Kyoto, arXiv and all that


Today, Kyoto conference HCP2012 has started. There is already an important news from LHCb that proves for the first time the existence of the decay B_s\rightarrow\mu^+\mu^-. They find close agreement with the Standard Model (see here). Another point scored by this model and waiting for new physics yet. You can find the program with all the talks to download here. There is a lot of expectations from the update on the Higgs search: The great day is Thursday. Meantime, there is Jester providing some rumors (see here on twitter side) and seem really interesting.

I have a couple of papers to put to the attention of my readers from arXiv. Firstly, Yuan-Sen Ting and Bryan Gin-ge Chen provided a further improved redaction of the Coleman’s lectures (see here). This people is doing a really deserving work and these lectures are a fundamental reading for any serious scholar on quantum field theory.

Axel Weber posted a contribution to a conference (see here) summing up his main conclusions on the infrared behavior of the running coupling and the two-point functions for a Yang-Mills theory. He makes use of renormalization group and the inescapable conclusion is that if one must have a decoupling solution, as lattice computations demand, then the running coupling reaches an infrared trivial fixed point. This is in close agreement with my conclusions on this matter and it is very pleasant to see them emerge from another approach.

Sidney Coleman (2011). Notes from Sidney Coleman’s Physics 253a arXiv arXiv: 1110.5013v4

Axel Weber (2012). The infrared fixed point of Landau gauge Yang-Mills theory arXiv arXiv: 1211.1473v1

A new year full of promises


We have left 2011 with a lot of exciting results from experiments. Neutrinos appear to move a bit faster than expected and Higgs provided some glimpses at CERN. Of course, this kind of Higgs appears somewhat boring at first being in the range of what Standard Model expected. But it is really too early to say something for sure. We expect definite answer for the next summer with a lot more data analyzed by people at CERN.

With the new year, I would like to point out to my readers a couple of nice papers that are really worthwhile reading. About CUDA and lattice QCD, my Portuguese friends, Pedro Bicudo and Nuno Cardoso,  made a relevant step beyond and made available their code for working for a generic SU(N) gauge group (see here, their code is here). As I have some time I will try their code. The work of these people is excellent and making their code worldwide available is really helpful for all our community.

Finally, Axel Maas put forward a revision of his very good review paper (see here). Axel gave important contributions to the current understanding of Yang-Mills theory and his paper yields a lucid description of these ideas that rely on a large effort on lattice computations and functional methods. Often, I complain about the fact that the community at large seems to not consider these lines of research reliable yet to work with. This is not true as the results they were able to get give since now sound results to work with and the most important of these are that Yang-Mill theory has indeed a mass gap and that this theory appears to display a running coupling reaching zero lowering momenta, a completely unexpected result that goes against common wisdom but this is just what lattice put out.

So, let me wish to you a great 2012 and I hope to share with you the excitement physics research is promising.

Nuno Cardoso, & Pedro Bicudo (2011). Generating SU(Nc) pure gauge lattice QCD configurations on GPUs with
CUDA and OpenMP arXiv arXiv: 1112.4533v1

Axel Maas (2011). Describing gauge bosons at zero and finite temperature arXiv arXiv: 1106.3942v2

QCD at finite temperature


The great news for me, in this week, has been the acceptance of my paper of QCD at finite temperature in Physical Review C (see here). This chance materialized after the excellent work of the referee that helped me to improve the paper in a significant way. For a good paper, such a way to review is a fundamental one and should be a rule. I have discussed this paper previously in my blog (see here and here) and I presented its content in a conference in Paris this year (see here). The contribution to proceedings is this.

I think that the main conclusions of this paper that should be emphasized is that the low-energy limit of QCD is a non-local Nambu-Jona-Lasinio model, a critical point exists at finite temperature with zero mass and zero chemical potential and that the instanton liquid picture of the vacuum of QCD is a very good one. These are fundamental questions in QCD that were waiting for an answer for so long.

I would like to thank all the people that, with their efforts and interest about my work, helped me to get these results published, in the end, in such an important journal.

Marco Frasca (2011). Chiral symmetry in the low-energy limit of QCD at finite temperature arXiv arXiv: 1105.5274v4

Marco Frasca (2011). Low-energy limit of QCD at finite temperature arXiv arXiv: 1110.0096v1

An interesting review


It is some time I am not writing posts but the good reason is that I was in Leipzig to IRS 2011 Conference, a very interesting event in a beautiful city.  It was inspiring to be in the city where Bach spent a great part of his life. Back to home, I checked as usual my dailies from arxiv and there was an important review by Boucaud, Leroy, Yaouanc, Micheli, Péne and Rodríguez-Quintero. This is the French group that produced striking results in the analysis of Green functions for Yang-Mills theory.

In this paper they do a great work by reviewing the current situation and clarifying  the main aspects of the analysis carried out using Dyson-Schwinger equations. These are a tower of equations for the n-point functions of a quantum field theory that can be generally solved by some truncation (with an exception, see here) that cannot be completely controlled. The reason is that the equation of lower order depends on n-point functions of higher orders and so, at some point, we have to decide the behavior of some of these higher order functions truncating the hierarchy. But this choice is generally not under control.

About these techniques there is a main date, Reigensburg 2007, when some kind of wall just went down. Since then, the common wisdom was a scenario with a gluon propagator going to zero when momenta go to zero while, in the same limit, the ghost propagator should go to infinity faster than the free case: So, the gluon propagator was suppressed and the ghost propagator enhanced at infrared. On the lattice, such a behavior was never explicitly observed but was commented that the main reason was the small volumes considered in these computations. On 2007, volumes reached a huge extension in lattice computations, till (27fm)^4, and so the inescapable conclusion was  that lattice produced another solution: A gluon propagator reaching a finite non-zero value and the ghost propagator behaving exactly as that of a free particle. This was also the prevision of the French group together with other researchers as Cornwall, Papavassiliou, Aguilar, Binosi and Natale. So, this new solution entered into the mainstream of the analysis of Yang-Mills theory in the infrared and was dubbed “decoupling solution” to distinguish it from the former one, called instead “scaling solution”.

In this review, the authors point out an important conclusion: The reason why authors missed the decoupling solution and just identified the scaling one was that their truncation forced the Schwinger-Dyson equation to a finite non-zero value of the strong coupling constant. This is a crucial point as this means that authors that found the scaling solution were admitting a non-trivial fixed point in the infrared for Yang-Mills equations. This was also the recurring idea in that days but, of course, while this is surely true for QCD, a world without quarks does not exist and, a priori, nothing can be said about Yang-Mills theory, a theory with only gluons and no quarks. Quarks change dramatically the situation as can also be seen for the asymptotic freedom. We are safe because there are only six flavors. But about Yang-Mills theory nothing can be said in the infrared as such a theory is not seen in the reality if not interacting with fermionic fields.

Indeed, as pointed out in the review, the running coupling was seen to behave as in the following figure (this was obtained by the German group, see here)

Running coupling of a pure Yang-Mills theory as computed on the lattice

This result is quite shocking and completely counterintuitive. It is pointing out, even if not yet confirming, that a pure Yang-Mills theory could have an infrared trivial fixed point! This is something that defies common wisdom and can explain why former researchers using the Dyson-Schwinger approach could have missed the decoupling solution. Indeed, this solution seems properly consistent with a trivial fixed point and this can also be inferred by the goodness of the fit of the gluon propagator with a Yukawa-like propagator if we content ourselves with the best agreement just in the deep infrared and the deep ultraviolet where asymptotic freedom sets in. In fact, with a trivial fixed point the theory is free in this limit but you cannot pretend agreement on all the range of energies with a free propagator.

Currently, the question of the right infrared behavior of the two-point functions for Yang-Mills theory is hotly debated yet and the matter that is at stake here is the correct understanding and management of low-energy QCD. This is one of the most fundamental physics problem and something I would like to know the answer.

Ph. Boucaud, J. P. Leroy, A. Le Yaouanc, J. Micheli, O. Péne, & J. Rodríguez-Quintero (2011). The Infrared Behaviour of the Pure Yang-Mills Green Functions arXiv arXiv: 1109.1936v1

Marco Frasca (2009). Exact solution of Dyson-Schwinger equations for a scalar field theory arXiv arXiv: 0909.2428v2

I. L. Bogolubsky, E. -M. Ilgenfritz, M. Müller-Preussker, & A. Sternbeck (2009). Lattice gluodynamics computation of Landau-gauge Green’s functions in
the deep infrared Phys.Lett.B676:69-73,2009 arXiv: 0901.0736v3


Paper on critical temperature revised


Yesterday, I have uploaded a new version of my paper on the critical temperature of chiral symmetry breaking in QCD (see here). The reason for this was that there are some points in need for a better clarification. The main of these is the mapping theorem: I have added a sketch of a proof. The reason for this is that there is a common misunderstanding about it and that some people think  that this theorem is for quantum field theories. Indeed, it just establishes a map between classical solutions of a scalar field and a Yang-Mills field but in the asymptotic limit of a coupling going to infinity. Quantum theory does not enter at all here but these classical asymptotic solutions can be used to build up a perturbation theory for quantum field theory in the infrared, that is for low-energies, that is the range of interest for all the phenomenology we would like to understand.

Another recurring question is if this mapping breaks in some way gauge invariance. The answer is a resounding no as the proof does not select a gauge at the start but anyhow if one wants quantization a gauge must be selected.

Finally, I have better clarified the derivation of the critical temperature and added some more relevant references. I hope in this way that my arguments can be better understood. Indeed, presentation is one of the most difficult aspects of scientific communication and sometime it is a sound explanation of attrition between authors and referees.

Back from Paris


It is several days that I have no more posted on the blog but for a very good reason: I was in Paris for the Eleventh Workshop on Non-Perturbative Quantum Chromodynamics (see here). It has been a beautiful chance to see Paris with the eyes of a tourist and being immersed in a lot of physics in the area I am currently contributing. The conference was held at the Institut d’Astrophyisique de Paris. This week was indeed plenty of information for people in high-energy physics due to the release by D0 of their measurements on the Wjj data, showing that the almost 5 sigma bump of CDF was not there (see here, here and here). In the conference there has been room for talks by experimentalists too and it was the most shocking part as I will explain below.

The talks were somehow interesting with a couple of days mostly dedicated to AdS/CFT approach for QCD. So, string theory got a lot of space even if I should say that more promising approaches seem to exist. The first day there have been a couple of talks that were very near my interest by Dario Zappalà and Marco Ruggieri. They were reporting on their very recent papers (here and here). With Marco, I spent all the week together while with Dario we have had a nice dinner near Latin Quartier. The question Dario presented was about the existence of massive excitations (let me say “persistence”) also beyond the critical temperature for Yang-Mills theory. We discussed together with Marco this result and Marco claimed that massive excitations should have melted beyond the critical temperature while my view is that the residual of mass should be due to temperature corrections to the mass spectrum of the theory. Marco in his talk presented the idea of measuring the chiral chemical potential on the lattice as this could give plain evidence of existence for the critical endpoint without the annoying sign problem. A proof of existence of the critical endpoint is somehow the Holy Grail of finite temperature QCD and something under a lot of studies both theoretically and on the lattice. So, Marco’s proposal can turn out a significant shortcut toward the reaching of this goal.

The second day Carl Bender gave a very beautiful talk telling us about PT invariant quantum mechanics. PT stays for Parity and Time reversal. The point to start from is the Dirac postulate about the Hamiltonian being Hermitian self-adjoint. Differently from the other postualates of quantum mechanics, this one is too much a mathematical requirement and one could ask if can be made somewhat looser. The paradigm Hamiltonian has the from H=p^2+ix^3. The answer is yes of course and we were left with the doubt that maybe this is the proper formulation of quantum mechanics rather the standard one. I suspect that this could represent a possible technique useful in quantum gravity studies.

I have already said of the two days on string theory. I have just noticed the talk by Luca Mazzucato showing how, with his approach, my scaling with \lambda^\frac{1}{4} for the energy spectrum could be recovered in a strong coupling expansion being \lambda the ‘t Hooft coupling. Unfortunately, Gabriele Veneziano could not partecipate.

On Wednesday there was the most shocking declaration from an experimentalist: “We do not understand the proton”. The reason for this arises from the results presented by people from CERN working at LHC. They showed a systematic deviation of their Montecarlo simulations from experimental data. This means for us, working in this area, that their modeling of low-energy QCD is bad and their possible estimation of the background unsure. There is no way currently to get an exact evaluation of the proton scattering section. I am somewhat surprised by this as so far, as I have always pointed out in this blog, at least the structure of the gluon propagator at low energies should be known exactly from the lattice. So, modeling the proton in such Montecarlo models should be a mitigated issue. This does not seem to be so and these different communities do not seem to talk each other at all. After these shocking news, the evening we took an excellent social dinner and I have had some fine discussions with foreigners colleagues that were well aware of the books from Umberto Eco. One of these, Karl Landsteiner, suggested us to visit the Pantheon to look at the Foucault pendulum. I, Marco Ruggieri and Orlando Oliveira took this initiative the next day and it was a very nice place to visit. If you are a physicist you can understand the emotion of being there seeing that sphere moving like Newton’s equations demand and inexorably proving the rotation of the Earth. Karl gave an interesting talk that day where AdS/CFT is used to obtain transport coefficients in heavy ion collisions.

In the same day, Orlando Oliveira gave his talk. Orlando is a friend of mine and gave relevant contribution to our understanding of the behavior of low-energy gluon propagator. He has been the author of one of the papers that, at Regensburg on 2007, started the end of the so called “scaling solution” for the gluon propagator (see here). Orlando is going ahead, starting from the acquired form of the gluon propagator, to understand low-energy phenomenology of nuclear forces. In this work, he and his colleagues introduce an octect of scalar fields having the aim to produce the gluon mass through a non-zero vacuum expectation value (see here) producing chiral symmetry breaking. My work and that of Orlando are somewhat overlapped in the initial part where we have an identical understanding of the low-energy behavior of  Yang-Mills theory.

On Friday, there have been a couple of significant events. The first one was my talk. This is a report on my recent paper. I will not discuss this point further leaving this material to your judgement. The second relevant event was given in the talks by Thierry Grandou and our Chairman and Organizer Herbert Fried. The relevant paper is here. While Grandou made a more mathematical introduction with a true important result: the resummation of all gluon exchange diagrams realizing some dream of having completely solved QCD, Fried provided a more concrete result giving the binding potential between quarks analytically obtained from the preceding theorem. We were somehow astonished by this that seems just a small step away from the Millenium prize. Berndt Mueller, one of the Organizers, suggested to Fried to determine the mass gap and wait a couple of years to get the prize. Indeed, this appears a true striking exact result in the realm of QCD.

All in all, an interesting conference in a special place: Paris. For me, it has been a very nice period of full immersion in physics with the company of very nice friends.

Update: Mary Ann Rotondo put online the slides of the talks (see here).

P. Castorina, V. Greco, D. Jaccarino, & D. Zappalà (2011). A reanalysis of Finite Temperature SU(N) Gauge Theory arXiv arXiv: 1105.5902v1

Marco Ruggieri (2011). The Critical End Point of Quantum Chromodynamics Detected by Chirally
Imbalanced Quark Matter arXiv arXiv: 1103.6186v1

Irene Amado, Karl Landsteiner, & Francisco Pena-Benitez (2011). Anomalous transport coefficients from Kubo formulas in Holography JHEP 05 (2011) 081 arXiv: 1102.4577v3

O. Oliveira, W. de Paula, & T. Frederico (2011). Linking Dynamical Gluon Mass to Chiral Symmetry Breaking via a QCD Low
Energy Effective Field Theory arXiv arXiv: 1105.4899v1

Marco Frasca (2011). Chiral symmetry in the low-energy limit of QCD at finite temperature arXiv arXiv: 1105.5274v2

H. M. Fried, Y. Gabellini, T. Grandou, & Y. -M. Sheu (2009). Gauge Invariant Summation of All QCD Virtual Gluon Exchanges Eur.Phys.J.C65:395-411,2010 arXiv: 0903.2644v2

The Tevatron affair and the “fat” gluon


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


with the spectrum given by


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?


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


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


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.


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