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 the gluon propagator from (gauge-fixed) lattice calculations. We obtain ground state masses of $1.8\,\text{GeV}$ and $2.4\,\text{GeV}$ for the scalar and pseudoscalar glueballs, respectively, and $2.4\,\text{GeV}$ and $3.7\,\text{GeV}$ 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 $3.5\,\text{GeV}$ and $4.1\,\text{GeV}$. We also find that the quality of the results hinges crucially on the self-consistency of the employed input.