arXiv subjects

Hai-Tao Shu

Publications and source records attributed to Hai-Tao Shu.

At least 19 recordsLinked to original sources

arXiv2026

Gradient Flow for the Jet Transport Coefficient: A Quenched Lattice Benchmark

We apply the gradient-flow framework to determine the nonperturbative medium contribution to the jet transport coefficient $\hat q$ using quenched lattice QCD in the temperature range $0.76T_c \leq T \leq 2.25T_c$. The calculation focuses on the leading-twist contribution at leading order for an asymptotically energetic quark propagating through a thermal pure-gluon plasma. In the infinite-energy limit, the operator-product expansion expresses $\hat q/T^3$ in pure gauge theory as the product of a perturbative short-distance coefficient and the entropy density $s/T^3$. The latter is determined from the gradient-flow energy-momentum tensor at three lattice spacings for each temperature and the former is estimated perturbatively at one-loop order. We find that $\hat q/T^3$ is strongly suppressed below $T_c$, rises rapidly across the deconfinement transition, and remains approximately constant at $\hat q/T^3\simeq1.1$ throughout the deconfined temperature range studied. This is statistically consistent with the previous quenched lattice determination based on a different renormalization procedure, providing a nontrivial validation of the gradient-flow framework for the jet transport coefficient. The systematic treatment of operator renormalization and matching provided by gradient flow becomes particularly important in full QCD, because the need to renormalize quark operators and account for their mixing with the gluonic sector can likewise be addressed within the same framework.

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arXiv2026

Static Quark-Antiquark Interactions Under Rotation

We study static quark--antiquark interactions in rotating SU(3) gluodynamics using quenched lattice simulations at imaginary angular velocity. At zero temperature, we extract the static potential from Wilson loops for quark--antiquark pairs aligned with the rotation axis, for transverse pairs with one source on the rotation axis, and for symmetric transverse pairs across the rotation axis. Within the present accuracy, no significant rotation dependence or anisotropy is observed in the zero-temperature potential. At finite temperature, imaginary rotation suppresses the color-averaged free energies obtained from Polyakov-loop correlators in both longitudinal and transverse geometries. Axial-diagonal comparisons are used to identify a bulk region where open-boundary artifacts are reduced. In this region, the large-distance longitudinal free-energy shift is well described by $ΔF_z(R_{xy})=A R_{xy}^2+B$. The transverse channels exhibit the same qualitative suppression, while their distance dependence additionally reflects the radial arrangement of the static sources and is compatible with a radial single-source free-energy shift in the bulk region. For the finite-temperature observables studied above $T_c$, the response weakens as the temperature is increased. These results provide lattice evidence for a position- and geometry-dependent response of bare static-source free energies to imaginary rotation in a gluonic medium.

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arXiv2026

Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}_2$ from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region $x\in[0.25,0.75]$ with controlled systematic uncertainties. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

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arXiv2026

Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD

We investigate the temperature dependence of the shear viscosity ($η$) and bulk viscosity ($ζ$) of the gluon plasma using lattice QCD over the range 0.76--2.25$\,T_c$, extending from below the transition temperature $T_c$ across the transition region and into the deconfined phase. At each temperature, we employ three large, fine lattices, which enables controlled continuum extrapolations of the energy-momentum tensor correlators. Using gradient flow together with a recently developed blocking technique, we achieve percent-level precision for these correlators, providing strong constraints for a model-based spectral analysis. Since the inversion to real-time information is intrinsically ill posed, we extract viscosities by fitting spectral functions whose ultraviolet behavior is matched to the best available perturbative result, while the infrared region is described by a Lorentzian transport peak. The dominant modeling uncertainty associated with the transport peak width is bracketed by varying it over a physically motivated range set by thermal scales. We find that the shear-viscosity-to-entropy-density ratio, $η/s$, exhibits a minimum near the transition temperature $T_c$ and increases for $T>T_c$, whereas the bulk-viscosity-to-entropy-density ratio, $ζ/s$, decreases monotonically over the entire temperature range studied.

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arXiv2026

Scale Setting and Strong Coupling Determination in the Gradient Flow Scheme for 2+1 Flavor Lattice QCD

We report on the determination of the gradient flow scales in $N_f=2+1$ QCD using highly improved staggered quark (HISQ) ensembles generated by the HotQCD Collaboration for bare gauge couplings ranging from $β= 6.423$ to $8.400$. Using bottomonium splittings, kaon decay constant, the decay constant of unmixed $η_s$ meson and the $ϕ$ meson mass we obtained the values of the gradient flow scales in physical units, $\sqrt{t_0} = 0.14428(48)$~fm and $w_0 = 0.17391(52)$~fm. Using the same physical inputs we revisit the determination of the potential $r_1$ scale and find $r_1 = 0.3112(24)$~fm. As a byproduct of our study we obtain the running of the gauge coupling in the gradient flow scheme. We find that within the uncertainties the running of the gradient flow coupling obtained on the lattice is compatible with the perturbative results up to flow radius $\sqrt{8 τ_F}=0.15$ fm.

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arXiv2025

Temperature Dependence of Heavy Quark Diffusion from (2+1)-flavor Lattice QCD

We present a lattice determination of the heavy-quark diffusion coefficient in (2+1)-flavor QCD with almost physical quark masses. The momentum and spatial diffusion coefficients are extracted for a wide temperature range, from $T=163$ MeV to $10$ GeV. The results are in agreement with previous works from the HotQCD collaboration, and show fast thermalization of the heavy quark inside the QGP. Near the chiral crossover temperature $T_c\simeq150$ MeV, our results are close to the AdS/CFT estimation computed at strong coupling.

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arXiv2025

Quark Transverse Spin-Momentum Correlation of the Nucleon from Lattice QCD: The Boer-Mulders Function

We present the first lattice QCD calculation of the quark transverse spin-momentum correlation, i.e., the naive time-reversal-odd Boer-Mulders function, of the nucleon, using large-momentum effective theory (LaMET). The calculation is carried out on an ensemble with lattice spacing $a=0.098$ fm and pion mass $338$ MeV, at various proton momenta up to $2.11$ GeV. We have implemented perturbative matching up to the next-to-next-to-leading order together with a renormalization-group resummation improvement. The result exhibits a decay behavior with increasing transverse separation $b_\perp$. We also compare the results in the nucleon and pion.

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arXiv2024

Quark Transverse Spin-Momentum Correlation of the Pion from Lattice QCD: The Boer-Mulders Function

We present the first lattice QCD calculation of the quark transverse spin-momentum correlation, i.e., the T-odd Boer-Mulders function, of the pion, using large-momentum effective theory (LaMET). The calculation is done at three lattice spacings $a=(0.098, 0.085, 0.064)$ fm and pion masses $\sim350$ MeV, with pion momenta up to $1.8$ GeV. The matrix elements are renormalized in a state-of-the-art scheme and extrapolated to the continuum and infinite momentum limit. We have implemented the perturbative matching up to the next-to-next-to-leading order and carried out a renormalization-group resummation. Our results provide valuable input for phenomenological analyses of the Boer-Mulders single-spin asymmetry.

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arXiv2024

Lattice $B$-field correlators for heavy quarks

We analyze the color-magnetic (or "$B$") field two-point function that encodes the finite-mass correction to the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$, using a range of gradient flow times for noise suppression and operator renormalization. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations to next-to-leading order of this correlation function, matching gradient-flowed correlators to MS-bar, are used to resolve nontrivial renormalization issues. We perform a spectral reconstruction based on perturbative model fits to estimate the coefficient $κ_B$ of the finite-mass correction to the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator with all renormalization issues incorporated at next-to-leading order, and is also applicable for actions with dynamical fermions.

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arXiv2024

SIMULATeQCD: A simple multi-GPU lattice code for QCD calculations

The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates to existing software. These challenges have to be balanced against constantly changing personnel. At the same time, there is a wide range of applications for HISQ fermions in QCD studies. This situation encourages the development of software featuring a HISQ action that is flexible, high-performing, open source, easy to use, and easy to adapt. In this technical paper, we explain the design strategy, provide implementation details, list available algorithms and modules, and show key performance indicators for SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. The code is publicly available on GitHub.

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arXiv2024

Transport and Connection to Heavy-ion Collisions via Heavy Flavor Probes

The heavy ion experiments in Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) are going through upgrade in the next five years, shifting their focus more on the hard processes in the new runs. One of the main goals is to draw a finer image for the quark gluon plasma (QGP). The heavy flavor probes , which witness the whole history of heavy ion collision are particularly sensitive to test the properties of QGP formed in such collisions. The lattice results for heavy flavor probes provide transport and phenomenological models crucial inputs to describe the experimental observations like the strong suppression of the nuclear modification factor $R_{AA}$ and the non-zero azimuthal anisotropy at low $p_T$. In the last two years we have seen significant advances in the lattice QCD studies of heavy flavor probes, including the in-medium quarkonium properties, the complex static quark-antiquark potential and the heavy quark diffusion from lattice simulations at nonzero temperature. These achievements substantially deepen our understanding of the fate of quarkonium, the screening/unscreening of the complex potential and the temperature and quark mass dependence of the heavy quark diffusion in thermal medium. In these proceedings, we review recent results and briefly discuss possible directions in these studies.

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arXiv2024

Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range 195 MeV $<T<$ 293 MeV, the spatial diffusion coefficients of the charm and bottom quarks are smaller than those obtained in phenomenological models that describe the $p_T$ spectra and elliptic flow of open heavy flavor hadrons.

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arXiv2023

Universality of the Collins-Soper kernel in lattice calculations

The Collins-Soper (CS) kernel is a nonperturbative function that characterizes the rapidity evolution of transverse-momentum-dependent parton distribution functions (TMDPDFs) and wave functions. In this Letter, we calculate the CS kernel for pion and proton targets and for quasi-TMDPDFs of leading and next-to-leading power. The calculations are carried out on the CLS ensemble H101 with dynamical $N_f=2+1$ clover-improved Wilson fermions. Our analyses demonstrate the consistency of different lattice extractions of the CS kernel for mesons and baryons, as well as for twist-two and twist-three operators, even though lattice artifacts could be significant. This consistency corroborates the universality of the lattice-determined CS kernel and suggests that a high-precision determination of it is in reach.

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arXiv2023

Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudo-scalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton.

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arXiv2023

Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320 MeV Pion Mass

We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks. For temperatures $195\,\mathrm{MeV}<T<352\,\mathrm{MeV}$, the heavy quark spatial diffusion coefficient is found to be significantly smaller than previous quenched lattice QCD and recent phenomenological estimates. The result implies very fast hydrodynamization of heavy quarks in the quark-gluon plasma created during ultrarelativistic heavy-ion collision experiments.

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arXiv2023

Viscosity of pure-glue QCD from the lattice

We calculate shear viscosity and bulk viscosity in SU(3) gauge theory on the lattice at $1.5 \,T_c$. The viscosities are extracted via a Kubo formula from the reconstructed spectral function which we determine from the Euclidean-time dependence of the corresponding channel of the energy-momentum tensor correlators. We obtain unprecedented precision for the correlators by applying gradient flow and blocking methods. The correlators are extrapolated to the continuum and then to zero flow time. To extract the viscosities we fit theoretically inspired models to the lattice data and crosscheck the fit results using the Backus Gilbert method. The final estimates for shear and bulk viscosity are $η/s = 0.15-0.48$ and $ζ/s = 0.017-0.059$.

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arXiv2023

Study of quarkonium in QGP from unquenched lattice QCD

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using $N_f=2+1$ flavors Highly Improved Staggered Quark (HISQ) action with physical strange quark mass $m_s$, and slightly heavy degenerate up and down quark masses $m_l=m_s/5$ that corresponds to $m_π\simeq 320$ MeV. Our results obtained at $T=220$ MeV and $T=251$ MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persist.

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arXiv2023

Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings $a=\{0.098,0.085,0.064,0.049\}$~fm and various pion masses ranging between $220$ and $350$ MeV, with proton momenta up to $2.8$ GeV. The result is non-perturbatively renormalized in the hybrid scheme with self renormalization which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.

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