arXiv subjects

Yong-Chull Jang

Publications and source records attributed to Yong-Chull Jang.

67 records · Page 4Linked to original sources

arXiv2012

Beyond the Standard Model corrections to $K^0-\bar{K}^0$ mixing

We calculate the B-parameters for operators arising in theories of new physics beyond the standard model (BSM) using HYP-smeared improved staggered fermions on the MILC asqtad lattices with N_f = 2+1 flavors. We use three different lattice spacings (a ~ 0.045, 0.06 and 0.09 fm) at a fixed ratio of light to strange quarks, m_l/m_s = 1/5, to obtain the continuum results. Operator matching is done using perturbative matching at one-loop order, and results are run to 2 or 3 GeV using two-loop running in the MS-bar scheme. For the chiral and continuum extrapolations, we use SU(2) staggered chiral perturbation theory. We present preliminary results with only statistical errors.

hep-lat↗

arXiv2012

Current Status of Indirect CP Violation in Neutral Kaon System

In the standard model (SM), the CP violation is introduced through a single phase in the CKM matrix. The neutral kaon system is one of the most precise channels to test how the SM theory describes the experiment data such as $ε_K$ accurately. The indirect CP violation is parametrized into $ε_{K}$, which can be calculated directly using lattice QCD. In this calculation, the largest uncertainty comes from two sources: one is $\hat{B}_K$ and the other is $V_{cb}$. We use the lattice results of $\hat{B}_K$ and exclusive $V_{cb}$ to calculate the theoretical estimate of $ε_K$, which turns out to be $3.1σ$ away from its experimental value. Here, the error is evaluated using the standard error propagation method.

hep-lat↗

arXiv2012

Covariance fitting of highly correlated data in lattice QCD

We address a frequently asked question on the covariance fitting of the highly correlated data such as our $B_K$ data based on the SU(2) staggered chiral perturbation theory. Basically, the essence of the problem is that we do not have an accurate fitting function enough to fit extremely precise data. When eigenvalues of the covariance matrix are small, even a tiny error of fitting function yields large chi-square and spoils the fitting procedure. We have applied a number of prescriptions available in the market such as the cut-off method, modified covariance matrix method, and Bayesian method. We also propose a brand new method, the eigenmode shift method which allows a full covariance fitting without modifying the covariance matrix at all. In our case, the eigenmode shift (ES) method and Bayesian method turn out to be the best prescription to the problem. We also provide a pedagogical example of data analysis in which the diagonal approximation and the cut-off method fail in fitting manifestly, but the ES method and the Bayesian approach work well.

hep-lat↗

arXiv2012

Kaon $B$-parameter from improved staggered fermions in $N_f=2+1$ QCD

We present a calculation of the kaon $B$-parameter, $B_K$, using lattice QCD. We use improved staggered valence and sea fermions, the latter generated by the MILC collaboration with $N_f=2+1$ light flavors. To control discretization errors, we use four different lattice spacings ranging down to $a\approx 0.045\;$fm. The chiral and continuum extrapolations are done using SU(2) staggered chiral perturbation theory. Our final result is $\hat{B}_K = 0.727 \pm 0.004 (\text{stat}) \pm 0.038 (\text{sys})$, where the dominant systematic error is from our use of truncated (one-loop) matching factors.

hep-lat↗

arXiv2011

Continuum extrapolation of $B_K$ with staggered fermions

We report on recent progress in the calculation of $B_K$ using HYP-smeared staggered fermions on the MILC asqtad lattices. Our main focus is on the continuum extrapolation, which is done using (up to) four different lattice spacings---$a\approx$ 0.12, 0.09, 0.06 and 0.045 fm. Since Lattice 2010, we have reduced the statistical errors on the $a\approx 0.09\;$fm lattices by a factor of $\sim 3$, and roughly doubled the size of the $a\approx0.045\;$fm ensemble. We find that these improvements have a very significant impact on the continuum extrapolation, with the $a\approx 0.12\;$fm data lying outside the range of applicability of simple functional forms. Hence we use only the three smallest lattice spacings to perform the extrapolation, finding $\hat{B}_K = B_K(\text{RGI}) = 0.725 \pm 0.004(\text{stat}) \pm 0.038(\text{sys}) $. This value is consistent with our published value from 2010 (based the three coarsest lattice spacings), but has smaller errors.

hep-lat↗

arXiv2011

Trouble shooting for covariance fitting in highly correlated data

We report a possible solution to the trouble that the covariance fitting fails when the data is highly correlated and the covariance matrix has small eigenvalues. As an example, we choose the data analysis of highly correlated $B_K$ data on the basis of the SU(2) staggered chiral perturbation theory. Basically, the essence of the problem is that we do not have an accurate fitting function so that we cannot fit the highly correlated and precise data. When some eigenvalues of the covariance matrix are small, even a tiny error of fitting function can produce large chi-square and spoil the fitting procedure. We have applied a number of prescriptions available in the market such as diagonal approximation and cutoff method. In addition, we present a new method, the eigenmode shift method which fine-tunes the fitting function while keeping the covariance matrix untouched.

hep-lat↗

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

$B_K$ 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↗

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↗