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

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    $\begingroup$ as far as I know there is exact theoretical computation of gluball masses due to its non purturbative structure. There are numerical lattice simulations. If ever some one comes up with a theoretical calculation, Clay prize for mathematics for the Yang-Mills and Mass Gap problem awaits. $\endgroup$ – Prathyush Nov 20 '12 at 15:10
  • $\begingroup$ Bob, why did you ask this question? $\endgroup$ – user1504 Nov 20 '12 at 22:13
  • $\begingroup$ Cause I'm studying these things and there are not clear references... why? $\endgroup$ – La buba Nov 21 '12 at 17:51

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


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