We present our recent study of gluon spectra in lattice QCD at finite temperature [1]. In it we combine recent full QCD simulations with Nf=2+1+1 twisted mass flavors carried out by the tmft collaboration [2] with a novel Bayesian approach [3] to the reconstruction of general spectral functions. This method is directly applicable to gluon correlation functions fixed to Landau gauge, whose spectra exhibit positivity violation. In these spectra we observe the presence of a well defined quasi-particle peak at all investigated temperatures, which provides the means to extract a gluon dispersion relation. The corresponding in-medium gluon masses defined from its zero momentum limit are shown to exhibit a behavior qualitatively consistent with weak coupling expectations.

[1] E.-M. Ilgenfritz, Jan M. Pawlowski, A.R., A. Trunin arXiv:1701.08610
[2] F. Burger et. al. (tmft Collaboration) arXiv:1510.02262
[3] A.R. arXiv:1611.00482