## Another success at SLAC

25/08/2008

Yesterday I was reading a copy of August of Physics World, that I receive being member of Institute of Physics, and come to a small piece about a recent measure at SLAC. BABAR collaboration was able to identify and measure the mass of the ground state of $\bar b b$ meson also called bottomonium and identified as $\eta_b(1S)$ (their paper is here). In order to reach their aims, they used the process $\Upsilon(3S)\rightarrow \gamma\eta_b(1S)$ and they were successful in obtaining a very precise value of the mass, $9388.9 ^{+3.1}_ {-2.3} (stat) +/- 2.7(syst)$ MeV, collecting about 20000 photons produced in the process.

We want to build on this beautiful result at SLAC by deriving the mass of the ground state of bottomonium. We already know, since the studies of charmonium, that a Coulomb-like potential does most of the job but not all. This is a great intuition by Politzer, one of the discoverers of asymptotic freedom (the others being Gross and Wilczek). The reason why this approximation works so well is that these quarks are really massive and so the interaction happens at very short distances and also a non-relativistic approximation does hold.

In order to verify how good is this approximation we consider our gluon propagator. This is given by

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

being

$B_n=(2n+1)\frac{\pi^2}{K^2(i)}\frac{(-1)^{n+1}e^{-(n+\frac{1}{2})\pi}}{1+e^{-(2n+1)\pi}}$

and

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

with $\sqrt{\sigma}=0.44$ GeV. At this stage we can derive the potential between quarks setting $p_0=0$ and Fourier transforming in space coordinates giving

$V(r)=-\alpha_s\sum_{n=0}^\infty B_n \frac{e^{-m_n r}}{r}$.

So, using the small distance approximation we get finally

$V(r)\approx -\frac{\alpha_s}{r}+\alpha_s\sum_{n=0}^\infty B_nm_n$

and we can estimate the constant to be $\epsilon=0.876\alpha_s\sqrt{\sigma}$. Finally, from PDG we have $\alpha_s(m_b)=0.22$ being $m_b=4.68$ GeV the mass of the bottom quark. $\eta_b(1S)$ is a singlet state and so no spin-orbit effect is present. Using standard formula for hydrogen atom we have finally

$m_{\eta_b}=2m_b-\frac{1}{4}\alpha_s^2 m_b+\epsilon=9.388$ GeV

that is the mass measured at SLAC. We just note the relevance of the constant term $\epsilon=0.0848$ GeV to reach the agreement, a very nice confirmation of our gluon propagator and the approximations used for heavy quark bound states.

As a final consideration we note as a good theory permits to do calculations to be compared with experiments. Bad theories do not have such a property proving themselves ugly already at the start.

## Dyson-Schwinger equations and Mathematica

22/08/2008

As always I read the daily arxiv sends to me and I have found a beatiful work due to Alkofer and collaborators. An important reason to mention it too here is that it gives an important tool to work with that can be downloaded. This tool permits to obtain Dyson-Schwinger equations for any field theory. Dyson-Schwinger equations are a tower of equations giving all the correlators of a quantum field theory so, if you know how to truncate this tower you will be able to get a solution to a quantum field theory in some limit.

The paper is here. The link to download the tool for Mathematica version 6.0 and higher is here.

I hope to have some time to study it and try a conversion for Maple. Currently I was not able to test it as on my laptop I have an older version of Mathematica but is just few hours away from testing on my desktop.

## Sorry but your paper is wrong!

19/08/2008

In our preceding posts we have largely discussed what are the results emerging from lattice about the gluon and ghost propagators and the running coupling and how functional methods, in the way they are currently adopted, fail to reach agreement with lattice computations at very large volumes. But we want to resume here what are the main conclusions that are obtained from such applications of functional methods. People working in this way fix the gluon propagator as

$D(p^2)=(p^2)^{k_D-1}F(p^2)$

and for the ghost

$G(p^2)=(p^2)^{k_G-1}H(p^2)$

then the claim is made that the relation $k_D+2k_G=0$ does hold while the functions $F,H$ are taken to be regular as momenta go to zero. From the relation between the exponents $k_D,k_G$ we can conclude that, excluding the trivial solution, if the gluon propagator goes to zero at lower momenta, that is $k_D>0$, than we must have $k_G<0$ that means that the ghost propagator must go to infinity at lower momenta. What they get is that the ghost propagator should go to infinity faster than a free particle. If this would be true all the confining scenarios (Zwanzinger-Gribov and Kugo-Ojima) hold true. The ghost holds a prominent role and, last but not least, a proper defined running coupling goes to a fixed point to lower momenta.

Lattice computations say that all this is blatantly wrong. Indeed, we have learned from them that

• Gluon propagator reaches a finite non-null value at lower momenta.
• Ghost propagator is that of a free particle and so ghosts play no role at lower momenta.
• Running coupling is seen to approach zero at lower momenta.

From this we can easily derive our exponents as defined by people working with functional methods: $k_D=1$ and $k_G=0$ so that $k_D+2k_G=1\ne 0$ and no relation between exponents is seen to exist. So we have got a clear cut criterion to say when a published paper about infrared behavior of Yang-Mills theory is blatantly wrong independently on the prestige of the journal that publishes it. This happens all the times the relation $k_D+2k_G=0$ is assumed to hold. I can grant that there are a lot around of these wrong papers published on the highest ranked journals. If you have time and you need fun try to search for them.

I would like to say that this belongs to dynamics of science. We are presently in a transition situation about our matter, a situation similar at that happened after the discovery of the $J/\psi$ resonance that took some time before people agreed on its nature. So, there is nothing to say to editors or referee and also to authors as mistakes are the most common facts in physics and very few people hit the right track after a wide cemetery of mistakes and wrong theories.

## Sean and Horacio

18/08/2008

I know Sean Carroll as some years ago I read his beautiful lectures on general relativity that become a book. Some years later I started to read his blog and this I do also today. Sean touched a lot of arguments in physics during these years but the most important for me are those about arrow of time and reality forming (measurement problem in quantum mechanics). These two matters are strongly linked and their understanding represents a great achievement in physics and this explains why a lot of ink, paper and digital data have been spent around the world. Sean has written an article on this on Scientific American (see here). Contrarily to some wisdom around this problem is really deep as there is no reason on Earth to accept environmental decoherence and multi-universe interpretation as the ultimate answers that finally do not grant any answer to a simple fact. This fact was explained to me quite simply by Giorgio Careri. Careri has been a professor of mine at department of physics of “La Sapienza” in Rome. A day I was walking to the new building of the department (Fermi building) together with some other students when we met him going into the opposite direction. I do not remember the reason why we started to talk but he said something I am still here to remember:”One of the deepest question physics should answer is why, having a four dimensional space-time, we can move backward and forward and we can stop in three of these dimensions but not in time?”. Currently an answer is still lacking being at the root of our understanding of how reality forms and the way it forms.

Horacio Pastawski is a researcher working at University of Cordoba in Argentina and has carried out with his a group a lot of relevant work that can be traced back on the most important archival journals in physics and on arxiv as well. Horacio’s group has found an answer to this matter through NMR experiments. The point can be traced back to the Boltzmann and Loschmidt controversy. In order to answer to the criticism of Loschmidt claiming that as all laws of mechanics are reversible one should conclude that H-theorem is false, Boltzmann put forward the so called Stosszahlansatz (molecular chaos hypothesis) to conclude that indeed H-theorem is right. Boltzmann’s hypothesis is purely statistical and being this true Boltzmann is right. So, the understanding of arrow of time passes through an explanation of Boltzmann’s Stosszahlansatz that we currently lack. But in 1998 Horacio’s group performed an NMR experiment with a complex molecule, ferrocene and cobaltocene, where they showed that an intrinsic instability appears in the thermodynamic limit provoking irreversibility (see here). This shows that Boltzmann is right and this also explains why we observe irreversibility all around in the macroscopic limit. Of course, this result met skepticism in the community and they had severe difficulties to get their paper published on an archival journal notwithstanding no flaw is appearing in their experimental procedure. Anyway, they published their results on Molecular Physics and Physica A and so these are part of scientific literature. But their results received an unexpected confirmation on PRL quite recently in a different perspective as these authors were trying to understand decoherence in quantum computation.

We see that thermodynamic limit plays a central role in our understanding of reality and this matches fairly well with the observed fact that macroscopic objects behave classically and gives also a satisfactory understanding of Boltzmann’s hypothesis that would be completely missing accepting acritically environmental decoherence and multi-verse.

## LHC: Toward the aims

14/08/2008

We are all waiting for the start-up of LHC foreseen for September 10th. People at CERN are working toward this goal and another success has been achieved with the first test of the clockwise injection system from the SPS to the LHC. We just report this milestone because as all physics community we are eager to see the first results flowing down from this machine. I think there will be particle physics before and after LHC and the former will be much different from the latter.

Here is the CERN news.

## And the ghosts disappear…

12/08/2008

Attilio Cucchieri and Tereza Mendes are two researchers working in Brazil at the forefront of our understanding of the behavior of Yang-Mills theory in the infrared. They do computations on the lattice and presently they have got the record of the largest lattice ever used to compute the behavior of propagators at the low momenta limit. Attilio has also done a lot of theoretical work in the same field. They are married but I think this is not the most relevant information for this post. Today they posted on arxiv the third revision of one of their relevant work about ghost propagator. This is a continuation of another paper of them published on PRL about the gluon propagator (see here and here). In both papers they cited one of my works as also their lattice computations support my theoretical analysis.

From their work we now know that Cucchieri and Mendes are ghostbusters. They proved on the lattice that the ghost behaves like a free particle and we know that “free particle” means no coupling. The ghost has disappeared and the Gribov-Zwanzinger scenario faded away. These authors ask a serious question: What is now the confining mechanism? Indeed, there is another question to be answered: What do Gribov copies serve to? They do not seem to be relevant in any part of QCD and so this also is a question to be answered. We have lived with such ghosts for a lot of time and now time is come to give up to cope with them.

We expect new striking works form Attilio and Tereza about QCD now that they contributed so strongly to set the scenario.

## A great intuition

11/08/2008

In the fall of August 2001 I was in Gargnano on Garda Lake in Italy to participate at the Conference “Mysteries, Puzzles and Paradoxes in Quantum Mechanics”. This was one of a series of Conferences with the same title organized by Rodolfo Bonifacio, a former full professor at University of Milan and now retired (latest news say that he is taking sun in Brasil). These Conferences were very successful as the participants were generally the most representative in the field of quantum optics and fundamental physics. I have had also the luck to meet interesting people that are still in touch with me like Federico Casagrande, an associate professor at University of Milan currently carrying on relevant research in quantum optics and laser physics. That year there was also Vittorio Giovannetti. Vittorio took a PhD in Physics at University of Camerino with Paolo Tombesi and David Vitali that are behind an international renowned group of quantum optics and gave also to the community a number of high quality researchers. At that time Vittorio was a post-doc at MIT and was working together with Seth Lloyd and another brilliant Italian post-doc Lorenzo Maccone. This collaboration produced a lot of relevant papers, mostly in applications of quantum mechanics, that appeared on Nature, PRL and several other high impact archival journals.

Bonifacio was involved with an original idea about intrinsic decoherence. He got a paper published on Nuovo Cimento B and another, with the collaboration of Camerino’s group, on PRA. After we listened at his talk about this interesting matter I exit the room where talks were taken place and exchanged some words with Vittorio and another person. In a while I averted my attention from Vittorio and the other person and started to mumbling thinking about decoherence. Than, looking at Vittorio I said loudly: “Yes, thermodynamic limit! Classical limit can be obtained from quantum mechanics much in the same way thermodynamics is obtained from statistical mechanics!”. Vittorio stared at me and repeated “Yes, thermodynamic limit.” than kept on talking with the other person. This was the start of a lot of papers I have got published on this matter and some interesting experimental work has also been done. The question is still open. The proceedings of the Conference are here.

Today there is a lot of confusion in physics about classical limit and interpretation of quantum mechanics. Indeed, there is a lot of people accepting without critics many-world interpretation without realizing that are out of the realm of physics in this case. If a theory has no criteria to undergo an experimental check is not a theory and we have to forget about this. I have seen a lot of unprepared people talking about many-worlds without elementary cognitions of physics. This is bad and this is why we are living this times today. Mathematics is not enough to be a physicist.