arXiv subjects

Weonjong Lee

Publications and source records attributed to Weonjong Lee.

At least 73 records · Page 4Linked to original sources

arXiv2013

Confinement From The Gauge Invariant Abelian Decomposition

A common approach while considering confinement is to study the dominance of an Abelian subgroup of the SU(3) gauge Links. A good way to find the Abelian component of the field is through the Cho-Guan-De gauge invariant Abelian Decomposition, which uses a carefully chosen direction vector $n$ to split the gauge field into an Abelian restricted field and a remnant coloured field. The restricted field can be further subdivided into topological and non-topological terms. We show that there is a choice of $n$ which allows us to exactly represent the Wilson Loop of full QCD as a function of only the restricted Abelian field without requiring any path ordering or additional path integrals. We present numerical evidence showing that the topological part of the restricted field dominates the string tension. We also show that $n$ contains certain topological objects, which, if they exist, will be at least partially responsible for confinement. These leave distinctive patterns in the restricted field strength, and we search for these structures in quenched lattice QCD.

hep-lat↗

arXiv2013

Performance of Kepler GTX Titan GPUs and Xeon Phi System

NVIDIA's new architecture, Kepler improves GPU's performance significantly with the new streaming multiprocessor SMX. Along with the performance, NVIDIA has also introduced many new technologies such as direct parallelism, hyper-Q and GPU Direct with RDMA. Apart from other usual GPUs, NVIDIA also released another Kepler 'GeForce' GPU named GTX Titan. GeForce GTX Titan is not only good for gaming but also good for high performance computing with CUDA. Nevertheless, it is remarkably cheaper than Kepler Tesla GPUs. We investigate the performance of GTX Titan and find out how to optimize a CUDA code appropriately for it. Meanwhile, Intel has launched its new many integrated core (MIC) system, Xeon Phi. A Xeon Phi coprocessor could provide similar performance with NVIDIA Kepler GPUs theoretically but, in reality, it turns out that its performance is significantly inferior to GTX Titan.

physics.comp-ph↗

arXiv2013

Update on $B_K$ and $\varepsilon_K$ with staggered quarks

We update our results for $B_K$ obtained using HYP-smeared staggered valence quarks on the MILC asqtad lattices. In the last year, we have added 5 new measurments on the fine ($a\approx 0.09\;$fm) ensembles, and 2 new measurements on the superfine ($a\approx 0.06\;$fm) ensembles. These allow a simultaneous extrapolation in $a^2$ and sea quark masses, reducing the corresponding systematic error significantly. Our updated result is $\hat{B}_K = 0.738 \pm 0.005 (\text{stat}) \pm 0.034 (\text{sys})$.

hep-lat↗

arXiv2013

Beyond the Standard Model B-parameters with improved staggered fermions in $N_f=2+1$ QCD

We calculate the kaon mixing B-parameters for operators arising generically in theories of physics beyond the standard model. We use HYP-smeared improved staggered fermions on the $N_f = 2+1$ MILC asqtad lattices. Operator matching is done perturbatively at one-loop order. Chiral extrapolations are done using "golden combinations" in which one-loop chiral logarithms are absent. For the combined sea-quark mass and continuum extrapolation, we use three lattice spacings: $a \approx 0.045, 0.06$ and $0.09 \text{fm}$. Our results have a total error of 5-6%, which is dominated by the systematic error from matching and continuum extrapolation. For two of the BSM $B$-parameters, we agree with results obtained using domain-wall and twisted-mass dynamical fermions, but we disagree by $(4-5)σ$ for the other two.

hep-lat↗

arXiv2013

Non-perturbative Renormalization of Bilinear Operators with Improved Staggered Quarks

We present renormalization factors for the bilinear operators obtained using the non-perturbative renormalization method (NPR) in the RI-MOM scheme with improved staggered fermions on the MILC asqtad lattices ($N_f = 2+1$). We use the MILC coarse ensembles with $20^3 \times 64$ geometry and $am_{\ell}/am_s = 0.01/0.05$. We obtain the wave function renormalization factor $Z_q$ from the conserved vector current and the mass renormalization factor $Z_m$ from the scalar bilinear operator. We also present preliminary results of renormalization factors for other bilinear operators.

hep-lat↗

arXiv2013

Neutral kaon mixing from new physics: matrix elements in $N_f=2+1$ QCD

We present results for matrix elements of $ΔS=2$ four-fermion operators arising generically in models of new physics. These are needed to constrain such models using the measured values of $\varepsilon_K$ and $ΔM_K$. We use lattice QCD with 2+1 flavors of improved staggered fermions on lattices generated by the MILC collaboration. We extrapolate to the continuum from three lattice spacings ranging down to $a\approx 0.045\;$fm. Total errors are $\sim 5-6%$, arising primarily from our use of one-loop matching between lattice and continuum operators. For two of the matrix elements, our results disagree significantly from those obtained using different fermion discretizations.

hep-lat↗

arXiv2013

Taste non-Goldstone, flavor-charged pseudo-Goldstone boson decay constants in staggered chiral perturbation theory

We calculate the axial current decay constants of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order. The results are a simple generalization of the results for the taste Goldstone case. New low-energy couplings are limited to analytic corrections that vanish in the continuum limit; certain coefficients of the chiral logarithms are modified, but they contain no new couplings. We report results for quenched, fully dynamical, and partially quenched cases of interest in the chiral SU(3) and SU(2) theories.

hep-lat↗

arXiv2013

Recent progress in staggered chiral perturbation theory

We present a review on recent progress in staggered chiral perturbation theory (SChPT). In the last decade, the scope of the application of SChPT has been extended beyond the level of calibration into the region of prediction with high precision. SChPT becomes an essential tool to do the data analysis reliably for physical observables calculated using improved staggered fermions. Here, we focus on the following examples: pion spectrum, pion decay constants, $\varepsilon_K$, and $π-π$ scattering amplitudes. In each subject, we review the recent progress and future prospects.

hep-lat↗

arXiv2012

Non-Perturbative Renormalization for Staggered Fermions (Self-energy Analysis)

We present preliminary results of data analysis for the non-perturbative renormalization (NPR) on the self-energy of the quark propagators calculated using HYP improved staggered fermions on the MILC asqtad lattices. We use the momentum source to generate the quark propagators. In principle, using the vector projection operator of $(\bar{\bar{γ_μ\otimes 1}})$ and the scalar projection operator $(\bar{\bar{1 \otimes 1}})$, we should be able to obtain the wave function renormalization factor $Z_q'$ and the mass renormalization factor $Z_q \cdot Z_m$. Using the MILC coarse lattice, we obtain a preliminary but reasonable estimate of $Z_q'$ and $Z_q \cdot Z_m$ from the data analysis on the self-energy.

hep-lat↗

arXiv2012

Chiral extrapolation of matrix elements of BSM kaon operators

Models of new physics induce K_0-K_0bar mixing through operators having Dirac structures other than the "left-left" form of the Standard Model. To carry out the chiral-continuum extrapolation of results from numerical simulations, one needs to know the quark mass and lattice spacing dependence of the corresponding B-parameters in the partially quenched theory at least at next-to-leading order. For simulations using staggered fermions (such as that we are doing with HYP-smeared valence fermions on the MILC asqtad lattices) one must determine this dependence using staggered chiral perturbation theory (SChPT). We have calculated the required dependence in both SU(3) and SU(2) SChPT, working at next-to-leading order, and we give here an overview of the methodology and results. The SU(3) SChPT result turns out to be much simpler than that for the Standard Model B_K operator, due to the absence of chiral suppression for the new operators. The SU(2) SChPT result turns out to be closely related to that for B_K: the chiral logarithms are identical, up to an operator-dependent sign. Our results are also useful for fermions with chiral symmetry as they provide, in the continuum limit, the partially quenched generalization of existing continuum results.

hep-lat↗

arXiv2012

Recent progress in calculation of $B_K$ using staggered fermions

We report on recent progress in the calculation of $B_K$ using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We have added measurements on fine ($a\sim 0.09 $fm) and superfine ($a\sim 0.06 $fm) ensembles at different values of the light sea quark mass ($a m_\ell$), as well as increased the statistics on some other ensembles. We find that the results on the fine lattices show a significantly stronger $am_\ell$ dependence than those on the superfine and coarse ($a\sim 0.12 $fm) lattices. We discuss different methods for accounting for these new results when doing the $a m_\ell$ and continuum extrapolations.

hep-lat↗

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

Taste non-Goldstone pion decay constants in staggered chiral perturbation theory

We calculate the next-to-leading order axial current decay constants of taste non-Goldstone pions and kaons in staggered chiral perturbation theory. This is an extension of the taste Goldstone decay constants calculation to that of the non-Goldstone tastes. We present results for the partially quenched case in the SU(3) and SU(2) staggered chiral perturbation theories and discuss the difference between the taste Goldstone and non-Goldstone cases.

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

Performance of SSE and AVX Instruction Sets

SSE (streaming SIMD extensions) and AVX (advanced vector extensions) are SIMD (single instruction multiple data streams) instruction sets supported by recent CPUs manufactured in Intel and AMD. This SIMD programming allows parallel processing by multiple cores in a single CPU. Basic arithmetic and data transfer operations such as sum, multiplication and square root can be processed simultaneously. Although popular compilers such as GNU compilers and Intel compilers provide automatic SIMD optimization options, one can obtain better performance by a manual SIMD programming with proper optimization: data packing, data reuse and asynchronous data transfer. In particular, linear algebraic operations of vectors and matrices can be easily optimized by the SIMD programming. Typical calculations in lattice gauge theory are composed of linear algebraic operations of gauge link matrices and fermion vectors, and so can adopt the manual SIMD programming to improve the performance.

hep-lat↗

arXiv2012

String tension from gauge invariant Magnetic Monopoles

We investigate the relationship between colour confinement and the monopoles derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and 't Hooft monopoles, do not require a singular gauge field and are defined for any choice of gauge (and are not just restricted to, for example, the maximum Abelian gauge). The Abelian decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to investigate the relationship between the gauge invariant monopoles and confinement both analytically and numerically, as well as retaining the maximal possible symmetry within the colour field so that it is able to see all the monopoles in an SU($N_C$) calculation. We describe how the Abelian decomposition is related to the Wilson Loop, so that the string tension may be calculated from the field strength related to the decomposed (or restricted) Abelian field. We discuss the structures in the colour field which may cause an area law in the Wilson Loop, which turn out to be magnetic monopoles. If these monopoles are present, they will lead to an area law scaling of the Wilson Loop and thus be at least partially responsible for confinement. We search for these monopoles in quenched lattice QCD. We show that the string tension is dominated by peaks in the restricted field strength, at least some of which are located close to structures in the colour field consistent with with theoretical expectations for the monopoles. We show that the string tension extracted from the monopole contribution to the restricted field is close to that of the entire original field; again suggesting that confinement can at least partially be explained in terms of these monopoles.

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↗