Finite temperature gluon spectral functions from $N_f=2+1+1$ lattice QCD

We investigate gluon spectral functions at finite temperature in Landau gauge, based on a subset of lattice QCD ensembles with $N_f=2+1+1$ dynamical twisted mass quarks flavors, generated by the tmfT collaboration. Our study uses a novel Bayesian approach for the extraction of non-positive definite spectral functions, which for each binned spatial momentum takes into account the gluon correlation functions at all available discrete imaginary frequencies. The spectral functions are extracted at three different lattice spacing, where for each of them, a scan of temperatures around the crossover transition is carried out at fixed scale. We find indications for the existence of a well defined quasi-particle peak. Due to a relatively small number of imaginary frequencies available, we focus on the momentum and temperature dependence of the position of this spectral feature. This dispersion relation reveals different in-medium masses for longitudinal and transversal gluons at high temperatures, qualitatively consistent with weak coupling expectations.