In our preceding posts we have largely discussed what are the results emerging from lattice about the gluon and ghost propagators and the running coupling and how functional methods, in the way they are currently adopted, fail to reach agreement with lattice computations at very large volumes. But we want to resume here what are the main conclusions that are obtained from such applications of functional methods. People working in this way fix the gluon propagator as
and for the ghost
then the claim is made that the relation does hold while the functions are taken to be regular as momenta go to zero. From the relation between the exponents we can conclude that, excluding the trivial solution, if the gluon propagator goes to zero at lower momenta, that is , than we must have that means that the ghost propagator must go to infinity at lower momenta. What they get is that the ghost propagator should go to infinity faster than a free particle. If this would be true all the confining scenarios (Zwanzinger-Gribov and Kugo-Ojima) hold true. The ghost holds a prominent role and, last but not least, a proper defined running coupling goes to a fixed point to lower momenta.
Lattice computations say that all this is blatantly wrong. Indeed, we have learned from them that
- Gluon propagator reaches a finite non-null value at lower momenta.
- Ghost propagator is that of a free particle and so ghosts play no role at lower momenta.
- Running coupling is seen to approach zero at lower momenta.
From this we can easily derive our exponents as defined by people working with functional methods: and so that and no relation between exponents is seen to exist. So we have got a clear cut criterion to say when a published paper about infrared behavior of Yang-Mills theory is blatantly wrong independently on the prestige of the journal that publishes it. This happens all the times the relation is assumed to hold. I can grant that there are a lot around of these wrong papers published on the highest ranked journals. If you have time and you need fun try to search for them.
I would like to say that this belongs to dynamics of science. We are presently in a transition situation about our matter, a situation similar at that happened after the discovery of the resonance that took some time before people agreed on its nature. So, there is nothing to say to editors or referee and also to authors as mistakes are the most common facts in physics and very few people hit the right track after a wide cemetery of mistakes and wrong theories.