We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320 MeV. 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.

We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5T_c$. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations of this correlation function under Wilson flow are used to enhance the extrapolations of the nonperturbative lattice correlator. The final estimate for the continuum correlator at zero flow time largely agrees with one obtained from a previous study using the multilevel algorithm. We perform a spectral reconstruction based on perturbative model fits to estimate the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator and is also applicable for actions with dynamical fermions.

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 $195\mathrm{MeV}<T<293\mathrm{MeV}$, 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.

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 pseudoscalar 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.

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 paper, 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.

We calculate shear viscosity and bulk viscosity in $SU(3)$ gauge theory on the lattice at $1.5T_c$. 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 cross-check the fit results using the Backus-Gilbert method. The final estimates for shear and bulk viscosity are $\eta /s=0.15–0.48$ and $\zeta /s=0.017–0.059$.