Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations

We present our first results on a direct computation of the complex in-medium heavy quark potential from realistic lattice QCD simulations. Ensembles with $N_{\tau }=12$ from the HotQCD and TUMQCD collaboration offer unprecedented high statistics, those with $N_{\tau }=16$ unprecedented time resolution, making possible a robust extraction of the real part from the spectral functions of Wilson line correlators. To this end we deploy a combination of a Bayesian reconstruction (BR method), as well as a Pad'e-like approximation. We corroborate findings made on less realistic lattices that $\mathrm{R}\mathrm{e}[V]$ smoothly transitions from a confining to a screened behavior at high temperatures and its values lie close to the color singlet free energies. A finite value of the $\mathrm{I}\mathrm{m}[V]$ is observed in the quark-gluon-plasma phase.