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Hyung-Jin Kim

Publications and source records attributed to Hyung-Jin Kim.

At least 37 records · Page 2Linked to original sources
arXiv2011

Multi GPU Performance of Conjugate Gradient Solver with Staggered Fermions in Mixed Precision

GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have implemented mixed precision algorithm to our multi GPU conjugate gradient solver. The single precision calculation use half of the memory that is used by the double precision calculation, which allows twice faster data transfer in memory I/O. In addition, the speed of floating point calculations is 8 times faster in single precision than in double precision. The overall performance of our CUDA code for CG is 145 giga flops per GPU (GTX480), which does not include the infiniband network communication. If we include the infiniband communication, the overall performance is 36 giga flops per GPU (GTX480).

physics.comp-ph↗
arXiv2011

Finite Volume Errors in $B_K$

We discuss finite volume errors in our calculations of $B_K$ using improved staggered fermions on the MILC asqtad lattices. Using GPUs, we are now able to extrapolate using next-to-leading order (NLO) staggered SU(2) chiral perturbation theory including the finite volume corrections arising from pion loops. We find that the impact of FV fitting is very small, giving a 0.5% shift in the continuum limit.

hep-lat↗
arXiv2011

Non-Goldstone pion masses with NLO in Staggered Chiral Perturbation Theory

We present results of the masses of taste non-Goldstone $(F \ne ξ_5)$ pions and kaons calculated up to the next-to-leading order in the SU(3) staggered chiral perturbation theory (SChPT). The results can be used to fit data and to understand taste symmetry breaking effect quantitatively. The final expressions for the non-Goldstone masses contain 20 low energy constants unique to the non-Goldstone sector. We have calculated the several cases such as the full QCD, partially quenched QCD, and quenched QCD in the $N_f=1+1+1$ flavor and $N_f=2+1$ flavor cases in the SU(3) and SU(2) SChPT. In this paper, we present only the SU(3) part.

hep-lat↗
arXiv2011

$B_K$ from improved staggered fermions using SU(3) chiral perturbation theory

We present recent progress in our calculation of $B_K$ with improved staggered fermions using chiral extrapolations based on SU(3) staggered chiral perturbation theory. We have accumulated significantly higher statistics on the coarse, fine, and ultrafine MILC asqtad lattices. This leads to a reduction in statistical error and an improved continuum extrapolation. Our updated result is $\hat{B}_K = B_K(\text{RGI}) = 0.737 \pm 0.003(\text{stat}) \pm 0.046 (\text{sys})$. This is consistent with the result obtained using chiral extrapolations based on SU(2) staggered chiral perturbation theory, although the total error is somewhat larger with the SU(3) analysis.

hep-lat↗
arXiv2011

Finite volume effects in $B_K$ with improved staggered fermions

We extend our recent unquenched ($N_f=2+1$ flavor) calculation of $B_K$ using improved staggered fermions by including in the fits the finite volume shift predicted by one-loop staggered chiral perturbation theory. The net result is to lower the result in the continuum limit by 0.6%. This shift is slightly smaller than our previous estimate of finite volume effects based on a direct comparison between different volumes. To include the finite volume effects in a reasonable time, we found it necessary to calculate them using Graphics Processing Units.

hep-lat↗
arXiv2010

$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD

We present results for kaon mixing parameter $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings ($a\approx 0.12$, $0.09$ and $0.06\;$fm), ten different valence quark masses ($m\approx m_s/10-m_s$), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly straightforward because parameters related to taste-breaking and matching errors appear only at next-to-next-to-leading order. We match to the continuum renormalization scheme (NDR) using one-loop perturbation theory. Our final result is from the SU(2) analysis, with the SU(3) result providing a (less accurate) cross check. We find $B_K(\text{NDR}, μ= 2 \text{GeV}) = 0.529 \pm 0.009 \pm 0.032$ and $\hat{B}_K =B_K(\text{RGI})= 0.724 \pm 0.012 \pm 0.043$, where the first error is statistical and the second systematic. The error is dominated by the truncation error in the matching factor. Our results are consistent with those obtained using valence domain-wall fermions on lattices generated with asqtad or domain-wall sea quarks.

hep-lat↗
arXiv2010

$B_K$ with improved staggered fermions: analysis using SU(2) staggered chiral perturbation theory

We report updated results for $B_K$ calculated using HYP-smeared staggered fermions on the MILC asqtad 2+1 flavor lattices. We use four different lattice spacings ($a \approx$ 0.12, 0.09, 0.06 and 0.045 fm) to control the continuum extrapolation. We use SU(2) staggered chiral perturbation theory to do the data analysis. We find that $B_K(\text{NDR}, μ=2 \text{GeV}) = 0.526 \pm 0.007 \pm 0.024$ and $\hat{B}_K = B_K(\text{RGI}) = 0.720 \pm 0.010 \pm 0.033$. Here the first error is statistical and the second systematic. The dominant source of error is that due to our use of a truncated (one-loop) matching factor.

hep-lat↗
arXiv2010

$B_K$ with improved staggered fermions: analysis using SU(3) staggered chiral perturbation theory

We report updated results for $B_K$ using HYP-smeared staggered valence quarks on MILC asqtad lattices based on an analysis using SU(3) staggered chiral perturbation theory. The most important new feature of our data sample is the inclusion of a fourth ("ultrafine") lattice spacing. This improves the control over the continuum extrapolation and errors due our use of one-loop perturbative matching. We present a complete updated error budget, which leads to $B_K(\text{NDR}, μ= 2 \text{GeV}) = 0.5309 \pm 0.0051 \pm 0.0424$ and $\hat{B}_K = B_K(\text{RGI}) = 0.727 \pm 0.07 \pm 0.058$. The results of the SU(3) analysis are inferior to those based on SU(2) staggered chiral perturbation theory, primarily because of the dependence on the Bayesian priors we use in the SU(3) fits.

hep-lat↗
arXiv2010

Systematic Uncertainties in $B_K$ with Improved Staggered Fermions

We study three sources of error in our calculation of $B_K$ using HYP-smeared staggered fermions on the MILC asqtad lattices. These are (1) dependence on the light sea quark mass; (2) finite volume effects; and (3) the impact of an order of magnitude increase in the number of measurements. Our main results are (1) the dependence on the light sea-quark mass is weaker than expected by naive dimensional analysis, (2) including finite volume effects in SU(2) staggered chiral perturbation theory fits leads to a very small change in $B_K$, of size $\approx 0.1%$, and (3) increasing the statistics on one of the coarse MILC lattices resolves a potential discrepancy with other coarse results.

hep-lat↗
arXiv2010

First results for $B_K$ on the ultrafine ($a=0.045$ fm) ensemble

We present preliminary results for $B_K$ from the MILC ultrafine lattices, based on a partial ensemble of 305 configurations. We use HYP-smeared improved staggered valence quarks. The analysis is done using fitting forms based on both SU(2) and SU(3) staggered chiral perturbation thery. For the SU(2) analysis, we find that the result using the NLO fit function is consistent with that from a partial NNLO fit. For the SU(3) analysis, where we have to use partially constrained fits due to the number of fit parameters, we find that our two preferred fits ("N-BB1" and "N-BB2") are also consistent, both with each other and with the results of the SU(2) fits. These results are used in companion proceedings to improve the control over the continuum extrapolation.

hep-lat↗
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↗
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

hep-lat↗
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.

hep-lat↗
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↗
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↗