## 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.

## Current status of Yang-Mills mass gap question

01/12/2010

I think that is time to make a point about the question of mass gap existence in the Yang-Mills theory. There are three lines of research in this area: Theoretical, numerical and experimental. I can suppose that the one that mostly interests my readers is the theoretical one. I would like to remember that, in order to get a Millenium Prize, one also needs to prove the existence of the theory. This makes the problem far from being trivial.

As for today, the question of existence of the mass gap both for scalar field theories and Yang-Mills theory should be considered settled. Currently there are two papers of mine, here and here both published in archival journals, proving the existence of the mass gap and give it in a closed analytical form. A proof has been also given by Alexander Dynin at Ohio State University here. Alexander does not give the mass gap in a closed form but gets a lower bound that permits him to conclude that Yang-Mills theory has a discrete spectrum with a mass gap. This is enough to declare this part of the problem solved. It is interesting to note that, differently from Poincaré conjecture, this solution does not require a mathematics that is too much complex. This can be understood from the fact that the corresponding classical equations of the theory already admit  massive solutions of free particle. The quantum theory can be built on these solutions and all this boils down to a trivial fixed point in the infrared for the quantum theory. Such a trivial fixed point, that explains also the lower bound Alexander is able to find, is a good news: We have a set of asymptotic states at diminishing momenta that can be used to do perturbation theory and do computations for physics! The reason why these relevant mathematical results did not get the proper exposition so far escape me and enters into the realm of things that I do not know. It is true that in this area there is a lot of caution and this can be understood as this problem received a lot of attention after Witten and Jaffe proposed it for a big money prize.

But, as I have already said, this problem has two questions to be answered and while computing the mass gap is quite easy, the other question is rather involved. To prove the existence of a quantum field theory is not a trivial matter and, for sure, we know that the Wiener integral exists and the Feynman integral does not (so far and only for mathematicians). What I prove in my papers is that the Euclidean theory exists for the scalar field theory (thanks to Glimm and Jaffe that already proved this) and that this theory matches the Yang-Mills theory in the limit of the gauge coupling going to infinity. It should be an asymptotic existence… Alexander by his side proves existence in a different way but here unfortunately I cannot say too much but I would appreciate that Alexander would write down some lines here about his work.

Other theoretical attempts are based on some educated guess as a starting point as could be the vacuum functional, the beta function or other parts of the theory that, for a full proof, should be derived instead. These attempts give a strong support to my work and that of Alexander. In these papers you will see a discrete spectrum and this is the one of a harmonic oscillator or simply the very existence of the mass gap itself. But, for physicists, the spectrum is the relevant conclusion as from it we can get the masses of physical states to be seen in accelerator facilities. This is the reason why I do not worry too much for mathematicians fussing about my papers.

Finally, I would like to spend a few words about numerical and experimental results. Experiments show clearly always bound states of quarks and gluons that are never seen as free. This is the better proof so far Nature gave us of the existence of the mass gap. Numerically, people computed both Green functions and the spectrum of the theory. I am convinced that these lines should merge. The spectrum on the lattice, both quenched and unquenched, displays the mass gap. Green functions, when one considers just the decoupling solution, are Yukawa-like, both on the lattice and from Dyson-Schwinger equations, and this again is a proof of existence of the mass gap.

I hope I have not forgotten anyone. Please, let me know. If you need explicit references here and there I will be pleased to post here. A lot of people is involved in this kind of research and I am happy to acknowledge the good work.

Finally, I would like to remember that one cannot be skeptical about mathematics as mathematics can only be either right or wrong. No other way.

## The nature of eta’

30/11/2010

$\eta'$ is a very peculiar particle. It mixes with $\eta$ that has a lower mass. Recently, in their report on KLOE-2 physics, this group reported here that $\eta'$ has a significant glue component besides quarks. This means that understanding its most important decay $\eta'\rightarrow\eta\pi^+\pi^-$ is not a trivial matter. As my readers may know, I have done a computation in my contribution to proceedings to QCD 10 conference where the decay process is seen to happen through an intermediate step with the $\sigma$ resonance followed by the decay of this into two pions. The agreement we get is so good to give a correct estimation of the decay constant of the $\eta$. This implies that the $\sigma$ is a true glue state. Of course our computation is rough enough to exclude mixing with other hadronic states that should exist.

Today, on arxiv, an interesting paper appeared authored by Rafel Escribano, Pere Masjuan, Juan José Sanz-Cillero (see here). These authors give an initial overview of the experimental status of the decay we have considered above. Then, using both the technique of Chiral Perturbation Theory (ChPT) and that of Resonant Chiral Perturbation Theory (RChPT), they try to fit experimental data. I have the luck to hear a talk of Juan José in Montpellier last year about this same matter and I was aware of his struggle to reach an agreement between a successful technique, as ChPT is, and experimental data for this particular process. The leading order of the theory is well below the experimental value and so, already in that first talk, Juan José showed the need for higher order corrections. But he proved that this cannot be enough and said at that time that some other states should be accounted for to reach a satisfactory agreement. This paper goes in this direction showing that if one accounts for the presence of the $\sigma$ and a0(980), the latter being dominant, the agreement is reached. These authors were also able to show a consistent relation between ChPT and RChPT that are in some way complimentary.

This paper is relevant as gives a strong support to the idea that I put forward about $\eta'$ decay. But these authors go further implying a higher level of understanding accounting for the presence of other hadronic states in a technical affordable way. I expect further improvement by them and it will be interesting to see how these could be obtained.

## Some relevant preprints

29/11/2010

My readers know that I keep myself up to date with the daily submissions at arxiv. Of course, I limit myself to the ones very near my research area. Today there have been some quite interesting papers by people working at the question of Green functions in the low-energy limit of QCD. I would like to point out three contributions at the Madrid conference of the last summer: Arlene Aguilar shows how low-energy phenomenology is consistent with our current understanding of the gluon propagator for the decoupling solution (see here). Joannis Papavassiliou shows how the solution for d=2+1 for the gluon propagator, solving numerically Dyson-Schwinger equations, is in agreement with lattice data (see here). Finally, there is the contribution of Eduardo Fraga, Ana Mizher and Maxim Chernodub about the use of a linear sigma model to understand the vacuum of QCD in a strong magnetic field (see here). These people were also present at Gent.

An original research paper appeared from Orlando Oliveira, Pedro Costa and Paulo Silva (see here). Orlando shocked me again with another bright idea. He and his colleagues managed to get an understanding of the behavior of low-energy physics from choosing the propagator through the scaling or the decoupling solution. The smart idea is to do so by deriving a Nambu-Jona-Lasinio model and solving this for known low-energy observables. As you may know, I worked out something like this in this paper that went published in the International Journal of Modern Physics E. I have sent an email to Orlando asking for a contribution by him or his colleagues in this blog. I hope they will take some time to do this as this paper is really striking and the idea really meaningful. Orlando said to me that this paper will appear soon on Physics Letters B.

Finally, I hope you will enjoy reading these papers as I did.

## The many faces of QCD (2)

10/11/2010

Back at home, conference ended. A lot of good impressions both from the physics side and other aspects as the city and the company. On Friday I held my talk. All went fine and I was goodly inspired so to express my ideas at best. You can find all the talks here. The pictures are here. Now it should be easier to identify me.

Disclaimer: The talks I will comment on are about results very near my research area. Talks I will not cite are important and interesting as well and the fact that I will not comment about them does not imply merit for good or bad. Anyhow, I will appreciate any comment by any participant to the conference aiming to discuss his/her work.

On Tuesday afternoon started a session about phases in QCD. This field is very active and is a field where some breakthroughs are expected to be seen in the near future. I have had a lot of fun to know Eduardo Fraga that was here with two of his students: Leticia Palhares and Ana Mizher. I invite you to read their talks as this people are doing a real fine work. On the same afternoon I listened to the talk of Pedro Bicudo. Pedro, besides being a nice company for fun, is also a very good physicist performing relevant work in the area of lattice QCD. He is a pioneer in the use of CUDA, parallel computing using graphic processors, and I intend to use his code, produced with his student Nuno Cardoso, on my machine to start doing lattice QCD at very low cost. On his talk you can see a photo of one of my graphic cards. He used lattice computations to understand the phase diagram of QCD. Quite interesting has been the talk of Jan Pawlowski about the phase diagram of two flavor QCD. He belongs to a group of people that produced the so called scaling solution and it is a great moment to see them to recognize the very existence of the decoupling solution, the only one presently seen on lattice computations.

On Wednesday the morning session continued on the same line of the preceding day. I would like to cite the work of Marco Ruggieri because, besides being a fine drinking companion (see below), he faces an interesting problem:  How does the ground state of QCD change in presence of a strong magnetic field? Particularly interesting is to see how the phase diagram gets modified. On the same line were the successive talks of Ana Mizher and Maxim Chernodub. Chernodub presented a claim that in this case vacuum is that of an electromagnetic superconductor due to $\rho$ meson condensation. In this area of research the main approach is to use some phenomenological model. Ana Mizher used a linear sigma model while Marco preferred the Nambu-Jona-Lasinio model. The reason for this is that the low-energy behavior of QCD is not under control and the use of well-supported effective models is the smarter approach we have at our disposal. Of course, this explains why the work of our community is so important: If we are able to model the propagator of the gluon in the infrared, all the parameters of the Nambu-Jona-Lasinio model are properly fixed and we have the true infrared limit of QCD. So, the stake is very high here.

In the afternoon there were some talks that touched very near the question of infrared propagators. Silvio Sorella is an Italian theoretical physicist living in Brazil. He is doing a very good work in this quest for an understanding of the low-energy behavior of QCD. This work is done in collaboration with several other physicists. The idea is to modify the Gribov-Zwanziger scenario, that by itself will produce the scaling solution currently not seen on the lattice, to include the presence of a gluon condensate. This has the effect to produce massive propagators that agree well with lattice computations. In this talk Silvio showed how this approach can give the masses of the lowest states of the glueball spectrum. This has been an important step forward showing how this approach can be used to give experimental forecasts. Daniel Zwanziger then presented a view of the confinement scenario. The conclusion was very frustrating: So far nobody can go to the Clay Institute to claim the prize. More time is needed. Daniel has been the one who proposed the scenario of infrared Yang-Mills theory that produced the scaling solution. The idea is to take into account the problem of Gribov copies and to impose that all the computations must be limited to the first Gribov horizon. If you do this the gluon propagator goes to zero lowering momenta and you get positivity maximally violated obtaining a confining theory. So, this scenario has been called Gribov-Zwanzinger. From lattice computations we learned that the gluon propagator reaches a non zero finite value lowering momenta and this motivated Silvio and others to see if one could maintain the original idea of Gribov horizon and agreement with lattice computations of the Gribov-Zwanzinger scenario. Matthieu Thissier presented a talk with an original view. The idea is to consider QCD with a small perturbation expansion at one loop and a mass term added by hand. He computed the gluon propagator and compared with lattice data till the infrared obtaining a very good agreement. Arlene Aguilar criticized strongly this approach as he worked with a coupling larger than one (a huge one said Arlene) even if he was doing small perturbation theory. I talked about this with Matthieu. My view is that the main thing to learn from this kind of  computations is that if you take a Yukawa-like propagator with a mass going at least as $m^2+cq^2$ (do you remember Orlando Oliveira talk?) the agreement with lattice data is surely fairly good and so, even if you have done something that is mathematically questionable, surely we apprehend an important fact! The afternoon session was concluded by the talk of Daniele Binosi. With Daniele we spent a nice night in Ghent. He is a student of Joannis Papavassiliou and, together with Arlene Aguilar, this group is doing fine work on numerically solving Dyson-Schwinger equations to get the full propagator of Yang-Mills theory. They get a very good agreement with lattice data and support the view that, on the full range of energies, the Cornwall propagator for the gluon with a logarithmic running mass reaching a constant in the infrared is the right description of the theory. Daniele presented a beautiful computation based on Batalin-Vilkoviski framework that supported the conclusions of his group. It should be said that he presented a different definition of the running coupling that grants a non-trivial fixed point at infrared. This is  a delicate matter as, already a proper definition of the running coupling for the infrared is not a trivial question. Daniele’s definition is quite different from that given by Andre Sternbeck in his talk as the latter has just the trivial fixed point as is emerging from the lattice computations.

On Thursday the first speaker was Attilio Cucchieri. Attilio and his wife, Tereza Mendes, are doing a fine work on lattice computations that reached a breakthrough at Lattice 2007 when they showed, with a volume of $(27fm)^4$, that the gluon propagator in the Landau gauge reaches a finite non-zero value lowering momenta. This was a breakthrough, confirmed at the same conference by two others groups (Orlando Oliveira by one side and I. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker and A. Sternbeck by the other side), as for long time it was believed that the only true solution was the scaling one and the gluon propagator should have gone  to zero lowering momenta. This became a paradigm so that papers have got rejected on the basis that they were claiming a different scenario. Attilio this time was on a very conservative side presenting an interesting technical problem. Tereza’s talk was more impressive showing that, with higher temperatures and increasing volumes, in the Landau gauge the plateau is still there. With Tereza and Attilio we spent some nice time in a pub discussing together with Marco Ruggeri about the history of their community, how they went to change everything about this matter and their fighting for this. I hope one day this people will write down this history because there is a lot to learn from it. In the afternoon session there was a talk by Reinhard Alkofer. Alkofer has been instrumental in transforming the scaling solution into a paradigm for a lot of years in the community. Unfortunately lattice computations talked against it and, as Bob Dylan one time said, times are changing. He helped the community with discovering a lot of smart students that have given an important contribution to it. In his talk he insisted with his view with a proposal for the functional form for the propagator (this was missing until now for the scaling solution) and a computation of the mass of the $\eta'$. $\eta'$ is a very strange particle. From ${\rm DA}\Phi{\rm NE}$ (KLOE-2) we know that this is not just a composite state of quarks but it contains a large part made of glue: It is like to have to cope with an excited hydrogen atom and so, also its decay is to be understood (you can read my paper here). So, maybe a more involved discussion is needed before to have an idea of how to get the mass of this particle. After Alkofer’s talk followed the talks of Aguilar and Papavassiliou. I would like to emphasize the relevance of the work of this group. Aguilar showed how they get an effective quark mass from Schwinger-Dyson equations when there is no enhancement in the ghost propagator. Papavassiliou proposed to extend the background field method to Schwinger-Dyson equations. I invite you to check the agreement they get for the Cornwall propagator of the gluon with lattice data in Arlene’s talk and how this can give the form $m^2+cq^2$  at lower momenta. My view is that, combining my recent results on strongly coupled expansions for Yang-Mills and scalar field theories and the results of this group, a meaningful scenario is emerging giving a complete comprehension of what is going on for Yang-Mills theory at lower energies. Joannis gave us an appointment for the next year in Trento. I will do everything I can to be there! Finally, the session was completed with Axel Mass’ talk. Axel has been a student of Alkofer and worked with Attilio and Tereza. He put forward a lattice computation of Yang-Mills propagators in two dimensions that, for me, should have completely settled the question but produced a lot of debate instead. He gave in his talk another bright idea: To study on the lattice a scalar theory interacting with gluons. I think that this is a very smart way to understand the mechanism underlying mass generation in these theories. From the works discussed so far it should appear clear that Schwinger mechanism (also at classical level (see my talk)!) is at work here.  The talk of Axel manifestly shows this. It would be interesting if he could redo the computations taking a massless scalar field to unveil completely the dynamical generation of masses.

On Friday the morning session started with an interesting talk by Hans Dierckx trying to understand cardiac behavior using string theory. A talk by Oliver Rosten followed. Oliver produced a PhD thesis on the exact renormalization group of about 500 pages (see here). His talk was very beautiful and informative and in some way gave a support to mine. Indeed, he showed, discussing on the renormalization group, how a strong coupling expansion could emerge. In some way we are complimentary. I will not discuss my talk here but you are free to ask questions. The conference was concluded by a talk of Peter van Baal. Peter has a terrible story about him and I will not discuss it here. I can only wish to him the best of the possible lucks.

Finally, I would like to thank the organizers for the beautiful conference they gave me the chance to join. The place was very nice (thanks Nele!) and city has an incredible beauty. I think these few lines do not do justice to them and all the participants for what they have given. See you again folks!

## The many faces of QCD

02/11/2010

After a long silence, due to technical impediments as many of you know, I turn back to you from Ghent (Belgium). I am participating at the conference “The many faces of QCD”. You can find the program here. The place is really beautiful as the town that I had the chance to look out yesterday evening. Organizers programmed a visit downtown tomorrow and I hope to see this nice town also at the sun light. The reason why this conference is so relevant is that it gathers almost all the people working on this matter of Green functions of Yang-Mills theory and QCD whose works I cited widely in my blog and in my papers. Now, I have the chance to meet them and speak to them. I am writing after the second day ended. The atmosphere is really exciting and discussion is always alive and it happens quite often that speakers are interrupted during their presentations. The situation this field is living is simply unique in the scientific community. They are at the very start of a possible scientific revolution as they are finally obtaining results of non-perturbative physics in a crucial field as that of QCD.

Disclaimer: The talks I will comment on are about results very near my research area. Talks I will not cite are important and interesting as well and the fact that I will not comment about them does not imply merit for good or bad. Anyhow, I will appreciate any comment by any participant to the conference aiming to discuss his/her work.

I would like to cite some names here but I fear to forget somebody surely worthwhile to be named. From my point of view, there have been a couple of talks that caught my attention more strongly than others, concerning computations on the lattice. This happened with the talk of Tereza Mendes yesterday and the one of Orlando Oliveira today. Tereza just studied the gluon propagator at higher temperatures obtaining again striking and unexpected results.  There is this plateau in the gluon propagator appearing again and again when lattice volume is increased. It would have been interesting to have also a look to the ghost and the running coupling. Orlando, by his side, showed for the first time an attempt to fit with the function $G(p)=\sum_n\frac{Z_n}{p^2+m^2_n}$ that you can recognize as the one I proposed since my first analysis to explain the infrared behavior of Yang-Mills theory. But Orlando went further and found the next to leading order correction to the mass appearing in a Yukawa-like propagator.  The idea is to see if the original hypothesis of Cornwall can agree with the current lattice computations. So, he shows that for the sum of propagators one can get even better agreement in the fitting increasing the number of masses (at least 4)  and for the Cornwall propagator you will need a mass corrected as $M^2+\alpha p^2$. Shocking as may seem, I computed this term this summer and you can find it in this paper of mine. Indeed, this is a guess I put forward after a referee asked to me an understanding of the next-to-leading corrections to my propagator and, as you can read from my paper, I guessed it would have produced a Cornwall-like propagator. Indeed, this is just a first infrared correction that can arise by expanding the logarithm in the Cornwall’s formula.

The question of the gluon condensate, that I treated in my blog extensively thanks to the help of Stephan Narison, has been presented today by Olivier Péne through a lattice computation. Olivier works in the group of Philippe Boucaud and contributed to the emerging of the now called decoupling solution for the gluon propagator. The importance of this work relies on the fact that a precise determination of the gluon condensate from lattice is fundamental for our understanding of low-energy behavior of QCD. For this analysis is important to have a precise determination of the constant $\Lambda_{QCD}$. Boucaud’s group produced an approach to this aim. Similarly, Andre Sternbeck showed how this important constant could be obtained by a proper definition of the running coupling and he showed a very fine agreement with the result of Boucaud’s group.

Finally, I would like to remember the talk of Valentine Zakharov. I talked extensively about Valentine in my previous blog’s entries. His discoveries in this area of physics are really fundamental and so it is important to have a particular attention to his talks. Substantially, he mapped scalar fields and Yang-Mills fields to get an understanding of confinement! As I am a strong supporter of this view, as my readers may know from my preceding posts, I was quite excited to see such a an idea puts forward by Valentine.

As conference’s program unfolds I will take you updated with an eyes toward the aspects that are relevant to my work. Meantime, I hope to have given to you the taste of the excitement this area of research conveys to us that pursue it.

## Quark-gluon plasma seen at CERN

22/09/2010

CERN announced today (see CERN announcement) that a relevant new effect has been observed by CMS experiment at LHC. Due to its deep similarities with the analogous effect seen at heavy ion collision facilities, it is possibly the first observation of a quark-gluon plasma in proton collisions in a high-energy experiment. A paper has been sent out for review. They made quark bound looser indeed. A first important finding from LHC.

## QCD 10

09/07/2010

Last week I have been in Montpellier (France). The occasion  was one of the most important as it was 25th anniversary of QCD Conference series that are held there with two year cadence. The organizer is Stephan Narison and this was QCD 10. Thanks to Stephan, it is the third time that I have the opportunity to go to Montpellier to talk with him and other fine people about QCD. I have this opportunity also to learn a lot about this matter and to improve the quality of my research. This time, Stephan managed also to remember that are passed 31 years since the seminal SVZ paper on sum rules in QCD by Misha Shifman, Arkady Vainshtein and Valentine Zakharov that made a major breakthrough in the field. I have the luck to exchange some words with Prof. Zakharov and he was really illuminating about the current situation of different aspects of this field. I hope to see him in Ghent (Belgium) in the fall this year. He is one of the organizer of the conference The Many Faces of QCD and I am a registered participant. Misha Shifman was also there and showed how a track toward understanding confinement can be pursued passing through supersymmetry (see here). I take this chance to remember that Shifman, Vainshtein and Zakharov achieved a fundamental result in computing the exact beta function of supersymmetric QCD (see here) but to these notable names we must add the name of Novikov.

The conference has been very well organized and the atmosphere was really friendly. Scientific content was absolutely interesting and some experimental groups presented firstly some new results here. You can take a look at all the talks here. Mine is this. About the questions that mostly urge me, I was impressed again by a talk of  COMPASS Collaboration (see also here). They confirm their finding that gluons do not seem to weigh too much in determining proton spin. As you know, this is what I expect from my theoretical analysis for low-energy QCD. Proton spin is mostly due to quark spins and orbital motion, the latter for the larger part.

Results from KLOE-2, at INFN of Frascati (Italy), are really striking. Talk is here. They have increasing evidence that $\sigma$ resonance is indeed a glueball but they are not claiming this yet. The track they followed till now is a really smart one and implies studies of $\eta'$ decay and studies of the invariant mass of the $\pi\pi$ pair obtained from it. They also showed that $\eta'$ has a significant glue component and this would imply (see also my talk), that its main decay process produces a $\sigma$ particle. Indeed, what these researchers have found is the first clear evidence of the analogous of an excited atom in strong interactions and the corresponding decay into the emission of the corresponding force carrier. Their approach is really striking and it is my personal conviction that a lot more should be expected from this collaboration ending a long research for the first glueball. But strongly linked to this, there is an interesting theoretical analysis by Vincent Mathieu together with Vicente Vento that strongly support all these ideas about $\eta'$ nature. Vincent gave the talk and we have had a very interesting exchange about. He was so kind to inform me about the conference at Ghent. We have had an interesting evening at a restaurant in Montpellier together with other very nice fellows (see below) about a riddle on a row of physicists, the colors of their hats and how to save their lives from a mad man aiming to kill all of them.

When you go to a conference like this, the chance to meet very interesting people is the highest. Indeed, I have had the opportunity to meet three Italian researchers: Francesco Dettori at LHCb from University of Cagliari (Italy), Luca Mucibello at CMS from University of Antwerpen (Belgium) and Silvia Pisano from Orsay (France).  We have had a lot of good time and discussions of any kind, ranging from physics to politics and other. I am aware that science is an international enterprise but I am Italian and is really a satisfaction to see such smart young countrymen being part of it notwithstanding mortifications our politicians are giving them and to research at large. On a similar side, I have also met people like Mihail Iliescu that is working at INFN and after a lot of time has not yet a position. He told me that he lost a permanent position in Romania after heavy cuts from their government. He is collaborating to a very interesting experiment about Kaon atoms with SIDDHARTA Collaboration.

The Conference was concluded with a dinner in a beautiful place near Montpellier. Stephan presented some dances from Madagascar while wine and food were really satisfactory. Then, after a walk downtown and a beer offered by Francesco, we left with the aim to maintain our bounds somehow.

Again a great experience in Montpellier. Thank you very much, Stephan!