arXiv subjects

Chik Him Wong

Publications and source records attributed to Chik Him Wong.

At least 19 recordsLinked to original sources

arXiv2026

Electric charge fluctuations from lattice QCD in the continuum limit

Electric charge fluctuations $χ_n^Q$ allow comparisons between theory and experiment, but are elusive on the lattice due to severe cutoff effects. We use a 4HEX action to obtain $χ_2^Q$ and, for the first time ever, $χ_4^Q$ in the continuum limit. We find disagreement with the hadron resonance gas (HRG) model, which we cannot explain with finite volume effects. We include light meson interactions in the HRG model via the S-matrix, reducing the tension for $χ_4^Q$, but worsening the agreement for $χ_2^Q$. We propose measuring the ratio $χ_4^Q/χ_2^Q$ at the LHC to investigate this tension.

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arXiv2026

Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($μ_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $μ_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $μ_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $μ_B\approx500$~MeV.

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arXiv2025

Finite density lattice QCD without extrapolations

Finite density lattice QCD usually relies on extrapolations in baryon chemical potential ($μ_B$), be it Taylor expansion, T' expansion (\cite{Borsanyi:2021sxv}) or analytical continuation. However, their range of validity is difficult to control. In the canonical formulation, the baryon density is the parameter of the system, not $μ_B$. Here we demonstrate that we can access finite density QCD in the canonical formulation with physical quark masses. We present first results with both the strangeness ($n_S$) and baryon ($n_B$) densities as parameters. Specifically, we compute the QCD pressure and chemical potentials as functions of $n_B$ and $n_S$. Our computations rely on high-statistics simulations with 2+1 4HEX-staggered fermions.

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arXiv2025

Finite density QCD phase structure from strangeness fluctuations

Charting the phase diagram of Quantum Chromodynamics (QCD) at large density is a challenging task due to the complex action problem in lattice simulations. Through simulations at imaginary baryon chemical potential $μ_B$ we observe that, if the strangeness neutrality condition is imposed, both the strangeness chemical potential $μ_S/μ_B$ and the strangeness susceptibility $χ_2^S$ take on constant values at the chiral transition for varying $μ_B$. We present new lattice data to extrapolate contours of constant $μ_S/μ_B$ or $χ_2^S$ to finite baryon chemical potential. We argue that they are good proxies for the QCD crossover because, as we show, they are only mildly influenced by criticality and by finite volume effects. We obtain continuum limits for these proxies up to $μ_B = 400$ MeV, through a next-to-next-to-leading order (N$^2$LO) Taylor expansion based on large-statistics data on $16^3 \times 8$, $20^3 \times 10$ and $24^3 \times 12$ lattices with our 4HEX improved staggered action. We show that these are in excellent agreement with existing results for the chiral transition and, strikingly, also with analogous contours obtained with the hadron resonance gas (HRG) model. On the $16^3 \times 8$ lattice, we carry out the expansion up to next-to-next-to-next-to-next-to-leading order (N$^4$LO), and extend the extrapolation beyond $μ_B=500$ MeV, again finding perfect agreement with the HRG model. This suggests that the crossover line constructed from this proxy starts deviating from the chemical freeze-out line near $μ_B\approx500$ MeV, as expected but not yet observed.

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arXiv2025

High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on $16^3 \times 8$ lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero, and fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-Weiss periodicity, which are exact properties of the QCD free energy. We use this ansatz to estimate the position of Lee-Yang zeros in the complex chemical potential plane. The temperature dependence of the imaginary part of the Lee-Yang zeros is then fitted with ansätze motivated by the universal behavior of the free energy near a 3D Ising critical point. In principle, this allows one to estimate the temperature of the critical endpoint. We consider several sources of systematic errors. On this single lattice spacing we find that with $84\%$ probability, the chiral critical endpoint is either below $103$~MeV temperature or it does not exist. We also identify some caveats of the method, which do not disappear even with the extremely high statistics of this present study. We discuss to what extent these can be eliminated by future high statistics lattice analyses.

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arXiv2025

Lattice QCD constraints on the critical point from an improved precision equation of state

In this Letter we employ lattice simulations to search for the critical point of quantum chromodynamics (QCD). We search for the onset of a first order QCD transition on the phase diagram by following contours of constant entropy density from imaginary to real chemical potentials under conditions of strangeness neutrality. We scan the phase diagram and investigate whether these contours meet to determine the probability that the critical point is located in a certain region on the $T-μ_B$ plane. To achieve this we introduce a new, continuum extrapolated equation of state at zero density with improved precision using lattices with $N_τ=8,10,12,16$ timeslices, and supplement it with new data at imaginary chemical potential. The current precision allows us to exclude, at the $2σ$ level, the existence of a critical point at $μ_B < 450$~MeV.

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arXiv2025

Search for a Lee-Yang edge singularity in high-statistics Wuppertal-Budapest data

Near a critical endpoint the Lee-Yang edge singularity approaches the real axis in the complex chemical potential plane. In the vicinity of the critical point the functional form of this approach depends on the universality class. Assuming a three dimensional Ising critical point in the QCD phase diagram the location of the critical endpoint can be extrapolated provided that the position of the Lee-Yang edge singularity is known at multiple temperatures. A popular method to estimate the position of a singularity is to model the free energy as a rational function of the baryon chemical potential $μ_\text{B}$. The parameters of this model can be constrained by the cumulants of the net baryon density taken at $μ_\text{B}^2\leq0$ . Using high-statistics simulations on a lattice $16^3\times8$ by the Wuppertal-Budapest Collaboration we estimate the location of the closest singularity in the QCD phase diagram. We also compare various models for the functional form of the free energy and discuss the predictive power of this approach.

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arXiv2025

Portable Lattice QCD implementation based on OpenCL

The presence of GPU from different vendors demands the Lattice QCD codes to support multiple architectures. To this end, Open Computing Language (OpenCL) is one of the viable frameworks for writing a portable code. It is of interest to find out how the OpenCL implementation performs as compared to the code based on a dedicated programming interface such as CUDA for Nvidia GPUs. We have developed an OpenCL backend for our already existing code of the Wuppertal-Budapest collaboration. In this contribution, we show benchmarks of the most time consuming part of the numerical simulation, namely, the inversion of the Dirac operator. We present the code performance on the JUWELS and LUMI Supercomputers based on Nvidia and AMD graphics cards, respectively, and compare with the CUDA backend implementation.

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arXiv2024

QCD deconfinement transition line up to $μ_B=400$ MeV from finite volume lattice simulations

The QCD cross-over line in the temperature ($T$) -- baryo-chemical potential ($μ_B$) plane has been computed by several lattice groups by calculating the chiral order parameter and its susceptibility at finite values of $μ_B$. In this work we focus on the deconfinement aspect of the transition between hadronic and Quark Gluon Plasma (QGP) phases. We define the deconfinement temperature as the peak position of the static quark entropy ($S_Q(T,μ_B)$) in $T$, which is based on the renormalized Polyakov loop. We extrapolate $S_Q(T,μ_B)$ based on high statistics finite temperature ensembles on a $16^3\times 8$ lattice to finite density by means of a Taylor expansion to eighth order in $μ_B$ (NNNLO) along the strangeness neutral line. For the simulations the 4HEX staggered action was used with 2+1 flavors at physical quark masses. In this setup the phase diagram can be drawn up to unprecedentedly high chemical potentials. Our results for the deconfinement temperature are in rough agreement with phenomenological estimates of the freeze-out curve in relativistic heavy ion collisions. In addition, we study the width of the deconfinement crossover. We show that up to $μ_B \approx 400$ MeV, the deconfinement transition gets broader at higher densities, disfavoring the existence of a deconfinement critical endpoint in this range. Finally, we examine the transition line without the strangeness neutrality condition and observe a hint for the narrowing of the crossover towards large $μ_B$.

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arXiv2024

Chiral and deconfinement properties of the QCD crossover have a different volume and baryochemical potential dependence

The crossover from hadronic to quark matter is understood to be both a deconfinement as well as a chiral symmetry restoring transition. Here, we study observables related to both aspects using lattice simulations: the Polyakov loop and its derivatives and the chiral condensate and its derivatives. At zero baryochemical potential, and infinite volume, the chiral and deconfinement crossover temperatures almost agree. However, chiral and deconfinement related observables have a qualitatively different chemical potential and volume dependence. In general, deconfinement related observables have a milder volume dependence. Furthermore, while the deconfinement transition appears to get broader with increasing $μ_B$, the width as well as the strength of the chiral transition is approximately constant. Our results are based on simulations at zero and imaginary chemical potentials using 4stout-improved staggered fermions with $N_τ=12$ time-slices and physical quark masses.

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arXiv2024

First dynamical simulations with minimally doubled fermions

For thermodynamics studies it is desirable to simulate two degenerate flavors and retain at least a remnant of the chiral symmetry. Staggered fermions can achieve this at the cost of rooting the determinant. Rooting can be avoided using minimally doubled fermions. This discretization describes two degenerate quark flavors while explicitly breaking hyper-cubic symmetry, thus, requiring additional counter-terms. We use one particular formulation of minimally doubled fermions called the Kirsten-Wilczek action and mitigate lattice artifacts by improving the spatial derivatives in the Dirac operator. In this pilot study we determine the counter-terms non-perturbatively to facilitate proper dynamical simulations.

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arXiv2024

Renormalization of Karsten-Wilczek Quarks on a Staggered Background

The Karsten-Wilczek action is a formulation of minimally doubled fermions on the lattice. It explicitly breaks hypercubic symmetry and introduces three counterterms with respective bare parameters. We present a tuning of the bare parameters of the Karsten-Wilczek action on staggered configurations at the physical point. We study the magnitude of the taste-splitting as a function of the lattice spacing.

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arXiv2024

Finite volume effects near the chiral crossover

The effect of a finite volume presents itself both in heavy ion experiments as well as in recent model calculations. The magnitude is sensitive to the proximity of a nearby critical point. We calculate the finite volume effects at finite temperature in continuum QCD using lattice simulations and set the focus on the vicinity of the chiral crossover. We investigate the impact of finite volumes at zero and small chemical potentials on the QCD transition through the chiral observables.

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arXiv2023

Continuum extrapolated high order baryon fluctuations

Fluctuations play a key role in the study of QCD phases. Lattice QCD is a valuable tool to calculate them, but going to high orders is challenging. Up to the fourth order, continuum results are available since 2015. We present the first continuum results for sixth order baryon fluctuations for temperatures between $T=130 - 200$ MeV, and eighth order at $T=145$ MeV in a fixed volume. We show that for $T \leq 145$ MeV, relevant for criticality search, finite volume effects are under control. Our results are in sharp contrast with well known results in the literature obtained at finite lattice spacing.

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arXiv2023

Can rooted staggered fermions describe nonzero baryon density at low temperatures?

Research on the QCD phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential $μ_B$ predict a sharp rise in the baryon density at low temperatures and $μ_B \gtrsim 3 m_π/2$, where $m_π$ is the Goldstone pion mass. We elucidate the nature of the non-analyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this non-analytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the non-analyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at $μ_B=0$. The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram.

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arXiv2023

Toward a novel determination of the strong QCD coupling at the Z-pole

We test here our recently introduced new lattice method for the $β$-function defined over infinite Euclidean space-time in the continuum from scale changes generated by infinitesimal or finite steps of the renormalized gauge coupling on the gradient flow. Harlander and Neumann calculated in this scheme the three-loop approximation to the continuum $β$-function. Our goal is the nonperturbative lattice implementation of the scheme which we tested originally in the chiral limit of the sextet model and in multi-flavor QCD with ten and twelve flavors of massless fermions. Results are reported here in the SU(3) Yang-Mills gauge sector without dynamical fermions and in ten-flavor QCD with massless femions. The three-loop gradient flow based $β$-function of Harlander and Neumann is used to connect the $Λ_{\overline{\rm MS}}$ scale of the SU(3) Yang-Mills gauge theory with the nonperturbative flow time scale $t_0$, or the equivalent Sommer scale $r_0$. Similarly, the $Λ_{\overline{\rm MS}}$ scale is connected with a selected nonperturbative scale in the ten-flavor theory, a pilot study of our new lattice based nonperturbative $β$-function for high precision determination of the strong coupling $α_s$ at the Z-boson pole in QCD with three massless fermion flavors. This goal is an important alternative to results from the finite volume based step $β$-function of the Alpha collaboration. Work is ongoing on direct application of the method to QCD with three massless fermion flavors.

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arXiv2022

Equation of state of a hot-and-dense quark gluon plasma: lattice simulations at real $μ_B$ vs. extrapolations

The equation of state of the quark gluon plasma is a key ingredient of heavy ion phenomenology. In addition to the traditional Taylor method, several novel approximation schemes have been proposed with the aim of calculating it at finite baryon density. In order to gain a pragmatic understanding of the limits of these schemes, we compare them to direct results at $μ_B>0$, using reweighting techniques free from an overlap problem. We use 2stout improved staggered fermions with 8 time-slices and cover the entire RHIC BES range in the baryochemical potential, up to $μ_B/T=3$.

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arXiv2022

From ten-flavor tests of the $β$-function to $α_s$ at the Z-pole

New tests are applied to two $β$-functions of the much-discussed BSM model with ten massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The renormalization scheme of the two $β$-functions is defined on the gauge field gradient flow in respective finite or infinite physical volumes at zero lattice spacing. Recently published results in the ten-flavor theory led to indicators of an infrared fixed point (IRFP) in the finite-volume step $β$-function in the strong coupling regime of the theory arXiv:2004.00754. We analyze our substantially extended set of ten-flavor lattice ensembles at strong renormalized gauge couplings and find no evidence or hint for IRFP in the finite-volume step $β$-function within controlled lattice reach. We also discuss new ten-flavor tests of the recently introduced lattice definition and algorithmic implementation of the $β$-function defined on the gradient flow of the gauge field over infinite Euclidean space-time in the continuum. Originally we introduced this new algorithm to match finite-volume step $β$-functions in massless near-conformal gauge theories with the infinite-volume $β$-function reached in the chiral limit from small fermion mass deformations of spontaneous chiral symmetry breaking. Results from the lattice analysis of the ten-flavor infinite-volume $β$-function are consistent with the absence of IRFP from our step $β$-function based analysis. We make important contact at weak coupling in infinite volume with gradient flow based three-loop perturbation theory, serving as a first pilot study toward the long-term goal of developing alternate approach to the determination of the strong coupling $α_s$ at the Z-boson pole in QCD.

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