My colleagues participating to “The many faces of QCD” in Ghent last year keep on publishing their contributions to the proceedings. This conference produced several outstanding talks and so, it is worthwhile to tell about that here. I have already said about this here, here and here and I have spent some words about the fine paper of Oliveira, Bicudo and Silva (see here). Today I would like to tell you about an interesting line of research due to Silvio Sorella and colleagues and a striking clue supporting my results on scalar field theory originating by Axel Maas (see his blog).

Silvio is an Italian physicist that lives and works in Brazil, Rio de Janeiro, since a long time. I met him at Ghent mistaking him with Daniele Binosi. Of course, I was aware of him through his works that are an important track followed to understand the situation of low-energy Yang-Mills theory. I have already cited him in my blog both for Ghent and the Gribov obsession. He, together with David Dudal, Marcelo Guimaraes and Nele Vandersickel (our photographer in Ghent), published on arxiv a couple of contributions (see here and here). Let me explain in a few words why I consider the work of these authors really interesting. As I have said in my short history (see here), Daniel Zwanzinger made some fundamental contributions to our understanding of gauge theories. For Yang-Mills, he concluded that the gluon propagator should go to zero at very low energies. This conclusion is at odds with current lattice results. The reason for this, as I have already explained, arises from the way Gribov copies are managed. Silvio and other colleagues have shown in a series of papers how Gribov copies and massive gluons can indeed be reconciled by accounting for condensates. A gluon condensate can explain a massive gluon while retaining all the ideas about Gribov copies and this means that they have also find a way to refine the ideas of Gribov and Zwanzinger making them agree with lattice computations. This is a relevant achievement and a serious concurrent theory to our understanding of infrared non-Abelian theories. Last but not least, in these papers they are able to show a comparison with experiments obtaining the masses of the lightest glueballs. This is the proper approach to be followed to whoever is aimed to understand what is going on in quantum field theory for QCD. I will keep on following the works of these authors being surely a relevant way to reach our common goal: to catch the way Yang-Mills theory behaves.

A real brilliant contribution is the one of Axel Maas. Axel has been a former student of Reinhard Alkofer and Attilio Cucchieri & Tereza Mendes. I would like to remember to my readers that Axel have had the brilliant idea to check Yang-Mills theory on a two-dimensional lattice arising a lot of fuss in our community that is yet on. On a similar line, his contribution to Ghent conference is again a striking one. Axel has thought to couple a scalar field to the gluon field and study the corresponding behavior on the lattice. In these first computations, he did not consider too large lattices (I would suggest him to use CUDA…) limiting the analysis to , and . Anyhow, also for these small volumes, he is able to conclude that the propagator of the scalar field becomes a massive one deviating from the case of the tree-level approximation. The interesting point is that he sees a mass to appear also for the case of the massless scalar field producing a groundbreaking evidence of what I proved in 2006 in my PRD paper! Besides, he shows that the renormalized mass is greater than the bare mass, again an agreement with my work. But, as also stated by the author, these are only clues due to the small volumes he uses. Anyhow, this is a clever track to be pursued and further studies are needed. It would also be interesting to have a clear idea of the fact that this mass arises directly from the dynamics of the scalar field itself rather than from its interaction with the Yang-Mills field. I give below a figure for the four dimensional case in a quenched approximation

I am sure that this image will convey the right impression to my readers as mine. A shocking result that seems to match, at a first sight, the case of the gluon propagator on the lattice (mapping theorem!). At larger volumes it would be interesting to see also the gluon propagator. I expect a lot of interesting results to come out from this approach.

Silvio P. Sorella, David Dudal, Marcelo S. Guimaraes, & Nele Vandersickel (2011). Features of the Refined Gribov-Zwanziger theory: propagators, BRST soft symmetry breaking and glueball masses arxiv arXiv: 1102.0574v1

N. Vandersickel,, D. Dudal,, & S.P. Sorella (2011). More evidence for a refined Gribov-Zwanziger action based on an effective potential approach arxiv arXiv : 1102.0866

Axel Maas (2011). Scalar-matter-gluon interaction arxiv arXiv: 1102.0901v1

Frasca, M. (2006). Strongly coupled quantum field theory Physical Review D, 73 (2) DOI: 10.1103/PhysRevD.73.027701