We analyze heavy quark free energies in 2-flavor QCD at finite temperature and the corresponding heavy quark potential at zero temperature. Static quark-antiquark sources in color singlet, octet and color averaged channels are used to probe thermal modifications of the medium. The temperature dependence of the running coupling, ${\alpha }_{qq}(r,T)$, is analyzed at short and large distances and is compared to zero temperature as well as quenched calculations. In part, we also compare our results to recent findings in 3-flavor QCD. We find that the characteristic length scale below which the running coupling shows almost no temperature dependence is almost twice as large as the Debye screening radius. Our analysis supports recent findings which suggest that ${\chi }_c$ and ${\psi }^{\prime }$ are suppressed already at the (pseudo) critical temperature and thus give a probe for quark gluon plasma production in heavy ion collision experiments, while $J/\psi$ may survive the transition and will dissolve at higher temperatures.

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 investigate the temperature dependence of the thermal dilepton rate and the electrical conductivity of the gluon plasma at temperatures of 1.1, 1.3, and $1.5T_c$ in quenched QCD. Making use of nonperturbatively clover-improved Wilson valence quarks allows for a clean extrapolation of the vector meson correlation function to the continuum limit. We found that the vector correlation function divided by $T^3$ is almost temperature independent in the current temperature window. The spectral functions are obtained by ${\chi }^2$ fitting of phenomenologically inspired Ansätze for the spectral function to the continuum extrapolated correlator data, where the correlations between the data points have been included. Systematic uncertainties arising from varying the Ansätze motivated from strong coupling theory as well as perturbation theory are discussed and estimated. We found that the electrical conductivity of the hot medium, related to the slope of the vector spectral function at zero frequency and momentum, is $0.2C_{em}\lesssim \sigma /T\lesssim 0.7C_{em}$ for $T=1.1T_c$ and $0.2C_{em}\lesssim \sigma /T\lesssim 0.4C_{em}$ for the higher temperatures. The dilepton rates and soft photon rates, resulting from the obtained spectral functions, show no significant temperature dependence, either.

We present the finite temperature spectra of both bottomonium and charmonium, obtained from a consistent lattice QCD based potential picture. Starting point is the complex in-medium potential extracted on full QCD lattices with dynamical u,d and s quarks, generated by the HotQCD collaboration. Using the generalized Gauss law approach, vetted in a previous study on quenched QCD, we fit Re[V] with a single temperature dependent parameter m_D, the Debye screening mass, and confirm the up to now tentative values of Im[V]. The obtained analytic expression for the complex potential allows us to compute quarkonium spectral functions by solving an appropriate Schrödinger equation. These spectra exhibit thermal widths, which are free from the resolution artifacts that plague direct reconstructions from Euclidean correlators using Bayesian methods. In the present adiabatic setting, we find clear evidence for sequential melting and derive melting temperatures for the different bound states. Quarkonium is gradually weakened by both screening (Re[V]) and scattering (Im[V]) effects that in combination lead to a shift of their in-medium spectral features to smaller frequencies, contrary to the mass gain of elementary particles at finite temperature.

We update lattice QCD results for second order cumulants of conserved charge fluctuations and correlations at nonzero temperature and vanishing values of the conserved charge chemical potentials. We compare these results to hadron resonance gas calculations with and without excluded volume terms as well as S-matrix results in the hadronic phase of QCD and comment on their current limitations. We, furthermore, use these results to characterize thermal conditions in the vicinity of the pseudocritical line of the chiral transition in QCD. We argue that the ratio of strange to baryon chemical potentials is a robust observable that, on the one hand, deviates only little from hadron resonance gas results, but, on the other hand, is very sensitive to the spectrum of strange baryon resonances.

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.