## Back from Paris

13/06/2011

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

## And you are calling it a gluon yet…

02/06/2010

One of the more questionable points I have discussed so far is: What are QCD asymptotic states at very low  momenta? This question is not trivial at all. If you will speak with experts in this matter, a common point they will share is that gluons carry color charge and so must form bound states. A claim like this has a strong implication indeed. The implication is that Yang-Mills Hamiltonian must display the same asymptotic states at both ends of the energy range. But the problem is exactly in the self-interaction of the theory that, at very low momenta, becomes increasingly large and gluons, asymptotic states of Yang-Mills theory in the asymptotic freedom regime, are no more good to describe physics. So, what are good states at low energies? I have already answered to this question a lot of times (recently here) and more and more confirmations are around. I would like just to cite a very nice paper I have seen recently on arxiv (see here) by Stanley Brodsky, Guy de Teramond and Alexandre Deur. These authors have nicely exploited AdS/CFT symmetry obatining striking results in the understanding of low-energy QCD. I would like to cite again the work of these authors as their soft-wall model is indeed a strong support to my view. It would be really interesting to get them working out a pure Yang-Mills model obtaining beta function and all that.

What one has at low end of momenta is a new set of states, glue states or glueballs if you prefer, that permits strong interactions. These states have already been seen in most laboratories around the World and belong to the open question of the understanding of the lower part of the hadronic spectrum.

07/10/2009

Stan Brodsky is a renowned physicist that has produced a lot of very good works. As I work on QCD, I try to be up-to-date as much as possible and I spend some time to read the most recent literature about. AdS/CFT applied to QCD is a very hot topic these times and I run into a beautiful paper by Stan and Guy de Téramond that was recently published in Physical Review Letters (a preprint is here). Their work is inspired by AdS/CFT in that they are able to map on a five dimensional Anti-de Sitter space a light-front Hamiltonian for QCD, producing a Schrödinger-like equation with a proper potential to get the spectrum of the theory. This equation is depending by a single proper variable and is exactly solvable. Two classes of models can be identified in this way that are those well-known in literature:

• Hard-wall model with a potential described by an infinite potential wall till a given cut-off that fixes the mass scale.
• Soft-wall model with a harmonic potential producing Regge trajectories.

So, these authors are able to give a clever formulation of two known models of QCD obtained from AdS/CFT conjecture and they manage them obtaining the corresponding spectra of mesons and baryons. I would like to emphasize that the hard-wall model was formulated by Joseph Polchinski and Matthew Strassler and was instrumental to show how successful AdS/CFT could be in describing QCD spectrum. This paper appeared in Physical Review Letters and can be found here. Now, leaving aside Regge trajectories, what Stan and Guy show is that the mass spectrum for glueballs in the hard wall model goes like

$m_n\approx 2n+L$

being $n$ an integer and $L$  the angular momentum. This result is interesting by its own. It appears to be in agreement both with my recent preprint and my preceding work and with most of the papers appeared about Yang-Mills theory in 2+1 dimensions. Indeed, they get this spectrum being the zeros of Bessel functions and the cut-off making the scale. Very simple and very nice.

I should say that today common wisdom prefers to consider Regge trajectories being hadron spectroscopy in agreement with them but, as glueballs are not yet identified unequivocally, I am not quite sure that the situation between a soft wall and hard wall models is so fairly well defined. Of course, this is a situation where experiments can decide and surely it is just a matter of a few time.

14/01/2009

My point of view about this question, as the readers of the blog may know, is that a general technique to strong coupling problems should be preferred to more aimed approaches. This by no means diminishes the value of these works. Another point I have discussed about the spectrum of AdS/QCD is what happens if one takes the lower state at about 1.19, does one recover the ground state seen in lattice QCD for the glueball spectrum as the next state?

The value of this approach relies on a serious possibility to verify, with a low energy theory, a higher level concept connecting gravity and gauge theories. Both sides have something to be earned.

## An inspiring paper

24/10/2008

These days I am closed at home due to the effects of flu. When such bad symptoms started to relax I was able to think about physics again.  So, reading the daily from arxiv today I have uncovered a truly inspiring paper from Antal Jakovac a and Daniel Nogradi (see here). This paper treats a very interesting problem about quark-gluon plasma. This state was observed at RHIC at Brookhaven. Successful hydrodynamical models permit to obtain values of physical quantities, like shear viscosity, that could be in principle computed from QCD. The importance of shear viscosity relies on the existence of an important prediction from AdS/CFT symmetry claiming that the ratio between this quantity and entropy density can be at least $1/4\pi$. If this lower bound would be proved true we will get an important experimental verification for AdS/CFT conjecture.

Jakovac and Nogradi exploit the computation of this ratio for SU(N) Yang-Mills theory. Their approach is quite successful as their able to show that the value they obtain is still consistent with the lower bound as they have serious difficulties to evaluate the error. But what really matters here is the procedure these authors adopt to reach their aim making this a quite simple alley to pursuit when the solution of Yang-Mills theory in infrared is acquired. The central point is again the gluon propagator. These authors assume simply the very existence of a mass gap taking for the propagator something like $e^{-\sigma\tau}$ in Euclidean time. Of course, $\sigma$ is the glueball mass. This is a too simplified assumption as we know that the gluon propagator is somewhat more complicated and a full spectrum of glueballs does exist that can contribute to this computation (see my post and my paper).

So, I spent my day to extend the computations of these authors to a more realistic gluon propagator.  Indeed, with my gluon propagator there is no need of one-loop computations as the identity at 0-loop $G_T=G_0$ does not hold true anymore for a non-trivial spectrum and one has immediately an expression for the shear viscosity. I hope to give some more results in the near future.