Glueball mass in non-abelian Yang Mills theory

How can the glueball mass be calculated in Yang-Mills theory?

Answer

In principle one has to calculate the pole of correlation functions involving gauge invariant operators like $\text{Tr}F_{\mu\nu}F^{\mu\nu}$. The problem is that due to asymptotic freedom, QCD is not solvable perturbatively at low energies. This is why nonperturbative techniques like lattice QCD are used to calculate such spectra. A key achievement in this direction was the calculation of the glueball spectrum by Morningstar and Peardon: http://arxiv.org/abs/hep-lat/9901004.

Another approach would be holographic QCD, where glueballs are mapped from the Yang-Mills theory to a theory of gravity and are represented by graviton modes propagating in space. It is relatively easy to compute their spectra within this formalism, in good agreement with lattice results: http://arxiv.org/abs/hep-th/0003115

As side remark: it is notable that within holographic QCD and in particular the Sakai-Sugimoto model, it is possible to calculate glueball decay to various mesons, which might help with the experimental confirmation of glueballs: http://arxiv.org/abs/arXiv:0709.2208