Apparent convergence in functional glueball calculations

We scrutinize the determination of glueball masses in pure Yang-Mills theory from functional equations, i.e. Dyson-Schwinger and Bethe-Salpeter equations. We survey the state-of-the-art input (dressed propagators and vertices) with an emphasis on the stability of the results under extensions of the employed truncations and explore the importance of different aspects of the bound state equations, focusing on the three lightest glueballs with $J^{PC} = 0^{++}$ , $0^{-+}$ and $2^{++}$ . As an important systematic extension compared to previous calculations we include two-loop diagrams in the Bethe-Salpeter kernels. In terms of the glueball spectrum we find only marginal mass shifts compared to previous results, indicating apparent convergence of the system. As a by-product, we also explore gauge invariance within a class of Landau-type gauges.