quark action. For comparison we also calculate $B_K$ with one-loop perturbative mixing coefficients. While this yields incorrect values at finite lattice spacing, a linear extrapolation to the continuum limit as a function of $a$ leads to a result consistent with those obtained with the Ward identity method.
We present a detailed description of the method and results of our calculation of the kaon B parameter using the Wilson quark action in quenched QCD at $beta=5.9-6.5$. The mixing problem of the $Delta s=2$ four-quark operators is solved non-perturbatively with full use of chiral Ward identities. We find $B_K(NDR, 2 GeV)=0.562(64)$ in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.
We present our result for the $Ktopipi$ decay amplitudes for both the $Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. Expanding on the earlier works by Bernard {it et al.} and by Donini {it et al.}, we show that mixings with four-fermion operators with wrong chirality are absent even for the Wilson fermion action for the parity odd process in both channels due to CPS symmetry. Therefore, after subtraction of an effect from the lower dimensional operator, a calculation of the decay amplitudes is possible without complications from operators with wrong chirality, as for the case with chirally symmetric lattice actions. As a first step to verify the possibility of calculations with the Wilson fermion action, we consider the decay amplitudes at an unphysical quark mass $m_K sim 2 m_pi$. Our calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091,{rm fm}$, $m_pi=280,{rm MeV}$, and $m_K=580,{rm MeV}$ on a $32^3times 64$ ($La=2.9,{rm fm}$) lattice. For the quark loops in the penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver method work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that ${rm Re}A_0 = 60(36) times10^{ -8},{rm GeV}$ and ${rm Im}A_0 =-67(56) times10^{-12},{rm GeV}$ for a matching scale $q^* =1/a$. The dependence on the matching scale $q^*$ for these values is weak.
The free energy between a static quark and an antiquark is studied by using the color-singlet Polyakov-line correlation at finite temperature in lattice QCD with 2+1 flavors of improved Wilson quarks. From the simulations on $32^3 times 12$, 10, 8, 6, 4 lattices in the high temperature phase, based on the fixed scale approach, we find that, the heavy-quark free energies at short distance converge to the heavy-quark potential evaluated from the Wilson loop at zero temperature, in accordance with the expected insensitivity of short distance physics to the temperature. At long distance, the heavy-quark free energies approach to twice the single-quark free energies, implying that the interaction between heavy quarks is screened. The Debye screening mass obtained from the long range behavior of the free energy is compared with the results of thermal perturbation theory.
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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