arXiv subjects
Publications and source records attributed to Weonjong Lee.
We review recent progress in calculating kaon spectrum, pseudoscalar meson decay constants, $B_K$, $ε'/ε$, $K\to ππ$ matrix elements, kaon semileptonic form factors, and moments of kaon distribution amplitudes on the lattice. We also address the issue of how best to improve the staggered fermion formulation for the action and operators.
Non-perturbative results for improvement and renormalization constants needed for on-shell and off-shell O(a) improvement of bilinear operators composed of Wilson fermions are presented. The calculations have been done in the quenched approximation at beta=6.0, 6.2 and 6.4. To quantify residual discretization errors we compare our data with results from other non-perturbative calculations and with one-loop perturbation theory.
We describe the extension of the improvement program for bilinear operators composed of Wilson fermions to non-degenerate dynamical quarks. We consider two, three and four flavors, and both flavor non-singlet and singlet operators. We find that there are many more improvement coefficients than with degenerate quarks, but that, for three or four flavors, nearly all can be determined by enforcing vector and axial Ward identities. The situation is worse for two flavors, where many more coefficients remain undetermined.
We present preliminary results of $B_K$ calculated using improved staggered fermions with the mixed action (valence quarks = HYP staggered fermions and sea quarks = AsqTad staggered fermions). We analyze the data based upon the prediction by Van de Water and Sharpe. A hint of consistency with the prediction is observed. We also present preliminary results of $B_8^{(3/2)}$ and $B_7^{(3/2)}$.
We investigate the effect of non-degenerate quarks on $B_K$. This effect is noticeably large for $B_K$ (significantly larger than statistical uncertainty). Hence, it is important to include this effect in order to determine $B_K$ with higher precision. We also observe that the quality of fitting for $B_K$ gets better when we include non-degenerate combinations to fit to the prediction by Van de Water and Sharpe. However, this effect on $B_7^{(3/2)}$ and $B_8^{(3/2)}$ turns out to be relatively small.
We present recent progress in understanding weak matrix elements on the lattice. We use HYP staggered fermions in quenched QCD to study numerically various properties of the $K^+\toπ^+$ amplitudes of the electroweak penguin operators $Q_7$ and $Q_8$. We check chiral Ward identities to probe the validity of using improved staggered fermions in the calculation of weak matrix elements. We address the issue of mixing with unphysical lower dimension operators, which causes a divergent term in the case of the $ΔI = 1/2$ amplitudes. We propose a particular subtraction method as the best choice. We also measure the gold-plated ratio $R$ originally suggested by Becirevic and Villadoro.
We study the improvement of staggered fermions using hypercubically smeared (HYP) links. We calculate the strange quark mass and the kaon B-parameter, $B_K$, in quenched QCD on a $16^3 \times 64$ lattice at $β=6.0$. We find $m_s(\bar{\rm MS},2 {\rm GeV})=101.2\pm1.3\pm4 $MeV and $B_K(\bar{\rm MS},2 {\rm GeV}) = 0.578 \pm 0.018\pm 0.042$, where the first error is from statistics and fitting, and the second from using one-loop matching factors. The scale ($1/a=1.95$GeV) is set by $M_ρ$, and $m_s$ is determined using the kaon mass. Comparing to quenched results obtained using unimproved staggered fermions and other discretizations, we argue that the size of discretization errors in $B_K$ is substantially reduced by improvement.
We calculate, at the one loop level, penguin diagrams for improved staggered fermion operators constructed using various fat links. The main result is that diagonal mixing coefficients with penguin operators are identical between the unimproved operators and the improved operators using such fat links as Fat7, Fat7+Lepage, $\bar{\rm Fat7}$, HYP (I) and HYP (II). In addition, it turns out that the off-diagonal mixing vanishes for those constructed using fat links of Fat7, $\bar{\rm Fat7}$ and HYP (II). This is a consequence of the the fact that the improvement by various fat links changes only the mixing with higher dimension operators and off-diagonal operators. The results of this paper, combined with those for current-current diagrams, provide the complete matching at the one loop level with all corrections of ${\cal O}(g^2)$ included.
We present results of $Re (A_0)$ and $Re (A_2)$ calculated using HYP staggered fermions on the lattice of $16^3 \times 64$ at $β=6.0$. These results are obtained using leading order chiral perturbation in quenched QCD. Buras's original RG evolution matrix develops a removable singularity for $N_f=3$. This subtlety is resolved by finding a finite solution to RG equation and the results are presented.
We present preliminary results for $ε'/ε$ calculated using HYP staggered fermions in the quenched approximation. We compare different choices of quenched penguin operators.
We study various methods of constructing fat links based upon the HYP (by Hasenfratz & Knechtli) and Fat7-bar (by W. Lee) algorithms. We present the minimum plaquette distribution for these fat links. This enables us to determine which algorithm is most effective at reducing the spread of plaquette values - a strong indicator of improved statistics for spectrum and static potential measurements, among other quantities.
We present results of the one-loop corrections originating from the penguin diagrams for the improved staggered fermion operators constructed using various fat links such as Fat7, Fat7+Lepage, $\bar{\rm Fat7}$, HYP (I) and HYP (II). The main results include the diagonal/off-diagonal mixing coefficients and the matching formula between the continuum and lattice operators.
We present a chronological review of the progress in calculating weak matrix elements using staggered fermions. We review the perturbative calculation of one-loop matching formula including both current-current diagrams and penguin diagrams using improved staggered fermions. We also present preliminary results of weak matrix elements relevant to CP violation calculated using the improved (HYP (II)) staggered fermions. Since the complete set of matching coefficients at the one-loop level became available recently, we have constructed lattice operators with all the $g^2$ corrections included. The main results include both $ΔI = 3/2$ and $ΔI = 1/2$ contributions.
We summarize the extent to which one can use Ward identities to non-perturbatively improve flavor singlet and non-singlet bilinears with three flavors of non-degenerate dynamical Wilson-like fermions.
We calculate the one-loop matching coefficients between continuum and lattice four-fermion operators for lattice operators constructed using staggered fermions and improved by the use of fattened links. In particular, we consider hypercubic fat links and SU(3) projected Fat-7 links, and their mean-field improved versions. We calculate only current-current diagrams, so that our results apply for operators whose flavor structure does not allow ``eye-diagrams''. We present general formulae, based on two independent approaches, and give numerical results for the cases in which the operators have the taste (staggered flavor) of the pseudo-Goldstone pion. We find that the one-loop corrections are reduced down to the 10-20% level, resolving the problem of large perturbative corrections for staggered fermion calculations of matrix elements.
We calculate one-loop matching factors for bilinear operators composed of improved staggered fermions. We compare the results for different improvement schemes used in the recent literature, all of which involve the use of smeared links. These schemes aim to reduce, though not completely eliminate, O(a^2) discretization errors. We find that all these improvement schemes substantially reduce the size of matching factors compared to unimproved staggered fermions. The resulting corrections are comparable to, or smaller than, those found with Wilson and domain-wall fermions. In the best case (``Fat-7'' and mean-field improved HYP links) the corrections are 10 % or smaller at 1/a = 2 GeV.
We study possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness and equivalence. As a result of these theorems, we show that, at one loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation.
We calculate one-loop matching factors for bilinear operators composed of improved staggered fermions. We compare the results for different improvement schemes used in the recent literature, including the HYP action and an action close to the Asqtad action. We find that all improvement schemes substantially reduce the size of the one-loop contributions to matching factors. The resulting corrections are comparable to, or smaller than, those found with Wilson and domain-wall fermions.