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We explore the interactions between a quark anti-quark pair in a thermalmedium based on lattice QCD ensembles with $N_f = 2+1$ dynamical HISQ flavors.Our dataset spans the phenomenologically relevant temperature range betweenT=140MeV-2GeV based on lattice sizes $N_\tau=10,12$ and $16$, with an aspectratio of $N_\sigma/N_\tau=4$. The peak position $\Omega$ and the width $\Gamma$of the spectral function of Wilson-line correlators in Coulomb gauge iscomputed. We assess the information content in the correlation functions anddeploy three complementary strategies to reconstruct spectral information:model fits, Pad\'e approximation and the Bayesian BR method. Limitations ofeach approach are carefully assessed.

In-medium static quark potential from spectral functions on realistic HISQ ensembles