A confirmation again


One of my main activities in the morning is reading the daily coming from arxiv. Sometime it happens to find significant papers to be put in a post like this. This morning I have found a beautiful paper by a cooperation of people from Germany, Russia and Australia working on lattice QCD (see here). This paper has been written by Igor Bogolubsky, Ernst-Michael Ilgenfritz, André Sternbeck and Michael Mueller-Preussker. I put here the following picture representing one of the main conclusions

propbimpsThis picture gives the gluon propagator with a number of points (96)^4 and shows clearly that it reaches a finite value at smaller momenta implying a massive gluon. Indeed, the authors of the paper extended the lattice computations moving from (80)^4 to (96)^4 points and add some other improvement in the computation itself. The value of beta is quite high being 5.7. The agreement with previous computations of Cucchieri and Mendes is excellent (see here). These latter authors worked with a number of points of (128)^4 while beta was taken to be 2.2.

The other two important conclusions they reach is that the ghost propagator goes like that of a free particle and the running coupling goes to zero at lower momenta. For the running coupling we emphasize that there is no common agreement about its definition in the infrared and the authors properly point out this. But a running coupling that goes to zero does not mean at all that there is no confinement. Quite the contrary as proved by Kazuhiko Nishijima (see here): It gives a proof of confinement.

So, we obtain again a clear proof of the scenario we have already obtained from a theoretical standpoint (see here and here) and we have discussed at length in this blog. I think that evidence of existence of the mass gap both on lattice and from theory are becoming overwhelming. We are just wating the dust to settle down and textbooks reporting these findings.

Update: After an email exchage with Andre Sternbeck he gave further clarifications about his group work correcting something not correct in the post. I post here his corrigenda:

“Our study was for the gauge group SU(3) and not for SU(2). That is
the reason why the Beta-Value is larger than that used for SU(2) by
Cucchieri et al. and by myself et al. in 2007. The lattice spacings are
roughly of the same order, but the numerical effort spent for a 96^4
lattice in SU(3) is much bigger than what had been necessary in SU(2).”

I take this chance to thank him a lot for his comments.

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