From unphysical gluon and ghost propagators to physical glueball propagators (in the Gribov-Zwanziger picture): A not so trivial task?

During recent years, a good agreement was found between the analytical derivation and the numerical simulation of the Landau gauge gluon and ghost propagators. We mention the Schwinger-Dyson and Gribov-Zwanziger formalism for the analytical work. Although the agreement between several approaches is nice, these propagators do not correspond to the relevant physical degrees of freedom. In the case of pure gauge theories, one should start to study the glueball correlators. We shall try to explain why it looks like a hard challenge to go from the unphysical to the physical propagators in the case of the Gribov-Zwanziger theory (but similar conclusions might hold for other approaches giving similar propagators).