arXiv subjects

Ting-Wai Chiu

Publications and source records attributed to Ting-Wai Chiu.

At least 19 recordsLinked to original sources

arXiv2026

Renormalization of meson susceptibilities and RG-invariant symmetry ratios in QCD

We analyze the ultraviolet divergence structure of meson susceptibilities in finite-temperature QCD, for lattice formulations with exact chiral symmetry. The bare susceptibility separates into additive divergences and a multiplicative renormalization $Z_\Gamma^{2}$. The additive divergences are temperature-independent, and are removed by the temperature subtraction. They consist of the leading power divergence $\alpha_\Gamma/(2a^2)$ from the identity operator, together with a mass-dependent logarithmic term $\propto m^2\ln(1/(am))$. Exact chiral symmetry forbids all mass-dependent \emph{power} divergences of the susceptibility. The multiplicative factor $Z_\Gamma^{2}$ has a logarithmic dependence on the lattice spacing, controlled by the operator anomalous dimension. We show that the symmetry ratio $\kappa_{AB} = (\chi_A^{\rm reg} - \chi_B^{\rm reg})/ (\chi_A^{\rm reg} + \chi_B^{\rm reg})$, built from temperature-subtracted susceptibilities of symmetry partners, is exactly renormalization-group invariant and scheme-independent. The additive divergence is removed by the subtraction, and the multiplicative factor cancels through the equality $Z_A = Z_B$. This equality holds for any number of flavors and any quark masses in a mass-independent scheme, unaffected by spontaneous symmetry breaking or the $U(1)_A$ anomaly. We derive the complete $Z$-factor chains for all meson channels and contrast the divergence structure with that of Wilson fermions, for which the explicit chiral-symmetry breaking induces a chiral-odd power-divergent mixing and spoils the equality $Z_A = Z_B$ on which the construction relies.

hep-lat↗

arXiv2026

RG-Invariant Symmetry Ratio for QCD: A Study of $U(1)_A$ and Chiral Symmetry Restoration

We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio $\kappa_{AB}$, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ $\kappa_{AB}$ to investigate the relative strength of $SU(2)_L \times SU(2)_R$ chiral symmetry and $U(1)_A$ axial symmetry breaking in $N_f=2+1+1$ lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164--385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the $U(1)_A$-sensitive scalar--pseudoscalar channel ($\kappa_{PS}$), probing the $\pi$--$\delta$ system; the $SU(2)_L \times SU(2)_R$-sensitive vector--axial-vector channel ($\kappa_{VA}$), probing the $\rho$--$a_1$ system; and an additional $U(1)_A$-sensitive tensor vector--axial-tensor vector channel ($\kappa_{TX}$), probing the $\rho_T$--$b_1$ system. At finite lattice spacing, we observe a clear hierarchy $\kappa_{PS} > \kappa_{VA} > \kappa_{TX}$. A controlled continuum extrapolation reveals that this hierarchy collapses, with all three symmetry-breaking strengths becoming statistically indistinguishable within our precision. This result provides a new, model-independent benchmark from a chirally symmetric lattice action. Our findings indicate that in the continuum limit the $SU(2)_L \times SU(2)_R$ and $U(1)_A$ channels in the nonsinglet sector reach degeneracy at the same temperature, already at the lowest simulated point of $164$~MeV, so that the two symmetries restore concurrently near the chiral crossover rather than at parametrically separated scales.

hep-lat↗

arXiv2025

Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks

We investigate the spatial $ z $-correlators of meson operators in $ N_f=2+1+1+1 $ lattice QCD with optimal domain-wall quarks across eight temperatures ranging from 325 to 3250 MeV. The meson operators include a complete set of Dirac bilinears for ten flavor combinations. Our findings reveal a hierarchical restoration of chiral symmetry in QCD with $ (u, d, s, c, b) $ quarks, progressing sequentially from $ SU(2)_L \times SU(2)_R \times U(1)_A $ to $ SU(3)_L \times SU(3)_R \times U(1)_A $, then to $ SU(4)_L \times SU(4)_R \times U(1)_A $, and finally to $ SU(5)_L \times SU(5)_R \times U(1)_A $ as the temperature increases. Additionally, we explore the emergence of the $ SU(2)_{CS} $ chiral-spin symmetry and compare the temperature windows for all flavor combinations. Our results indicate that the temperature windows for the emergent $SU(2)_{CS}$ symmetry are primarily dominated by the $ \bar{u} b $ and $ \bar{s} b $ sectors.

hep-lat↗

arXiv2024

Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD

The spatial $z$-correlators of meson operators in $N_f=2+1+1$ lattice QCD with optimal domain-wall quarks at the physical point are studied for seven temperatures in the range of 190-1540 MeV. The meson operators include a complete set of Dirac bilinears (scalar, pseudoscalar, vector, axial vector, tensor vector, and axial-tensor vector), and each for six flavor combinations ($\bar u d$, $\bar u s$, $\bar s s$, $\bar u c$, $\bar s c$, and $\bar c c$). In Ref. \cite{Chiu:2023hnm}, we focused on the meson correlators of $u$ and $d$ quarks, and discussed their implications for the effective restoration of $SU(2)_L \times SU(2)_R$ and $U(1)_A$ chiral symmetries, as well as the emergence of approximate $SU(2)_{CS}$ chiral spin symmetry. In this work, we extend our study to meson correlators of six flavor contents, and first observe the hierarchical restoration of chiral symmetries in QCD, from $SU(2)_L \times SU(2)_R \times U(1)_A $ to $SU(3)_L \times SU(3)_R \times U(1)_A $, and to $SU(4)_L \times SU(4)_R \times U(1)_A $, as the temperature is increased from 190 MeV to 1540 MeV. Moreover, we compare the temperature windows for the emergence of the approximate $SU(2)_{CS}$ symmetry in light and heavy vector mesons, and find that the temperature windows are dominated by the $(\bar u c, \bar s c, \bar c c)$ sectors.

hep-lat↗

arXiv2023

Symmetries of meson correlators in high temperature QCD with physical $(u/d, s, c)$ domain-wall quarks

The correlation function of meson interpolators in $N_f=2+1+1$ lattice QCD with optimal domain-wall quarks at the physical point are studied for six temperatures in the range $ T \sim$ 190-770 MeV. The meson interpolators include a complete set of Dirac bilinears, and each for six combinations of quark flavors. In this paper, we focus on the meson correlators of $u$ and $d$ quarks, and discuss their implications for the effective restoration of $U(1)_A$ and $SU(2)_L \times SU(2)_R$ chiral symmetries, as well as the emergence of the approximate $SU(2)_{CS}$ chiral spin symmetry.

hep-lat↗

arXiv2022

Topological susceptibility in finite temperature QCD with physical $(u/d, s, c)$ domain-wall quarks

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150 $ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ χ_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $χ_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $ MeV, we extract the topological susceptibility $χ_t(T)$ in the continuum limit. To compare our results with others, we survey the continuum extrapolated $χ_t(T)$ in lattice QCD with $N_f=2+1(+1)$ dynamical quarks at/near the physical point, and discuss their discrepancies. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.

hep-lat↗

arXiv2022

Finite temperature QCD with physical $(u/d, s, c)$ domain-wall quarks

In order to understand the role of QCD in the early universe, we perform hybrid Monte-Carlo simulation of lattice QCD with $N_f=2+1+1$ optimal domain-wall quarks at the physical point, on the $64^3 \times (6,8,10,12,16,20,64)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this Proceeding, we present our first result on the topological susceptibility of the QCD vacuum. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ χ_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $χ_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $~MeV, we extract the topological susceptibility $χ_t(T)$ in the continuum limit.

hep-lat↗

arXiv2022

ImageMech: From image to particle spring network for mechanical characterization

The emerging demand for advanced structural and biological materials calls for novel modeling tools that can rapidly yield high-fidelity estimation on materials properties in design cycles. Lattice spring model (LSM), a coarse-grained particle spring network, has gained attention in recent years for predicting the mechanical properties and giving insights into the fracture mechanism with high reproducibility and generalizability. However, to simulate the materials in sufficient detail for guaranteed numerical stability and convergence, most of the time a large number of particles are needed, greatly diminishing the potential for high-throughput computation and therewith data generation for machine learning frameworks. Here, we implement CuLSM, a GPU-accelerated CUDA C++ code realizing parallelism over the spring list instead of the commonly used spatial decomposition, which requires intermittent updates on the particle neighbor list. Along with the image-to-particle conversion tool Img2Particle, our toolkit offers a fast and flexible platform to characterize the elastic and fracture behaviors of materials, expediting the design process between additive manufacturing and computer-aided design. With the growing demand for new lightweight, adaptable, and multi-functional materials and structures, such tailored and optimized modeling platform has profound impacts, enabling faster exploration in design spaces, better quality control for 3D printing by digital twin techniques, and larger data generation pipelines for image-based generative machine learning models.

cond-mat.mtrl-sci↗

arXiv2020

Beauty mesons in $N_f=2+1+1+1 $ lattice QCD with exact chiral symmetry

We present the first study of $N_f=2+1+1+1$ lattice QCD with domain-wall quarks. The $(b, c, s)$ quarks are physical, while the $(u, d)$ quarks are heavier than their physical masses, with the pion mass $ \sim 700 $ MeV. The gauge ensemble is generated by hybrid Monte Carlo simulation with the Wilson gauge action for the gluons, and the optimal domain-wall fermion action for the quarks. Using point-to-point quark propagators, we measure the time-correlation functions of quark-antiquark meson interpolators with quark contents $\bar b b$, $\bar b c$, $\bar b s$, and $ \bar c c$, and obtain the masses of the low-lying mesons. They are in good agreement with the experimental values, plus some predictions which have not been observed in experiments. Moreover, we also determine the masses of $(b, c, s)$ quarks.

hep-lat↗

arXiv2020

First study of $N_f=2+1+1$ lattice QCD with physical domain-wall quarks

Using 10-16 units of Nvidia DGX-1, we have generated the first gauge ensemble for $N_f=2+1+1$ lattice QCD with physical $(u/d, s, c)$ domain-wall quarks, on the $ 64^4 $ lattice with lattice spacing $a \sim 0.064 $ fm ($ L > 4 $ fm, and $ M_πL > 3 $). The salient feature of this gauge ensemble is that the chiral symmetry is preserved to a high precision and all topological sectors are sampled ergodically. In this paper, we present the first results of the topological susceptibility and the ground-state hadron mass spectra.

hep-lat↗

arXiv2019

Topological susceptibilty in lattice QCD with exact chiral symmetry -- the index of overlap-Dirac operator versus the clover topological charge in Wilson flow

Using an ensemble of 535 gauge configurations (on the $24^4 \times 48 $ lattice with $ a \simeq 0.06 $~fm and $ M_π \simeq 260 $~MeV) which are generated by hybrid Monte Carlo (HMC) simulation of $N_f=2$ lattice QCD with the optimal domain-wall quark, we compute the index of the overlap-Dirac operator, and also measure the clover topological charge in the Wilson flow, $Q_{\text{clover}}(t) $, by integrating the flow equation from $ t = 0 $ to $ t = 128 $ with $δt = 0.01 $. We observe that $Q_{\text{clover}}(t) $ of each configuration converges to a value close to an integer, and its nearest integer $Q_c(t) = \text{round} [Q_{\text{clover}}(t)] $ becomes invariant for $ t \ge t_c $, with the $ \max\{t_c \} \sim 77 $ for all 535 configurations. For each configuration, we compare the asymptotically-invariant $ Q_c $ with the index of overlap-Dirac operator at $t=0$. It turns out that there are 167 configurations with $Q_c \ne \text{index}(D_{o}) $, amounting to $31.2\%$ of the total 535 configurations. However, the histograms of $ Q_c $ and $ \text{index}(D_o) $ are almost identical. Consequently, the topological susceptibility using the asymptotically-invariant $ Q_c $ agrees with that using the index of overlap-Dirac operator at $ t=0 $. This implies that the topological susceptibility in lattice QCD with exact chiral symmetry can be obtained from the asymptotically-invariant $ Q_c $ in the Wilson flow.

hep-lat↗

arXiv2019

New $N_f=2$ Pseudofermion Action for Monte-Carlo Simulation of Lattice Field Theory with Domain-Wall Fermions

We construct a novel $ N_f = 2 $ pseudofermion action for Monte-Carlo simulation of lattice gauge theory with domain-wall fermions (DWF), of which the effective four-dimensional lattice Dirac operator is equal to the overlap-Dirac operator with the argument of the sign function equal to $ H = c γ_5 D_w (1 + d D_w)^{-1} $, where $ c $ and $ d $ are parameters, and $D_w$ is the standard Wilson-Dirac operator plus a negative parameter $-m_0 \; (0 < m_0 < 2)$. This new action is particularly useful for the challenging simulations of lattice gauge theories with large $N_f = 2n $ DWF, on the large lattices, and in the strong-coupling regime.

hep-lat↗

arXiv2019

Improved study of the $β$-function of $SU(3)$ gauge theory with $N_f = 10 $ massless domain-wall fermions

I perform an improved study of the $β$-function of $ SU(3) $ lattice gauge theory with $N_f=10$ massless optimal domain-wall fermions in the fundamental representation, which serves as a check to what extent the scenario in the previous work [arXiv:1603.08854; Proc. Sci. LATTICE2016 (2017) 228] is valid. In the finite-volume gradient flow scheme with $ c = \sqrt{8t}/L = 0.3 $, the renormalized couplings $g^2 (L,a) $ of four primary lattices ($ L/a = \{ 8, 10, 12, 16 \}$) are tuned (in $ 6/g_0^2 $) to the same $ g_c^2 $ with statistical error less than $0.5 \% $, in contrast to the previous work where $ g^2(L,a) $ were obtained by the cubic-spline interpolation. Then the renormalized couplings $ g^2(sL, a) $ of the scaled lattices ($ sL/a = \{16, 20, 24, 32\} $ with $s=2$) are computed at the same $ 6/g_0^2 $ of the corresponding primary lattices. Using the renormalized couplings of four lattice pairs $ (sL,L)/a = \{ (16,8), (20,10), (24,12), (32,16) \} $, the step-scaling $β$-function $ [g^2(sL,a) - g^2(L,a)]/\ln (s^2) $ is computed and extrapolated to the continuum limit $ β(s,g_c^2) $, as summarized in Table III. Based on the four data points of $ β(s,g_c^2) $ at $ g_c^2 = \{ 6.86(2), \ 6.92(3), \ 7.03(2), \ 7.16(2) \} $, I infer that the theory is infrared near-conformal, or conformal with the fixed-point $ g_*^2 = 7.55(36) $. This corrects the scenario in the previous work with $ g_*^2 \sim 7.0 $, and also suggests that the interpolation method cannot give a reliable determination of the $β$-function, especially in the regime close to the infrared fixed-point.

hep-lat↗

arXiv2018

Simulation of dynamical (u,d,s,c) domain-wall/overlap quarks at the physical point

We perform hybrid Monte-Carlo simulation of $N_f=2+1+1 $ lattice QCD with domain-wall quarks at the physical point. The simulation is carried out on the $ L^3 \times T = 64^3 \times 64 $ lattice with lattice spacing $a \sim 0.064 $ fm ($ L > 4 $ fm, and $ M_πL > 3 $), using the Nvidia DGX-1 (8 V100 GPUs interconnected by the NVLink). To attain the maximal chiral symmetry for a finite extent ($N_s=16$) in the fifth dimension, we use the optimal domain-wall fermion for the quark action, together with the exact one-flavor action for domain-wall fermion. We outline the salient features of our simulation (without topology freezing, and small residual mass), together with the preliminary result of the masses of $ π^\pm $, $ K^\pm $, and $ D^\pm $.

hep-lat↗

arXiv2017

Mass Spectra of $D_s$ and $Ω_c$ in Lattice QCD with $N_f= 2+1+1$ Domain-Wall Quarks

We perform hybrid Monte Carlo simulation of lattice QCD with $N_f=2+1+1 $ optimal domain-wall quarks on the $32^3 \times 64 $ lattice with lattice spacing $a \sim 0.06$ fm, and generate a gauge ensemble with physical $s$ and $c$ quarks, and pion mass $\sim 280 $ MeV. Using 2-quark (meson) and 3-quark (baryon) interpolating operators, the mass spectra of the lowest-lying states containing $s$ and $c$ quarks ($D_s$ and $Ω_c$) are extracted \cite{Chen:2017kxr}, which turn out in good agreement with the high energy experimental values, together with the predictions of the charmed baryons which have not been observed in experiments. For the five new narrow $Ω_c$ states observed by the LHCb Collaboration \cite{Aaij:2017nav}, the lowest-lying $Ω_c(3000)$ agrees with our predicted mass $3015(29)(34)$ MeV of the lowest-lying $Ω_c$ with $J^P = 1/2^{-}$. This implies that the $ J^P $ of $ Ω_c(3000) $ is $ 1/2^- $.

hep-lat↗

arXiv2017

Mass Preconditioning for the Exact One-Flavor Action in Lattice QCD with Domain-Wall Fermion

The mass-preconditioning (MP) technique has become a standard tool to enhance the efficiency of the hybrid Monte-Carlo simulation (HMC) of lattice QCD with dynamical quarks, for 2-flavors QCD with degenerate quark masses, as well as its extension to the case of one-flavor by taking the square-root of the fermion determinant of 2-flavors with degenerate masses. However, for lattice QCD with domain-wall fermion, the fermion determinant of any single fermion flavor can be expressed as a functional integral with an exact pseudofermion action $ ϕ^\dagger H^{-1} ϕ$, where $ H^{-1} $ is a positive-definite Hermitian operator without taking square-root, and with the chiral structure \cite{Chen:2014hyy}. Consequently, the mass-preconditioning for the exact one-flavor action (EOFA) does not necessarily follow the conventional (old) MP pattern. In this paper, we present a new mass-preconditioning for the EOFA, which is more efficient than the old MP which we have used in Refs. \cite{Chen:2014hyy,Chen:2014bbc}. We perform numerical tests in lattice QCD with $ N_f = 1 $ and $ N_f = 1+1+1+1 $ optimal domain-wall quarks, with one mass-preconditioner applied to one of the exact one-flavor actions, and we find that the efficiency of the new MP is more than 20\% higher than that of the old MP.

hep-lat↗

arXiv2017

Lattice QCD with $N_f = 2+1+1 $ domain-wall quarks

We perform hybrid Monte Carlo simulation of (2+1+1)-flavors lattice QCD with the optimal domain-wall fermion (which has the effective 4D Dirac operator exactly equal to the Zolotarev optimal rational approximation of the overlap Dirac operator). The gauge ensemble is generated on the $32^3 \times 64 $ lattice with the extent $ N_s = 16 $ in the fifth dimension, and with the plaquette gauge action at $ β= 6/g^2 = 6.20 $. The lattice spacing ($ a \simeq 0.063 $ fm) is determined by the Wilson flow, using the value $ \sqrt{t_0} = 0.1416(8) $ fm obtained by the MILC Collaboration for the $(2+1+1)$-flavors QCD. The masses of $s$ and $c$ quarks are fixed by the masses of the vector mesons $ ϕ(1020) $ and $ J/ψ(3097) $ respectively; while the mass of the $u/d$ quarks is heavier than their physical values, with the unitary pion mass $ M_π\simeq 280$ MeV (and $ M_πL \simeq 3 $). We compute the point-to-point quark propagators, and measure the time-correlation functions of meson and baryon interpolators. Our results of the mass spectra of the lowest-lying hadrons containing $ s $ and $ c $ quarks are in good agreement with the high energy experimental values, together with the predictions of the charmed baryons which have not been observed in experiments.

hep-lat↗

arXiv2016

The $β$-function of $SU(3)$ gauge theory with $ N_f = 10 $ massless fermions in the fundamental representation

We present the first study of the discrete $β$-function of the $ SU(3) $ gauge theory with 10 massless domain-wall fermions in the fundamental representation. The renormalized coupling is obtained by the finite-volume gradient flow scheme, and the discrete $β$-function is extrapolated to the continuum limit by the step-scaling method. Our result of the discrete $β$-function (with $ s = 2 $) suggests that this theory possesses an infrared fixed point around $ g_c^2 \sim 7.0 $ for $ c = \sqrt{8t}/L = 0.3 $.

hep-lat↗