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Weonjong Lee

Publications and source records attributed to Weonjong Lee.

At least 19 recordsLinked to original sources
arXiv2025

2025 update on $\varepsilon_K$ in the Standard Model with lattice QCD inputs

We present theoretical results for the indirect CP violation parameter, $ |\varepsilon_K| $, evaluated directly within the Standard Model using lattice QCD inputs including $ B_K $, $ |V_{cb}| $, $ |V_{us}| $, $ |V_{ud}| $, $ \xi_0 $, $ \xi_2 $, $ F_K $, and the charm quark mass $ m_c $. Our analysis reveals a significant tension at the $ \sim 5\sigma $ level ($ 4.6\sigma $ to $ 5.2\sigma $) between the Standard Model prediction and the experimental value of $ |\varepsilon_K| $. The Standard Model prediction, informed by lattice QCD inputs, accounts for only approximately 65% of the experimental value, leaving a 35% discrepancy unexplained. Notably, this tension vanishes when using the inclusive determination of $ |V_{cb}| $, derived from heavy quark expansion. The discrepancy is therefore tied to the well-known tension between the exclusive and inclusive determinations of $ |V_{cb}| $. We further report results for $ |\varepsilon_K| $ obtained using the Brod--Gorbahn--Stamou (BGS) method based on $ u\text{--}t $ unitarity, which yields an even stronger discrepancy, in the range of $ 4.9\sigma $ to $ 5.5\sigma $, when combined with lattice QCD inputs.

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arXiv2024

2024 Update on $\varepsilon_K$ with lattice QCD inputs

We report recent progress on $\varepsilon_K$ evaluated directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, exclusive $|V_{cb}|$, $|V_{us}|$, $|V_{ud}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only $2/3 \cong 65\%$ of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35\%, which represents a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 4.1\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on the QCD sum rule approach. We also report results for $|\varepsilon_K|$ obtained using the Brod-Gorbahn-Stamou (BGS) method for $\eta_i$ of $u-t$ unitarity, which leads to even a stronger tension of $5.7\sigma \sim 4.2\sigma$ with lattice QCD inputs.

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arXiv2024

Progress report on testing robustness of the Newton method in data analysis on 2-point correlation function using a MILC HISQ ensemble

We report recent progress in data analysis on the two point correlation functions which will be prerequisite to obtain semileptonic form factors for the $B_{(s)} \to D_{(s)}\ell\nu$ decays. We use a MILC HISQ ensemble for the measurement. We use the HISQ action for light quarks, and the Oktay-Kronfeld (OK) action for the heavy quarks ($b$ and $c$). We used a sequential Bayesian method for the data analysis. Here we test the new fitting methodology of Benjamin J.~Choi in a completely independent manner.

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arXiv2024

Current progress on the semileptonic form factors for $\bar{B} \to D^{\ast} \ell \bar{\nu}$ decay using the Oktay-Kronfeld action

We present recent progress in calculating the semileptonic form factors $h_{A_1}(w)$ for the $\bar{B} \to D^{\ast} \ell \bar{\nu}$ decays. We use the Oktay-Kronfeld (OK) action for the charm and bottom valence quarks and the HISQ action for light quarks. We adopt the Newton method combined with the scanning method to find a good initial guess for the $\chi^2$ minimizer in the fitting of the 2pt correlation functions. The main advantage is that the Newton method lets us to consume all the time slices allowed by the physical positivity. We report the first, reliable, but preliminary results for $h_{A_1}(w)/\rho_{A_1}$ at zero recoil ($w=1$). Here we use a MILC HISQ ensemble ($a = 0.12$ fm, $M_{\pi}$ = 220 MeV, and $N_f = 2 + 1 + 1$ flavors).

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arXiv2023

2023 Update of $\varepsilon_K$ with lattice QCD inputs

We report recent progress on $\varepsilon_K$ evaluated directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $|V_{ud}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only 66\% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 34\%, which corresponds to a strong tension in $|\varepsilon_K|$ at the $4.9\sigma \sim 3.9\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on the QCD sum rule approach.

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arXiv2023

2022 Update on $\varepsilon_K$ with lattice QCD inputs

We present recent updates for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 65% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35%, which leads to a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 3.9\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on the QCD sum rule approach, although this inclusive tension is small ($\approx 1.4\sigma$) but keeps increasing as time goes on.

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arXiv2022

Improved data analysis on two-point correlation function with sequential Bayesian method

We report our progress in data analysis on two-point correlation functions of the $B$ meson using sequential Bayesian method. The data set of measurement is obtained using the Oktay-Kronfeld (OK) action for the bottom quarks (valence quarks) and the HISQ action for the light quarks on the MILC HISQ lattices. We find that the old initial guess for the $\chi^2$ minimizer in the fitting code is poor enough to slow down the analysis somewhat. In order to find a better initial guess, we adopt the Newton method. We find that the Newton method provides a natural test to check whether the $\chi^2$ minimizer finds a local minimum or the global minimum, and it also reduces the number of iterations dramatically.

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arXiv2022

Deep learning study on the Dirac eigenvalue spectrum of staggered quarks

We study the chirality of staggered quarks on the Dirac eigenvalue spectrum using deep learning (DL) techniques. The Kluberg-Stern method to construct staggered bilinear operators conserves continuum property such as recursion relations, uniqueness of chirality, and Ward identities, which leads to a unique and characteristic pattern (we call it "leakage pattern (LP)") in the matrix elements of the chirality operator sandwiched between two quark eigenstates of staggered Dirac operator. DL analysis gives $99.4(2)\%$ accuracy on normal gauge configurations and $0.998$ AUC (Area Under ROC Curve) for classifying non-zero mode octets in the Dirac eigenvalue spectrum. It confirms that the leakage pattern is universal on normal gauge configurations. The multi-layer perceptron (MLP) method turns out to be the best DL model for our study on the LP.

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arXiv2022

2021 Update on $\varepsilon_K$ with lattice QCD inputs

We present recent updates for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 66\% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 34\%, which leads to a strong tension in $|\varepsilon_K|$ at the $4.5\sigma \sim 3.7\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on the QCD sum rule approach.

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arXiv2020

Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators

We investigate general properties of the eigenvalue spectrum for improved staggered quarks. We introduce a new chirality operator $[\gamma_5 \otimes 1]$ and a new shift operator $[1 \otimes \xi_5]$, which respect the same recursion relation as the $\gamma_5$ operator in the continuum. Then we show that matrix elements of the chirality operator sandwiched between two eigenstates of the staggered Dirac operator are related to those of the shift operator by the Ward identity of the conserved $U(1)_A$ symmetry of staggered fermion actions. We perform a numerical study in quenched QCD using HYP staggered quarks to demonstrate the Ward identity. We introduce a new concept of leakage patterns which collectively represent the matrix elements of the chirality operator and the shift operator sandwiched between two eigenstates of the staggered Dirac operator. The leakage pattern provides a new method to identify zero modes and non-zero modes in the Dirac eigenvalue spectrum. This method is as robust as the spectral flow method but requires much less computing power. Analysis using a machine learning technique confirms that the leakage pattern is universal, since the staggered Dirac eigenmodes on normal gauge configurations respect it. In addition, the leakage pattern can be used to determine a ratio of renormalization factors as a by-product. We conclude that it might be possible and realistic to measure the topological charge $Q$ using the Atiya-Singer index theorem and the leakage pattern of the chirality operator in the staggered fermion formalism.

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arXiv2020

Semileptonic $B \to D^{(\ast)} \ell\nu$ Decay Form Factors using the Oktay-Kronfeld Action

We report recent progress in calculating semileptonic form factors for the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to D \ell \bar{\nu}$ decays using the Oktay-Kronfeld (OK) action for bottom and charm quarks. We use the second order in heavy quark effective power counting $\mathcal{O}(\lambda^2)$ improved currents in this work. The HISQ action is used for the light spectator quarks. We analyzed four $2+1+1$-flavor MILC HISQ ensembles with $a\approx 0.09\,\mathrm{fm}$, $0.12\,\mathrm{fm}$ and $M_\pi \approx 220\,\mathrm{MeV}$, $310\,\mathrm{MeV}$: $a09m220$, $a09m310$, $a12m220$, $a12m310$. Preliminary results for $B\to D^\ast\ell\nu$ decays form factor $h_{A_1}(w)$ at zero recoil ($w=1$) are reported. Preliminary results for $B \to D\,\ell\nu$ decays form factors $h_\pm(w)$ over a kinematic range $1<w<1.3$ are reported as well.

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arXiv2020

Leptonic decays of $B_{(s)}$ and $D_{(s)}$ using the OK action

We present recent progress in the lattice calculation of leptonic decay constants for $B_{(s)}$ and $D_{(s)}$ mesons using the Oktay-Kronfeld (OK) action for charm and bottom valence quarks, whose masses are tuned non-perturbatively. The calculations are done on 6 HISQ ensembles generated by the MILC collaboration with $N_f=2+1+1$ flavors. We also use the HISQ action for the light spectator quarks. Results are presented for the ratios $f_{B_s}/f_B$ and $f_{D_s}/f_D$, which reflect $SU(3)$ flavor symmetry breaking, and are independent of the renormalization constants of the axial currents.

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arXiv2020

Chiral Ward identities for Dirac eigenmodes with staggered fermions

We study chiral properties of eigenvalue spectrum for staggered quarks. We present a new method to identify would-be zero modes and nonzero modes using their symmetry and chiral properties. Here, we review the traditional method with HYP improved staggered quarks, and extend it to a completely new method which uses the chiral Ward identities and leakage patterns to achieve the goal.

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arXiv2020

Improvement of heavy-heavy and heavy-light currents with the Oktay-Kronfeld action

The CKM matrix elements $V_{cb}$ and $V_{ub}$ can be obtained by combining data from the experiments with lattice QCD results for the semi-leptonic form factors for the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to \pi \ell \bar{\nu}$ decays. It is highly desirable to use the Oktay-Kronfeld (OK) action for the form factor calculation on the lattice, since the OK action is designed to reduce the heavy quark discretization error down to the $\mathcal{O}(\lambda^4)$ level in the power counting rules of the heavy quark effective theory (HQET). Here, we present a matching calculation to improve heavy-heavy and heavy-light currents up to the $\lambda^3$ order in HQET, the same level of improvement as the OK action. Our final results for the improved currents are being used in a lattice QCD calculation of the semi-leptonic form factors for the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to D \ell \bar{\nu}$ decays.

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arXiv2019

2019 Update on $\varepsilon_K$ with lattice QCD inputs

We present updated results for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $ξ_0$, $ξ_2$, $ξ_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 65\% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35\%, which leads to a strong tension in $|\varepsilon_K|$ at the $4.6σ\sim 4.2σ$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on QCD sum rules.

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arXiv2018

Update on $B\to D^\ast \ell \nu$ form factor at zero-recoil using the Oktay-Kronfeld action

We present an update on the calculation of $\bar{B}\to D^\ast \ell \bar{\nu}$ semileptonic form factor at zero recoil using the Oktay-Kronfeld bottom and charm quarks on $N_f=2+1+1$ flavor HISQ ensembles generated by the MILC collaboration. Preliminary results are given for two ensembles with $a\approx 0.12$ and $0.09$ fm and $M_\pi\approx 310$ MeV. Calculations have been done with a number of valence quark masses, and the dependence of the form factor on them is investigated on the $a\approx 0.12$ fm ensemble. The excited state is controlled by using multistate fits to the three-point correlators measured at 4--6 source-sink separations.

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arXiv2018

2018 Update on $\varepsilon_K$ with lattice QCD inputs

We present updated results for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $ξ_0$, $ξ_2$, $ξ_\text{LD}$, $F_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 70% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 30%, which leads to a strong tension in $|\varepsilon_K|$ at the $4σ$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on QCD sum rules.

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