## Today in arXiv

08/04/2011

After the excitation for the findings at Tevatron, we turn back to routine. Of course, I have never forgotten to cast a glance at arXiv where it is crystal clear the vitality of the physics community. I want to put down these few lines to point to your attention a couple of papers appeared today on the preprint archive. Today, Nele Vandersickel uploaded her PhD Thesis (see here). She has got her PhD on March this year. Nele was one of the organizers of the beautiful and successful conference in Ghent (Belgium) where I was present last year (see here, here and here). But most important is her research work with the group of Silvio Sorella and David Dudal that is the central theme of her thesis. Nele does an excellent job in presenting a lot of introductory material, difficult to find in the current literature, beside her original research. Sorella and Dudal have accomplished an interesting research endeavor by supporting the Gribov-Zwanziger scenario, at odds in the initial formulation with lattice data, with their view that condensates must be accounted for. In this way, Gribov-Zwanziger scenario can be taken to agree with lattice computations.  These theoretical studies describe a consistent approach and these authors were able to obtain the masses of the first glueball states. I would like to conclude with my compliments for the PhD reached by Nele and for the excellent wotk her and the other people in the group were able to realize.

The other fine paper I have found is a report by a group of authors, “Discoverig Technicolor”, giving a full account of the current situation for this theoretical approach to the way particles acquire their masses. As you know, the original formulation of the Higgs particle that entered into the Standard Model contains some drawbacks that motivated several people to find better solutions. Technicolor is one of these. One assumes the existence of a set of Fermions with a self-interaction. We know that this kind of models, as Nambu-Jona-Lasinio is, are able to break symmetries and generate masses to massless particles. Indeed, one can formulate a consistent theory with respect to all the precision tests of the Standard Model as also discussed in this report. This means in turn that in accelerator facilities one should look for some other Fermions and their bound states that can also mimic a standard Higgs scalar boson. It is important to note that in this way some drawbacks of the original Higgs mechanism are overcome. Of course, the relevance of this report cannot be underestimated in view of the results coming out from LHC and we could know very soon if an idea like Technicolor is the right  one or not. For sure, this is time for answers in the end.

Nele Vandersickel (2011). A study of the Gribov-Zwanziger action: from propagators to glueballs arXiv arXiv: 1104.1315v1

J. R. Andersen, O. Antipin, G. Azuelos, L. Del Debbio, E. Del Nobile, S. Di Chiara, T. Hapola, M. Jarvinen, P. J. Lowdon, Y. Maravin, I. Masina, M. Nardecchia, C. Pica, & F. Sannino (2011). Discovering Technicolor arXiv arXiv: 1104.1255v1

## Mass generation and supersymmetry

30/07/2010

I have uploaded a paper on arxiv with a new theorem of mine. I have already exposed the idea in this blog but, so far, I have had no much time to make it mathematically sound.  The point is that the mechanism I have found that gives mass to Yang-Mills and scalar fields implies supersymmetry. That is, if I try to apply it to the simplest gauge theory, in a limit of a strong self-interaction of a massless Higgs field, all the fields entering into the theory acquire identical masses  and the couplings settle down to the proper values for a supersymmetric model. Being this result so striking, I was forced to produce a theorem at the classical level, as generally done with the standard Higgs mechanism, and let it widely known. My next step is to improve the presentation and extend this result after a fully quantum treatment. This is possible as I have already shown in the case of a Yang-Mills theory.

My view is that just a mechanism could be seen in Nature to produce masses and I expect that this is the same already seen for QCD. So, supersymmetry is mandatory. This will imply a further effort for people at work to uncover Higgs particle as they should also say to us what kind of self-interaction is in action here and if it is a supersymmetric particle, as it should.

The interesting point is that all the burden of the spectrum of the standard model will rely, not on the mechanism that generates masses but on the part of the model that breaks supersymmetry.

Interesting developments are expected in the future. Higgs is always Higgs but a rather symmetric one. So, stay tuned!

## Higgs mechanism is essential

30/10/2009

As the readers of my blog know, I have developed, in a series of papers, the way to manage massive solutions out of massless theories, both in classical and quantum cases. You can check my latest preprints here and here. To have an idea, if we consider an equation

$\Box\phi+\lambda\phi^3=0$

then a solution is

$\phi(x)=\mu\left(\frac{2}{\lambda}\right)^\frac{1}{4}{\rm sn}(p\cdot x+\theta,i)$

provided

$p^2=\mu^2\left(\frac{\lambda}{2}\right)^\frac{1}{2}$

being $\mu$ and $\theta$ two arbitrary constants and $\rm sn$ a Jacobi elliptical function. We see that a massless theory has massive solutions arising just from a strong nonlinearity into the equation of motion. The question one may ask is: Does this mechanism work to give mass to particles in the Standard Model? The answer is no and this can already be seen at a classical level. To show this, let us consider the following Yukawa model

$L=\bar{\psi}(i\gamma\cdot\partial-g\phi)\psi+\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4$

being $g$ a Yukawa coupling. Assuming $\lambda$ very large, one is reduced to the solution of the following Dirac equation that holds at the leading order

$\left(i\gamma\cdot\partial-g\mu\left(\frac{2}{\lambda}\right)^\frac{1}{4}{\rm sn}(p\cdot x+\theta,i)\right)\psi=0$

and this equation is exactly solved in a closed form, provided the fermion has exactly the same mass of the boson, that is $g=\sqrt{\lambda/2}$. So, we see that the massless fermion acquires mass too but it must be degenerate with respect to the bosonic field. This would imply that one needs a different scalar field for each fermion and such bosons would have the same masses of the fermions. This is exactly what happens in a supersymmetric theory but the theory we are considering is not. So, it would be interesting to reconsider all this with supersymmetry, surely something to do in the near future.

This means that Higgs mechanism is essential yet in the Standard Model to understand how to achieve a finite mass for all particles in the theory. We will see in the future what Nature reserved us about.

## What is mass?

30/08/2009

I should confess that one of the reasons why I have chosen to be a physicist is that physics, like no other sciences, is able to give answers to fundamental open questions that until a few years ago were only discussed by philosophers. Most of these questions are ancient as our species and the possibility that we have means to get truth is too strong to lose our time with other activities. So, I managed to learn such means and today I am here writing on this blog trying to explain you what these truths are. Sometime, I am at the forefront of research and so, what can be believed a truth may lose this quality as we deepen our understanding. Indeed, dynamics of science adds one more element of charm to all this matter.

One of such old questions is: “What are we made of?”. This question has been an open question till the dawn of the 20th century with the fundamental experiments carried out by Ernst Rutherford. Till then we have learned so much about matter that this question changed form becoming: “What is mass?”. This question has become compelling with the birth of the Standard Model due to Sheldon Lee Glashow, Steven Weinberg and Abdus Salam. Indeed, in order to maintain symmetry we must ask all particles to be massless and some mechanism must exist giving mass to them. In the sixties and seventies of last century we moved toward a real understanding of this concept. The idea is to rely on the Higgs mechanism and a scalar particle must exist to grant masses to the other particles in the model. As you may know this particle has not yet been seen and it is the only missing element of an otherwise very successful model. We are confident for several reasons that the Higgs mechanism could turn out the right answer to the question on mass but we are no more so confident that should have the simple aspect given originally in the Standard Model. Indeed, this appears as an open door on a Pandora’s vase of new exciting physics.

But whatever will be the mechanism at work for the masses of leptons and quarks, the answer to the main question is not there. For one reason, both electrons and quarks that form protons and neutrons are really light and do not count too much on the determination of our mass. Most of the mass is in the nuclei and we have to understand where such mass comes from. This arises from bound states of quarks glued together in some way as should yield QCD at low energies. This gives you an idea of why is so important to understand QCD at very low energy. In this way we would be able to answer a fundamental question philosophers discussed for so long time.

So, for our everyday life, it is not so relevant to comprehend the real mechanism that gives mass to elementary particles . What we need is to prove the existence of a mass gap in Yang-Mills theory and so the way bound states form in QCD. As you may know, this is not an easy task and involves a lot of talented people around the World that, with a lot of inventive, is trying to do such computations. So far, only computers succeeded in giving an answer and this is so good that we have the most important observed parameters precise to one percent. The hope is to have a technique to work out such computations analytically, as happens for weak coupled physics. I am deeply involved in such enterprise and I think that what will come out will have a large impact on our knowledge. I can only say: Stay tuned!