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Weonjong Lee

Publications and source records attributed to Weonjong Lee.

At least 109 records · Page 6Linked to original sources
arXiv2010

Multi GPU Performance of Conjugate Gradient Algorithm with Staggered Fermions

We report results of the performance test of GPUs obtained using the conjugate gradient (CG) algorithm for staggered fermions on the MILC fine lattice ($28^3 \times 96$). We use GPUs of nVIDIA GTX 295 model for the test. When we turn off the MPI communication and use only a single GPU, the performance is 35 giga flops in double precision, which corresponds to 47% of the peak. When we turn on the MPI communication and use multi-GPUs, the performance is reduced down to 12.3 giga flops. The data transfer through the infiniband network and PCI-E bus I/O is a main bottle neck. We suggest two potential solutions of how to optimize the data transfer.

hep-lat↗
arXiv2010

One loop matching factors for improved staggered four-fermion operators with improved glue

We present results for matching factors for staggered four-fermion operators constructed using HYP-smeared fat links both in the action and the operators. We use perturbation theory to calculate the matching factors and work to one-loop order. The new feaure of this work is the use of the Symanzik-improved gauge action, as opposed to the Wilson gauge action. Our results are needed for our ongoing calculation of weak matrix elements using HYP-smeared staggered valence quarks and operators on MILC lattices. We give explicit results for matching factors of the operator needed to calculate $B_K$. We compare the impact of the improvement of the gauge action on one-loop coefficients with that of mean-field improvement of the operators.

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arXiv2010

One-loop matching factors for staggered bilinear operators with improved gauge actions

We present results for one-loop perturbative matching factors using bilinear operators composed of improved staggered fermions, using unimproved (Wilson) and improved (Symanzik, Iwasaki, and DBW2) gluon actions. We consider two fermions actions---HYP/$\bar{\text{Fat7}}$-smeared and "asqtad". The former is being used in calculations of electroweak matrix elements, while the latter have been used extensively by the MILC collaboration. We observe that using the improved gluon action leads to small reductions in the perturbative corrections, but that these reductions are smaller than those obtained when moving from the tadpole-improved naive staggered action to either HYP-smeared or asqtad action.

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arXiv2009

Determination of $B_K$ using improved staggered fermions (II) SU(2) chiral perturbation theory fit

We present results for $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. In this report, the data is analyzed using the results of SU(2) staggered chiral perturbation theory (SChPT). We outline the derivation of the NLO SU(2) SChPT result, explain our fitting procedure, and outline how we estimate systematic errors. We also show the light sea-quark mass and lattice spacing dependence for both SU(2) and SU(3)-based analyses. Our preliminary result from the SU(2) analysis is $B_K(\text{NDR}, μ= 2 \text{GeV}) = 0.512 \pm 0.014 \pm 0.034$ and $\hat{B}_K = B_K(\text{RGI})= 0.701 \pm 0.019 \pm 0.047$. This is somewhat more accurate than our result from the SU(3) analysis. It is consistent with results obtained using valence domain-wall fermions

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arXiv2009

Determination of $B_K$ using improved staggered fermions (I): SU(3) chiral perturbation theory fit

We present the results for $B_K$ calculated using HYP-smeared staggered fermions using lattices generated by the MILC collaboration using the asqtad staggered action. We have done the calculation on 8 ensembles of these lattices, including three different lattice spacings ($a=0.12, 0.09, 0.06$ fm). We fit the data to forms based on those predicted by SU(3) mixed-action partially-quenched staggered chiral perturbation theory. Our preliminary result is $ B_K(\text{NDR},μ=2\text{GeV}) = 0.528 \pm 0.011 \pm 0.048 $, where the first error is statistical and the second systematic. The error turns out to be larger than that from an analysis using SU(2) chiral perturbation theory.

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arXiv2009

Determination of $B_K$ using improved staggered fermions (III) Finite volume effects

We study the finite-volume effects in our calculation of $B_K$ using HYP-smeared improved staggered valence fermions. We calculate the predictions of both SU(3) and SU(2) staggered chiral perturbation theory at one-loop order. We compare these to the results of a direct calculation, using MILC coarse lattices with two different volumes: $20^3$ and $28^3$. From the direct calculation, we find that the finite volume effect is $\approx 2%$ for the SU(3) analysis and $\approx 0.9%$ for the SU(2) analysis. We also show how the statistical error depends on the number of measurements made per configuration, and make a first study of autocorrelations.

hep-lat↗
arXiv2009

One loop matching factors for staggered bilinear operators with improved glue

We present results for matching factors for bilinear operators composed of HYP-smeared staggered fermions and constructed using HYP-smeared fat links. The matching factors are calculated perturbatively at one-loop order. The new feature of our calculation compared to previous work on HYP-smeared staggered fermions is the use of the Symanzik-improved gluon propagator, which allows our results to be applied to our ongoing simulations based on configurations generated by the MILC collaboration. We address the issue of the relative efficiency of various improvement schemes in reducing one-loop corrections to the matching factors.

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arXiv2008

Scaling behavior and sea quark dependence of pion spectrum with HYP-smeared staggered fermions

We study the pion spectrum (and in particular taste-symmetry breaking within it) using HYP-smeared valence staggered fermions on the coarse and fine MILC lattices (which have asqtad staggered sea quarks). We focus on the dependence on lattice spacing and sea-quark mass. We also update our results on source dependence. Our main conclusion is that on the MILC fine lattices the appropriate power-counting for SU(3) staggered chiral perturbation theory may have discretization errors entering at next-to-leading order rather than at leading-order.

hep-lat↗
arXiv2008

Calculating $B_K$ using HYP staggered fermions

We give an update on our calculation of $B_K$ using HYP-smeared valence staggered quarks. We have results for $B_K$ at tree-level on several coarse MILC lattices ($a\approx 0.12 $fm) and one of the fine lattices ($a\approx 0.09 $fm), using 10 light valence quarks ranging down to $m_s^{\rm phys}/10$. We have generalized staggered chiral perturbation theory to our mixed action setup, and outline the results. We explain our present fitting strategy, and give some preliminary results.

hep-lat↗
arXiv2008

Taste symmetry breaking with HYP-smeared staggered fermions

We study the impact of hypercubic (HYP) smearing on the size of taste breaking for staggered fermions, comparing to unimproved and to asqtad-improved staggered fermions. As in previous studies, we find a substantial reduction in taste-breaking compared to unimproved staggered fermions (by a factor of 4-7 on lattices with spacing $a\approx 0.1 $fm). In addition, we observe that discretization effects of next-to-leading order in the chiral expansion (${\cal O}(a^2 p^2)$) are markedly reduced by HYP smearing. Compared to asqtad valence fermions, we find that taste-breaking in the pion spectrum is reduced by a factor of 2.5-3, down to a level comparable to the expected size of generic ${\cal O}(a^2)$ effects. Our results suggest that, once one reaches a lattice spacing of $a\approx 0.09 $fm, taste-breaking will be small enough after HYP smearing that one can use a modified power counting in which ${\cal O}(a^2) \ll {\cal O}(p^2)$, simplify fitting to phenomenologically interesting quantities.

hep-lat↗
arXiv2008

$B_K$ in unquenched QCD using improved staggered fermions

We present preliminary results for $B_K$ calculated using improved staggered fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad staggered sea quarks). We investigate the effect of non-degenerate quarks on $B_K$ and attempt to estimate the ${\cal O}(a^2)$ effect due to non-Goldstone pions in loops. We fit the data to continuum partially quenched chiral perturbation theory. We find that the quality of fit for $B_K$ improves if we include non-degenerate quark mass combinations. We also observe, however, that the fitting curve deviates from the data points in the light quark mass region. This may indicate the need to include taste-breaking in pion loops.

hep-lat↗
arXiv2007

Structure of logarithmically divergent one-loop lattice Feynman integrals

For logarithmically divergent one-loop lattice Feynman integrals I(p,a), subject to mild general conditions, we prove the following expected and crucial structural result: I(p,a) = f(p)log(aM)+g(p)+h(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is a mass scale which may be chosen arbitrarily. The f(p) and h(p,M) are shown to be universal and coincide with analogous quantities in the corresponding continuum integral when the latter is regularized either by momentum cut-off or dimensional regularization. The non-universal term g(p) is shown to be a homogeneous polynomial in p of the same degree as f(p). This structure is essential for consistency between renormalized lattice and continuum formulations of QCD at one loop.

hep-lat↗
arXiv2007

Eradication of singularities in the next-to-leading order RG evolution for the ΔS = 1 effective Hamiltonian with 3 quark flavours

We consider the renormalization group evolution for the operators in the $ΔS=1$ effective Hamiltonian with 3 active quark flavors, which is needed in the numerical analysis of data sets for $ε'/ε$ calculated in lattice QCD. Singularities are present in the original solution of Buras et al. at next-to-leading order. We show how these can be eradicated through a method of analytic continuation to obtain the correct finite solution in this case. Furthermore, we trace the origin of the singularities to a breakdown of the approach of Buras et al. in the 3 flavour case, and show how it can be rectified so that singularitites are absent from the beginning.

hep-lat↗
arXiv2007

General properties of logarithmically divergent one-loop lattice Feynman integrals

We prove that logarithmically divergent one-loop lattice Feynman integrals have the general form I(p,a) = f(p)log(aM)+g(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is an arbitrary mass scale. The f(p) is shown to be universal and to coincide with the analogous quantity in the corresponding continuum integral (regularized, e.g., by momentum cut-off). This is essential for universality of the lattice QCD beta-function and anomalous dimensions of renormalized lattice operators at one loop. The result and argument presented here are simplified versions of ones given in arXiv:0709.0781. A noteworthy feature of the argument here is that it does not involve Taylor expansion in external momenta, hence infra-red divergences associated with that expansion do not arise.

hep-lat↗
arXiv2007

Improvement of the pion spectrum with HYP-smeared staggered fermions

We extend our previous study of taste-symmetry breaking using HYP-smeared staggered fermions in two ways. First, we improve the statistics of a comparison of unimproved and HYP-smeared staggered fermions on quenched lattices with $a\approx 0.1 $fm. This allows us to obtain a signal for all pion tastes, rather than just a subset, and thus to make a complete comparison. In addition, it allows us to differentiate between wall and local sources. Second, we compare HYP-smeared valence quarks to asqtad valence quarks on 2+1 flavor unquenched MILC lattices. We find that taste breaking is substantially reduced by HYP-smearing, bringing the size of this discretization effect (which is the dominant such effect with staggered fermions) down to the size expected generically for any fermion type.

hep-lat↗
arXiv2007

Renormalisation group evolution for the $ΔS = 1$ effective Hamiltonian with $N_f=2+1$

We discuss the renormalisation group (RG) evolution for the $ΔS = 1$ operators in unquenched QCD with $N_f = 3$ ($m_u=m_d=m_s$) or, more generally, $N_f = 2+1$ ($m_u=m_d \ne m_s$) flavors. In particular, we focus on the specific problem of how to treat the singularities which show up only for $N_f=3$ or $N_f = 2+1$ in the original solution of Buras {\it et al.} for the RG evolution matrix at next-to-leading order. On top of Buras {\it et al.}'s original treatment, we use a new method of analytic continuation to obtain the correct solution in this case. It is free of singularities and can therefore be used in numerical analysis of data sets calculated in lattice QCD.

hep-lat↗
arXiv2006

Pion spectrum using improved staggered fermions

We present results for the pion multiplet spectrum calculated using both unimproved staggered fermions and improved HYP-smeared staggered fermions. In the case of unimproved staggered fermions, we observe (consistent with previous work) that ${\cal O}(a^2)$ taste symmetry breaking effects are large and comparable to the $\approx {\cal O}(p^2)$ contributions to their masses. Higher order ${\cal O}(a^2 p^2)$ effects are also substantial enough to be seen. For HYP-smeared staggered fermions, we find that taste breaking is much reduced. The ${\cal O}(a^2)$ effects are observable, but are noticeably smaller than those obtained with AsqTad-improved staggered fermions, and much smaller than those obtained using unimproved staggered fermions, while ${\cal O}(a^2 p^2)$ effects are suppressed to such a level that we cannot observe them given our statistical errors. From this numerical study, we conclude that HYP staggered fermions are significantly better that AsqTad fermions from the perspective of taste symmetry breaking.

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