## Yang-Mills scenario: Yet a confirmation

12/12/2011

While CERN is calming down rumors (see here), research activity on Yang-Mills theories keeps on going on.  A few days ago, a paper by Axel Weber appeared on arxiv  (see here). As my readers know, having discussed this at length, in these last years there has been a hot debate between the proponents of the so called “scaling solution” and the “decoupling solution” for the propagators and the running coupling of a pure Yang-Mills theory in the infrared limit. Scaling solution describes a scenario with the gluon propagator reaching zero with lowering momenta, a ghost propagator enhanced with respect to the tree level one and the running coupling reaching a finite non zero value in the same limit. Decoupling solution instead is given by a gluon propagator reaching a finite non-zero value at lower momenta, a ghost propagator behaving like the one of a free particle (tree level) and the running coupling going to zero in this limit.. It is quite easy to recognize in the decoupling solution all the chrisms of a trivial infrared fixed point for a pure Yang-Mills theory against common wisdom that pervaded the community for a lot of years. So, for some years, having lattice computations unable to tell which solution was the right one, scaling solution seemed the only one to be physically viable and almost accepted by a large part of the community.

Things started to change after the Lattice Conference in Regensburg on 2007 when some groups where able to display lattice computations on very huge volumes. The striking result was that lattice computations confirmed the decoupling solution against common wisdom. What was really shocking here is that the gluon becomes massive at the expenses of the BRST sysmmetry that seems now to acquire an even more relevant role in the understanding of Yang-Mills theory.

The idea of Axel Weber is to perform an $\epsilon$-expansion for the Yang-Mills Lagrangian with a massive term to fix the scale. The striking result he gets is that both the scaling and the decoupling solutions are there but the former is unstable with respect to the renormalization group flow in dimensions greater than 2. So, this computation confirms again the scenario that I and other authors were able to devise.

Today, we have reached a deep understanding of the infrared physics of a Yang-Mills field theory. Scientific community is urged to take a look to the work of these people that could accelerate progress in a large body of physics research.

Axel Weber (2011). Epsilon expansion for infrared Yang-Mills theory in Landau gauge arXiv arXiv: 1112.1157v1

Marco Frasca (2007). Infrared Gluon and Ghost Propagators Phys.Lett.B670:73-77,2008 arXiv: 0709.2042v6