I think that, by now, it's understood that the gluon propagator in QCD has a dynamically generated mass. Ok, so my question is the following: where does the extra polarization degree of freedom come from? Or, asking in another way: suppose you try to define an S matrix for QCD, apart from the usual problems for doing so, would it be unitary? How?

In the case of a Higgs mechanism, it is clear that the extra degree of freedom comes from "eating" the Higgs, as they say. But and where does is come from in theories where the mass is dynamically generated?