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

We explore the interactions between a quark anti-quark pair in a thermal medium based on lattice QCD ensembles with \(N_f = 2+1\) dynamical HISQ flavors. Our dataset spans the phenomenologically relevant temperature range between T=140MeV-2GeV based on lattice sizes \(N_\tau=10,12\) and \(16\), with an aspect ratio 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 is computed. We assess the information content in the correlation functions and deploy three complementary strategies to reconstruct spectral information: model fits, Padé approximation and the Bayesian BR method. Limitations of each approach are carefully assessed.