Finite-temperature gluon spectral functions from

We investigate gluon correlation functions and spectral functions at finite temperature in Landau gauge on lattice QCD ensembles with $$N_f=2+1+1$$ dynamical twisted-mass quarks flavors, generated by the tmfT collaboration. They cover a temperature range from $$0.8\le T/T_C\le 4$$ using the fixed-scale approach. Our study of spectral properties is based on a novel Bayesian approach for the extraction of non-positive-definite spectral functions. For each binned spatial momentum we take into account the gluon correlation functions at all available discrete imaginary frequencies. Clear indications for the existence of a well defined quasi-particle peak are obtained. 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. The corresponding dispersion relation reveals different in-medium masses for longitudinal and transversal gluons at high temperatures, qualitatively consistent with weak coupling expectations