Paper with a proof of confinement has been accepted

28/03/2018

Recently, I wrote a paper together with Masud Chaichian (see here) containing a mathematical proof of confinement of a non-Abelian gauge theory based on Kugo-Ojima criterion. This paper underwent an extended review by several colleagues well before its submission. One of them has been Taichiro Kugo, one of the discoverers of the confinement criterion, that helped a lot to improve the paper and clarify some points. Then, after a review round of about two months, the paper has been accepted in Physics Letters B, one of the most important journals in particle physics.

This paper contains the exact beta function of a Yang-Mills theory. This confirms that confinement arises by the combination of the running coupling and the propagator. This idea was around in some papers in these latter years. It emerged as soon as people realized that the propagator by itself was not enough to grant confinement, after extended studies on the lattice.

It is interesting to point out that confinement is rooted in the BRST invariance and asymptotic freedom. The Kugo-Ojima confinement criterion permits to close the argument in a rigorous way yielding the exact beta funtion of the theory.

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Good news from Moriond

20/03/2018

Some days ago, Rencontres of Moriond 2018 ended with the CERN presenting a wealth of results also about the Higgs particle. The direction that the two great experiments, ATLAS and CMS, took is that of improving the measurements on the Standard Model as no evidence has been seen so far of possible new particles. Also, the studies of the properties of the Higgs particle have been refined as promised and the news are really striking.

In a communicate to the public (see here), CERN finally acknowledge, for the first time, a significant discrepancy between data from CMS and Standard Model for the signal strengths in the Higgs decay channels. They claim a 17% difference. This is what I advocated for some years and I have published in reputable journals. I will discuss this below. I would like only to show you the CMS results in the figure below.

ATLAS, by its side, is seeing significant discrepancy in the ZZ channel (2\sigma) and a 1\sigma compatibility for the WW channel. Here are their results.

On the left the WW channel is shown and on the right there are the combined \gamma\gamma and ZZ channels.

The reason of the discrepancy is due, as I have shown in some papers (see here, here and here), to the improper use of perturbation theory to evaluate the Higgs sector. The true propagator of the theory is a sum of Yukawa-like propagators with a harmonic oscillator spectrum. I solved exactly this sector of the Standard Model. So, when the full propagator is taken into account, the discrepancy is toward an increase of the signal strength. Is it worth a try?

This means that this is not physics beyond the Standard Model but, rather, the Standard Model in its full glory that is teaching something new to us about quantum field theory. Now, we are eager to see the improvements in the data to come with the new run of LHC starting now. In the summer conferences we will have reasons to be excited.


It was twenty years ago today . . .

16/08/2011

ResearchBlogging.org

With these beautiful words starts a recollection paper by the founder of arXiv, Paul Ginsparg. This is worth the reading as this history spans a number of years exactly overlapping the computer revolution that definitely changed our lives. What Paul also changed through these new information tools was the way researchers should approach scientific communication. It is a revolution that is not stopped yet and all the journals I submit my papers have a link to arXiv for direct uploading of the preprint. This change has had also a great impact on the way these same journals should present to authors, readers and referees as well at their website.

For my readers I would like just to point out how relevant was all this for our community with the Grisha Perelman’s case. I think all of you are well aware that Perelman never published his papers on a journal: You can find both of them on arXiv. Those preprints paid as much as a Fields medal and a Millenium prize. Not bad I should say for a couple of unpublished papers. Indeed, it is common matter to have a paper largely discussed well before its publication and often a preprint becomes a case in the community without not even seeing the light of a publication. It is quite common for us doing research to console colleagues complaining about the harsh peer-review procedure by saying that today exists arXiv and that is enough to make your work widely known.

I was a submitter since 1994, almost at the very start, and I wish that the line of successes of this idea will never end.

Finally, to prove how useful is arXiv for our community, I would like to point out to you, for your summer readings a couple of papers. The first one is this from R. Aouane, V. Bornyakov, E.-M. Ilgenfritz, V. Mitrjushkin, M. Müller-Preussker, A. Sternbeck. My readers should know that these researchers always do a fine work and get important results on their lattice computations. The same happens here where they study the gluon and ghost propagators at finite temperature in the Landau gauge. Their conclusion about Gribov copies is really striking, comforting my general view on this matter (see here), that Gribov copies are not essential not even when one rises the temperature. Besides, they discuss the question of a proper order parameter to identify the phase transition that we know exists in this case.

The next paper is authored by Tereza Mendes, Axel Maas and Stefan Olejnik (see here). The idea in this work is to consider a gauge, the \lambda-gauge, with a free parameter interpolating between different gauges to see the smoothness of the transition and the way of change of the propagators. They reach a volume of 70^4 but Tereza told me that the errors are too large yet for a neat comparison with smaller volumes. In any case, this is a route to be pursued and I am curious about the way the interpolated propagator behaves at the deep infrared with larger lattices.

Discussions on Higgs identification are well alive yet ( you can see here). take a look and enjoy!

Paul Ginsparg (2011). It was twenty years ago today … arXiv arXiv: 1108.2700v1

R. Aouane, V. Bornyakov, E. -M. Ilgenfritz, V. Mitrjushkin, M. Müller-Preussker, & A. Sternbeck (2011). Landau gauge gluon and ghost propagators at finite temperature from
quenched lattice QCD arXiv arXiv: 1108.1735v1

Axel Maas, Tereza Mendes, & Stefan Olejnik (2011). Yang-Mills Theory in lambda-Gauges arXiv arXiv: 1108.2621v1


What’s going on with Higgs particle?

03/08/2011

ResearchBlogging.org

The aftermath of the EPS Conference is quite exciting on a side. Higgs hunting points to an unexpected direction even if some residuals of an old expectation are still there. I just want to show you the graphs of this conference from Tevatron and LHC


From these it is very clear that the excluded range of mass is become significantly large restricting the possibilities to the intervals of a mass around 140 GeV or to a massive Higgs implying a strongly coupled theory. The evidence for a 140 GeV Higgs particle is yet small, about two sigmas, and we cannot exclude that this is a fluke but, to support this clue, it appears both at Tevatron and LHC. A small peak at around 250 GeV is seen only by ATLAS and could disappear in the future.

What I would like to emphasize here is that the possibility of a strongly coupled Higgs is well alive and this can have deep implications for the model and physics at large. There are several reasons for this. First of all, a strongly coupled Higgs field implies supersymmetry (see here). This result is inescapable and some breaking pattern of supersymmetry must be devised to get the right mass spectrum of the Standard Model. But this is already old and well-acquired matter. The most important point is that there will be a completely new way to approach quantum field theory. So far, quantum field theory has been managed just using weak perturbation theory but a strongly coupled Higgs would mean that we will also have to devise a perturbative technique the other way round, i.e. with a coupling increasingly large.

So, I will keep on support this view of a heavy Higgs as, being a theoretical physicist, consequences will be devastating and largely more exciting of any other possibility. We will be eager to see the improvement in the next months from the measurement datasets. Certainly, on 2012 all the curtains will be definitely down.

Marco Frasca (2010). Mass generation and supersymmetry arXiv arXiv: 1007.5275v2


Paper on critical temperature revised

06/07/2011

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.


Evidence of a QCD critical endpoint at RHIC

21/06/2011

ResearchBlogging.org

A critical endpoint in QCD is a kind of holy grail in nuclear physics. It has been theorized as a point where deconfinement occurs and hadronic matter leaves place to some kind of plasma of quarks and gluons. We know that the breaking of chiral symmetry is something that people has proposed several years ago and we recently gave a proof of existence of such a transition (see here). But here the situation is more complex: We have essentially two physical variables to describe the phase diagram and these are temperature and chemical potential. This makes lattice computations a kind of nightmare. The reason is the sign problem. Some years ago Zoltan Fodor and Sandor Katz come out with a pioneering paper (see here) doing lattice computation and seeing the chemical potential taking an imaginary factor: The infamous sign problem. Discretization implies it but a theoretical physicist can happily lives just ignoring it. Fodor and Katz evaded the problem just taking an absolute value but this approach was criticized casting doubt on their results at chemical potential different from zero. It should be said that they gave evidence of existence for the critical point and surely their results are unquestionably correct with zero chemical potential in close agreement with my and others findings. A lucid statement of the problems of lattice computations for finite temperatures and densities was recently given by Philippe de Forcrand (see here).

So far, people has produced several results just working around with phenomenological model like a Nambu-Jona-Lasinio or sigma model. This way of work arises from our current impossibility to manage QCD at very low energies but, on the other side, we are well aware that these models seem to represent reality quite well. The reason is that a Nambu-Jona-Lasinio is really the low-energy limit for QCD but I will not discuss this matter here having done this before (see here). Besides, the sigma model arises naturally in the low-energy limit interacting with quarks. The sigma field is a true physical field that drives the phase transitions in low-energy QCD.

While the hunt for the critical point in the lattice realm is already open since the paper by Fodor and Katz, the experimental side is somewhat more difficult to exploit. The only facility we have at our disposal is RHIC and no much proposals are known to identify the critical point from the experimental data were available since a fine proposal by Misha Stephanov a few years ago (see here and here). The idea runs as follows.  At the critical point, fluctuations are no more expected to be Gaussian and all the correlations are extended to all the hadronic matter  as the correlation length is diverging. Non-Gaussianity implies that if we compute cumulants, linked to higher order moments of the probability distribution, these will depend on the correlation length with some power and, particularly, moments like skewness and kurtosis, that are a measure of deviation from Gaussianity, start to change. Particularly, kurtosis is expected to change sign. So, if we are able to measure such a deviation in a laboratory facility we are done and we get evidence for a critical point and critical behavior of hadronic matter. We just note that Stephanov accomplishes his computations using a sigma model and this is a really brilliant hindsight.

At RHIC a first evidence of this has been obtained by STAR Collaboration (see here). These are preliminary results but further data are expected this year. The main result is given in the following figureWe see comparison with data from lattice as red balls for Au+Au collisions and the kurtosis goes down to negative values! The agreement with lattice data is striking and this is already evidence for a critical endpoint. But this is not enough as can be seen from the large error bar. Indeed further data are needed to draw a definitive conclusion and, as said, these are expected for this year. Anyhow, this is already a shocking result. Surely, we stay tuned for this mounting evidence of a critical endpoint. This will represent a major discovery for nuclear physics and, in some way, it will make easier lattice computations with a proper understanding of the way the sign problem should be settled.

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

Z. Fodor, & S. D. Katz (2001). Lattice determination of the critical point of QCD at finite T and  \mu JHEP 0203 (2002) 014 arXiv: hep-lat/0106002v2

Philippe de Forcrand (2010). Simulating QCD at finite density PoS (LAT2009)010, 2009 arXiv: 1005.0539v2

M. A. Stephanov (2008). Non-Gaussian fluctuations near the QCD critical point Phys.Rev.Lett.102:032301,2009 arXiv: 0809.3450v1

Christiana Athanasiou, Krishna Rajagopal, & Misha Stephanov (2010). Using Higher Moments of Fluctuations and their Ratios in the Search for
the QCD Critical Point Physical review D arXiv: 1006.4636v2

Xiaofeng Luo (2011). Probing the QCD Critical Point with Higher Moments of Net-proton
Multiplicity Distributions arXiv arXiv: 1106.2926v1


Back from Paris

13/06/2011

ResearchBlogging.org

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


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