The Tevatron affair and the “fat” gluon

25/01/2011

Tevatron is again at the forefront of the blogosphere mostly due to Jester and Lubos. Top quark seems the main suspect to put an end to the domain of the Standard Model in particle physics. Indeed, years and years of confirmations cannot last forever and somewhere some odd behavior must appear. But this is again an effect at 3.4 sigma and so all could reveal to be a fluke and the Standard Model will escape again to its end. But in the comment area of the post in the Lubos’ blog there is a person that pointed out my proposal for a “fat” gluon. “Fat” here stays just for massive and now I will explain this idea and its possible problems.

The starting point is the spectrum of Yang-Mills theory that I have obtained recently (see here and here). I have shown that, at very low energies, the gluon field has a propagator proportional to

$G(p)=\sum_{n=0}^\infty(2n+1)\frac{\pi^2}{K^2(i)}\frac{(-1)^{n+1}e^{-(n+\frac{1}{2})\pi}}{1+e^{-(2n+1)\pi}}\frac{1}{p^2-m_n^2+i\epsilon}$

with the spectrum given by

$m_n=\left(n+\frac{1}{2}\right)\frac{\pi}{K(i)}\sqrt{\sigma}$

being $\sigma$ the string tension being about $(440\ MeV)^2$. If we go beyond the leading order of such a strong coupling expansion one gets that the masses run with momenta. This has been confirmed on the lattice quite recently by Orlando Oliveira and Pedro Bicudo (see here). The interesting point about such a spectrum is that is not bounded from above and, in principle, one could take n large enough to reach TeV energies. These glueballs are very fat indeed and could explain CDF’s results if these should be confirmed by them, their colleagues at D0 and LHC.

It should be emphasized that these excitations of the glue field have spin zero and so will produce t-tbar pairs in a singlet state possibly explaining the charge asymmetry through the production rate of such very massive glueballs.

A problem can be seen immediately from the form of the propagator that has each contribution in the sum exponentially smaller as n increases. Indeed, this has a physical meaning as this is also what appears in the decay constants of such highly massive gluons (see here). Decay constants are fundamental in the computation of cross sections and if they are very near zero so could be the corresponding cross sections. But Oliveira and Bicudo also showed that these terms in the propagator depend on the momenta too, evading the problem at higher energies. Besides, I am working starting from the low energy part of the theory and assuming that such a spectrum will not change too much at such high energies where asymptotic freedom sets in and gluons seem to behave like massless particles. But we know from the classical theory that a small self-interaction in the equations is enough to get masses for the field and massless gluons are due to the very high energies we are working with. For very high massive excitations this cannot possibly apply. The message I would like to convey with this analysis is that if we do not know the right low-energy behavior of QCD we could miss important physics also at high-energies. We cannot live forever assuming we can forget about the behavior of Yang-Mills theory in the infrared mostly if the mass spectrum is not bounded from above.

Finally, my humble personal conviction, also because I like the idea behind Randall-Sundrum scenario, is that KK gluons are a more acceptable explanation if these CDF’s results will prove not to be flukes. The main reason to believe this is that we would obtain for the first time in the history of mankind a proof of existence for other dimensions and it would be an epochal moment indeed. And all this just forgetting what would imply for me to be right…

Frasca, M. (2008). Infrared gluon and ghost propagators Physics Letters B, 670 (1), 73-77 DOI: 10.1016/j.physletb.2008.10.022

Frasca, M. (2009). Mapping a Massless Scalar Field Theory on a Yang–Mills Theory: Classical Case Modern Physics Letters A, 24 (30) DOI: 10.1142/S021773230903165X

P. Bicudo, & O. Oliveira (2010). Gluon Mass in Landau Gauge QCD arxiv arXiv: 1010.1975v1

Frasca, M. (2010). Glueball spectrum and hadronic processes in low-energy QCD Nuclear Physics B – Proceedings Supplements, 207-208, 196-199 DOI: 10.1016/j.nuclphysbps.2010.10.051

What is Science?

16/01/2011

Reading this Lubos’ post about a very good site (this one) I entered into the comment area and I have found the following declaration by him:

Science is a meritocracy where answers are determined by objective criteria, and for most of the difficult questions, only one or a few people know the right answer and the scientific method exists to isolate this special right answer…

Of course, I subscribe this that is widely known to people doing research. I would just change the word “meritocracy” by “dictatorship of truth”. But there is an intermediate age where the truth takes time to become acclaimed and this is time for opinions and before to become aware of the people that firstly reached the goal, there is a struggle for the truth to be acquired. I would like to remember here the status of quantum field theory in the sixties when bootstrap and similar failures appeared as a paradigm and very few brave people were doing research in the right directions taking us to the triumph of today. In this kind of dynamics, at a first stage it is very difficult to be able to tell, also for very well trained people, where the right track is lying. In physics our luck resides in experiments. This makes things simpler when technology helps us to perform them otherwise time to decide for the best are increasingly longer. So, merit as claimed by Lubos is something that sets in at the very end of the process.

In my specific field of activity, QCD, we are in a better situation as a lot of laboratories around the World have facilities to perform important measurements to reach the goal. And this situation is even better as we can use powerful computers to solve the theory. My view as a physicist is that, without a sound comparison of the spectrum of the theory with experiments, nobody can claim to have properly solved the mass gap problem. All my present effort is going into this direction because there is nothing more exciting than having hit the right behavior of Nature (our mother not the bitch…). I take this chance to remember here the effort in this direction of Silvio Sorella, that with the help of other fine colleagues, is going to show how his approach indeed fulfill these expectations of glueball masses (see here). These authors give a correct idea about what is the  right approach to be followed for the problem of low-energy QCD.

Finally, I would like to emphasize the relevance of sites like the one pointed out by Lubos. This site has also been posted by Sean Carroll (see here) in his blog. I have pointers to my blog there and in the more successful Mathoverflow. Unfortunately, I have no much time to spend on contributing to these sites but these are very good places to know about science and the right one. So, this is also my invitation for my readers to contribute to them actively.

D. Dudal, M. S. Guimaraes, & S. P. Sorella (2010). Glueball masses from an infrared moment problem and nonperturbative
Landau gauge arxiv arXiv: 1010.3638v3

A more prosaic explanation

09/01/2011

The aftermath of some blogosphere activity about CDF possible finding at Tevatron left no possible satisfactory explanation beyond a massive octet of gluons that was already known in the literature and used by people at Fermilab. In the end we need some exceedingly massive gluons to explain this asymmetry. If you look around in the net, you will find other explanations that go beyond ordinary known physics of QCD. Of course, speaking about known physics of QCD we leave aside what should have been known so far about Yang-Mills theory and mass gap. As far as one can tell, no generally accepted truth is known about otherwise all the trumpets around the World would have already sung.

But let us do some educated guesses using our recent papers (here and here) and a theorem proved by Alexander Dynin (see here). These papers show that the spectrum of a Yang-Mills theory is discrete and the particles have an internal spectrum that is bounded below (the mass gap) but not from above. I can add to this description that there exists a set of spin 0 excitations making the ground state of the theory and ranging to infinite energy. So, if we suppose that the annihilation of a couple of quarks can generate a particle of this with a small chance, having enough energy to decay in a pair t-tbar in a singlet state, we can observe an asymmetry just arising from QCD.

I can understand that this is a really prosaic explanation but it is also true that we cannot live happily forgetting what is going on after a fully understanding of a Yang-Mills theory and that we are not caring too much about. So, before entering into  the framework of very exotic explanations just we have to be sure to have fully understood all the physics of the process and that we have not forgotten anything.

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

Marco Frasca (2009). Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical
Case Mod. Phys. Lett. A 24, 2425-2432 (2009) arXiv: 0903.2357v4

Alexander Dynin (2009). Energy-mass spectrum of Yang-Mills bosons is infinite and discrete arxiv arXiv: 0903.4727v2

An important hit from CDF at Tevatron

05/01/2011

I look around in the blogosphere to see if important news that escaped me were starting to come out. This is a typical reason to read blogs. In a few hours I saw the posts from Jester and Lubos informing me of a new paper from CDF (see here) appeared on arxiv. This paper contains a possible hint of new physics as they observe a 3.4 sigma effect of charge asymmetry in top-anti-top pair production that disagrees with the Standard Model prediction. They improve on preceding measurements by D0 and CDF due to the increased luminosity and now the effect begins to be an important real discover. As such, all this should be shortly confirmed at LHC.

The idea behind these measurements is to see charge asymmetry effects arising at the next-to-leading order by interference terms in QCD. This asymmetry translates into a forward-backward asymmetry. This effect should be really small as QCD is a charge symmetric theory and, indeed, at the leading order no difference is seen for top or antitop. As these top pairs are produced by proton-antiproton collisions this is a pure effect arising from strong interactions and so, any unexpected effect should be ascribed to problems with our current understanding of QCD. CDF improves significantly the result showing a large disagreement with the prediction of the Standard Model. But what is really interesting here is that they show inequivocally that this effect is mass dependendent. They measure the invariant mass of top-antitop pairs and find that their results are consistent with a resonance of a mass of 450 Gev. It is like a massive gluon entered into the process producing the asymmetry! It should not be forgotten that at this high energies QCD should settle at an asymptotic freedom regime and one could safely do a perturbative analysis of this process. Indeed, there is paper, cited in this CDF’s work, that do so assuming a massive gluon. CDF analysis relies on this paper to do a theoretical analysis of their results.

In the comments of Lubos’ post you can find an answer to the question if this massive particle could be supersymmetric. Anyhow, this particle is strongly interacting whatever its nature. With this in mind, we can try to do a simple analysis through the idea that Yang-Mills theory has a mass gap. As already said, if the coupling of the theory is finite, gluons and their excitations must be massive (see here and here). The spectrum of the theory is not bounded from above and so these massive excitations should be expected also at higher energies. This analysis is in agreement also with a recent work of Alexaner Dynin at Ohio State University (see here). Indeed, this spectrum is the same of a harmonic oscillator and so such massive gluons should be expected at any energy scale in principle. Of course, to confirm such a hypothesis, a full computation of charge asymmetry should be performed and eventually found in agreement with CDF measurements. But a mass gap in Yang-Mills theory should mean a massive spectrum and the absence of any bound from above could imply this (take this cum grano salis).

At 3.4 sigma we are in a fluke possiility yet. We have to stay tuned for this result to be finally confirmed in a near future.

What’s up with 2d Yang-Mills theory?

24/12/2010

Being near Christmas I send my wishes to all my friends around the World. Most of them are physicists like Attilio Cucchieri that I cited a lot in this blog with his wife Tereza Mendes for their beautiful works on Yang-Mills propagators. Attilio asked to me again about the behavior of 2d Yang-Mills propagators and my approach to the theory. As you know, lattice computations due to Axel Maas (see here) showed without doubt that here, differently from the higher dimensional case, the scaling solution appears. This is an important matter as ‘t Hooft showed in 1974 (see here) that, in the light cone gauge, Yang-Mills theory has no dynamics. Indeed, the Lagrangian takes a very simple form

${\cal L}=-\frac{1}{2}{\rm Tr}(\partial_- A_+)^2$

and the nonlinear part is zero due to the fact that the field has just two Lorentzian indexes. Please, note that here $A_\pm=\frac{1}{\sqrt{2}}(A_1\pm A_0)$ and  $x_\pm=\frac{1}{\sqrt{2}}(x_1\pm x_0)$. Now, you can choose the time variable as you like and if you take this to be $x_+$ you see that there are no dynamical equations left for the gluon field! You are not able to do this in higher dimensions where the dynamics is not trivial and the field develops a mass gap already classically. Two-dimensional QCD is not trivial as there remains a static (nonlocal) Coulomb interaction between quarks. You can read the details in ‘t Hooft’s paper.

Now, in my two key papers (here and here) I proved that, at the classical level the Yang-Mills field maps on a quartic massless scalar field in the limit of the coupling going to infinity. So, I am able to build a quantum field theory for the Yang-Mills equations in this limit thanks to this theorem. But what happens in two dimensions? The scalar field Lagrangian in the light-cone coordinate becomes

${\cal L}=-\partial_+\phi\partial_-\phi-\lambda\phi^4$

and you can see that, whatever is your choice for the time variable, this field has always a dynamics. In 2d I am not able to map the two fields and, if I choose a different gauge for the Yang-Mills field, I can find propagators that are no more bounded to be massive or Yukawa-like. Indeed, the scaling solution is obtained. This is a bad news for supporters of this solution but this is plain mathematics. It is interesting to note that the scalar field appears to have nontrivial massive solutions also in this case. No mass gap is expected for the Yang-Mills field instead.

Thank you a lot Attilio for pointing me out this question!

Merry Xmas to everybody!

Yang-Mills and string theory

09/12/2010

As I pointed out in a recent post, the question of the mass gap for Yang-Mills theory should be considered settled. This implies an understanding of the way mass arises in our world. It is seen that mass is a derived concept and not a fundamental one. I have given an explanation of this here. In a Yang-Mills theory, massive excitations appear due to the presence of a finite nonlinearity. The same effect is seen for a massless quartic scalar field and, indeed, these fields map each other at a classical level. It is interesting to note that a perturbation series with a coupling going to zero can miss this conclusion and we need a dual perturbation with the coupling going to infinity to uncover it. The question we would like to ask here is: What does all this mean for string theory?

As we know, string theory has been claimed not to have any single proposal for an experimental verification. But, of course, without entering into a neverending discussion, there are some important points that could give strong support to the view string theory entails. Indeed, so far there are two essential points that research on string theory produced and that should be confirmed as soon as possible: AdS/CFT correspondence and supersymmetry. Both these theoretical results are strongly supported by the research pursued by our community. For the first point, understanding of QCD spectrum, with or without quarks, through the use of AdS/CFT correspondence is a very active field of research with satisfactory results. I have discussed here this matter several times and I have pointed out the very good work of Stan Brodsky and Guy de Teramond as an example for this kind of research (e.g. see this). Soft-wall model discussed by these authors seems in a very good agreement with the current scenario that is arisen in our understanding of Yang-Mills theory that I emphasized several times in this blog.

About supersymmetry I should say that I am at the forefront since I have presented this paper. The mass gap obtained in Yang-Mills theory arising from nonlinearities has an interesting effect when considered for the quartic scalar field interecting with a gauge field and spinor fields. Taking a coupling for the self-interaction of the scalar field being very large, all the conditions for supersymmetry are fulfilled and all the interacting fields get identical masses and coupling. This implies that, if the mechanism that produces mass in QCD and Standard Model is the same, the Higgs field must be supersymmetric. I call this field Higgs, notwithstanding it has lost some important characteristics of a Higgs field, because is again a scalar field inducing masses to the other fields interacting with it. So, if current experiments should confirm this scenario this would be a big hit for physics ending with a complete understanding of the way mass arises in our world both for the macroscopic and the microscopic world.

So, we can conclude that our research area is producing some relevant conclusions that could address research in more fundamental areas as quantum gravity in a well-defined direction. I think we will get some great news in the near future. As for the present, I am happy to have given an important contribution to this research line.

Today on arxiv

07/12/2010

As usual I read the daily coming from arxiv for some new papers to talk you about. This morning I have found some interesting ones I would like to say something on. Firstly, I would like to point out to you the paper by Marco Ruggieri and Raoul Gatto (see here). These authors discuss the behavior of QCD in presence of a strong magnetic field. The main tool they consider is the Nambu-Jona-Lasinio model. As you may know, I showed that this is the low-energy limit of QCD (see here and here) but there is also a paper by Kondo (see here) giving the same conclusion even if an expression for the Nambu-Jona-Lasinio constant is not obtained. Gatto and Ruggieri arrive at the important conclusion that a strong magnetic field changes in some way the phase diagram of QCD. I think that this conclusion is strongly supported by the consistency of the model they use. By my side, I think that this area of research is very promising to test my derivation of low-energy QCD.

An important paper as well is the one posted by BESIII Collaboration (see here). This paper gives the most precise measure of the $\eta'\rightarrow\eta\pi\pi$ decay obtained so far due to their larger statistics. They arrive at the important conclusion that for this decay interactions of the decay products is important. This conclusion is really important as implies a production of intermediate resonances as $\sigma$ and a0(980) as already discussed in my preceding post. The reason why this is so important is that this gives a strong support to the view of the $\sigma$ resonance as a glueball and to our current understanding of QCD given above.

Indeed, today there is again a paper of Juan Sanz-Cillero discussing this matter (see here). A more extended discussion has been given in my post here.