Thanks to a useful comment by Rafael Frigori (see here) I become aware of a series of beautiful papers by an Italian group at Universita’ della Calabria. I was mostly struck by a recent paper written by R. Fiore, R. Falcone, M. Gravina and A. Papa (see here) that appeared in Nuclear Physics B (see here). This paper belongs to a long series of works about the behavior of Yang-Mills theory at non-null temperature and its critical behavior. Indeed, using high-temperature expansion and Polyakov loops one arrives at the main conclusion that the ratio between the lowest and the higher state of the theory must be 3/2. This ratio depends on the universality class the theory belongs to and so, on the kind of effective theory one has in the proper temperature limit (below or above ). It should be said that, in order to get a proper verification of the above prediction, people use lattice computations. Fiore et al. use a lattice of points and, as all this kind of computations are done on lattices having such a dimension, one can cast some doubt about the fact that the true ground state of the theory is really hit. Indeed, this happens in all this kind of computations done to get a glueball spectrum that seem at odd with those giving the gluon propagator producing a lower screening mass at about 500 MeV (see my post here). A state at about 500 MeV is seen at accelerator facilities as resonance or f0(600) but is not predicted by any lattice computation. One of the reasons to reduce lattice volume is that one can reach higher values of granting the reaching of a non-perturbative regime, the one interesting for us.
What can we say about this ratio with our theory? We have put on arxiv a paper that answer this question (see here). These results were also presented at QCD 08 in Montpellier (see here). We assume that the cannot be seen at such small volumes but its excited state can be obtained. This implies that one can exchange the with the lowest state and as the higher one. Then this ratio gives exactly 3/2 as expected. We can conclude on the basis of this analysis that this ratio is the same independently on the temperature but, the one to be properly measured is given in the paper of Craig McNeile (see here) that gives close agreement between lattice and theoretical predictions.
So, we would like to see lattice computations of Yang-Mills spectra at lower lattice spacing and increased volumes granting in this way the proper value of the ground state. This is overwhelming important in view of the fact that no real understanding exists of the existence of the resonance with lattice computations. This will implies, as discussed above, a deeper understanding of the spectrum of the theory also at higher temperatures.