Spectrum of scalar and pseudoscalar glueballs from functional methods

We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang-Mills theory using a parameter-free fully self-contained truncation of Dyson-Schwinger and Bethe-Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of $1.9\,\text{GeV}$ and $2.6\,\text{GeV}$ for the scalar and pseudoscalar glueballs, respectively, and $2.6\,\text{GeV}$ and $3.9\,\text{GeV}$ for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict masses for the second excited states at $3.7\,\text{GeV}$ and $4.3\,\text{GeV}$. The quality of the results hinges crucially on the self-consistency of the employed input. The masses are independent of a specific choice for the infrared behavior of the ghost propagator providing further evidence that this only reflects a nonperturbative gauge completion.