## Intrinsic decoherence observed again!

25/05/2013

Decoherence is the effect that causes a quantum system to behave classically. The most known of this kind of effects is due to environment where the interaction of an open quantum system with its surrounding is the reason for the loss of quantum coherence. This effect is well-proven on an experimental ground and must be considered acquired knowledge. On the other side, it is a correct scientific question to ask if a closed quantum system ever displays classical behavior for some reason. I have already put forward my take in this blog (see here). This week, on Physical Review Letters (see here and here), it is appeared a paper showing how intrinsic decoherence comes out in an experimental setup of two coupled kicked rotors. Kicked rotors are the epitome of studies on classical chaos and corresponding quantum behavior. It is known that, classically, such a system display diffusion above a certain threshold, firstly computed by Boris Chirikov. The corresponding quantum system localizes instead when its classical counterpart is chaotic. This is the hallmark of a proper quantum behavior that refrains from chaos proper to classical nonlinear systems. The main reason is that the Schrödinger equation is just linear and superposition principle applies. On 1988, S. Adachi, M. Toda, and K. Ikeda showed a real beautiful result that two of such coupled systems lose quantum coherence (see here). The paper by Bryce Gadway, Jeremy Reeves, Ludwig Krinner, and Dominik Schneble (see here) is an experimental proof of the fact that the original theoretical result is a correct insight and we have again a proof that environmental decoherence is not all the story. An interesting recount is given here. This paper is really striking and open the door to a new class of experiments where closed quantum systems, possibly with a lot of systems involved, will be studied to give a full understanding of the quantum-classical transition.

Bryce Gadway, Jeremy Reeves, Ludwig Krinner, & Dominik Schneble (2012). Evidence for a Quantum-to-Classical Transition in a Pair of Coupled
Quantum Rotors Phys. Rev. Lett. 110, 190401 (2013) arXiv: 1203.3177v2

Adachi, S., Toda, M., & Ikeda, K. (1988). Quantum-Classical Correspondence in Many-Dimensional Quantum Chaos Physical Review Letters, 61 (6), 659-661 DOI: 10.1103/PhysRevLett.61.659

## CMS harbors new physics beyond the Standard Model

17/05/2013

In these days is ongoing LHCP 2013 (First Large Hadron Collider Physics Conference) and CMS data seem to point significantly toward new physics. Their measurements on the production modes for WW and ZZ are agreeing with my recent computations (see here) and overall are deviating slightly from Standard Model expectations giving

$\frac{\sigma}{\sigma_SM}=0.80\pm 0.14$

Note that Standard Model is alive and kicking yet but looking at the production mode of WW you will read

$\frac{\sigma_{WW}}{\sigma_{WW\ SM}}=0.68\pm 0.20$

in close agreement with results given in my paper and improved respect to Moriond that was $0.71\pm 0.21$. The reason could be that: Higgs model is a conformal one. Data from ZZ yield

$\frac{\sigma_{ZZ}}{\sigma_{ZZ\ SM}}=0.92\pm 0.28$

that is consistent with the result for WW mode, though. I give here the full table from the talk

For the sake of completeness I give here also the same results from ATLAS at the same conference that, instead, seems to go the other way round obtaining overall $1.30\pm 0.20$ and this is already an interesting matter.

At CMS, new physics beyond the Standard Model is peeping out and, more inteestingly, the Higgs model tends to be a conformal one. If this is true, supersymmetry is an inescapable consequence (see here). I would like to conclude citing the papers of other people working on this model and that will be largely cited in the foreseeable future (see here and here).

Marco Frasca (2013). Revisiting the Higgs sector of the Standard Model arXiv arXiv: 1303.3158v1

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

T. G. Steele, & Zhi-Wei Wang (2013). Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV
Higgs Mass? Physical Review Letters 110, 151601 arXiv: 1209.5416v3

Krzysztof A. Meissner, & Hermann Nicolai (2006). Conformal Symmetry and the Standard Model Phys.Lett.B648:312-317,2007 arXiv: hep-th/0612165v4

14/05/2013

Today, I made a serious mistake. I have sent again a rejected paper to the same journal. The point is that this is the kind of journal that has several Editors that can manage papers. So, one could improperly think that a rejected paper sent to different Editors could in the end go through. The Editor that received my paper did not even think to an error and called for a bad practice warning the Editor in Chief of the journal.

I never applied this practice. The reason is that I have currently about 70 papers published in peer-reviewed journals and so, I have the greatest respect for the work of people that permitted to achieve this result of mine. Worst, I have written more than one hundred papers and a part of them is unpublished for a reason or the other and generally I am in difficulty to get trace of all of this. Indeed, it is quite common practice to send a rejected paper to another journal. The paper I sent out was written about three years ago and I have forgotten about it. In these day, I am revisiting my computations on the scalar field theory both classically and quantum and turned back to this article. Wrongly, I thought I had not sent it to this journal before and that is it.

American Physical Society obviated to this problem by producing a database, available to authors, with all their history.  In other cases this is practically impossible to trace and when the number of papers is overwhelming an error can occur. So, my apologize for this and I do it publicly.

## Tartaglia-Pascal triangle and quantum mechanics

26/04/2013

The paper I wrote with Alfonso Farina and Matteo Sedehi about the link between the Tartaglia-Pascal triangle and quantum mechanics is now online (see here). This paper contains as a statement my theorem that provides a connection between the square root of a Wiener process and the Schrödinger equation that arose a lot of interest and much criticisms by some mathematicians (see here). So, it is worthwhile to tell how all this come about.

On fall 2011, Alfonso Farina called me as he had an open problem after he and his colleagues got published a paper on Signal, Image and Video Processing, a journal from Springer, where it was shown how the Tartaglia-Pascal triangle is deeply connected with diffusion and the Fourier equation. The connection comes out from the binomial coefficients, the elements of the Tartaglia-Pascal triangle, that in some limit give a Gaussian and this Gaussian, in the continuum, is the solution of the Fourier equation of heat diffusion. This entails a deep connection with stochastic processes. Stochastic processes, for most people working in the area of radar and sensors, are essential to understand how these device measure through filtering theory. But, in the historic perspective Farina & al. put their paper, they were not able to get a proper connection for the Schrödinger equation, notwithstanding they recognized there is a deep formal analogy with the Fourier equation. This was the open question: How to connect Tartaglia-Pascal triangle and Schrödinger equation?

People working in quantum physics are aware of the difficulties researchers have met to link stochastic processes a la Wiener and quantum mechanics. Indeed, skepticism is the main feeling of all of us about this matter. So, the question Alfonso put forward to me was not that easy. But Alfonso & al. paper contains also a possible answer: Just start from discrete and then go back to continuum. So, the analog of the heat equation is the Schrödinger equation for a free particle and its kernel and, indeed, the evolution of a Gaussian wave-packet can be managed on the discrete and gives back the binomial coefficient. What you get in this way are the square root of binomial coefficients. So, the link with the Tartaglia-Pascal triangle is rather subtle in quantum mechanics and enters through a square root, reminiscent of the Dirac’s work and his greatest achievement, Dirac equation. This answered Alfonso’s question and in a way that was somewhat unexpected.

Then, I thought that this connection could be deeper than what we had found. I tried to modify Itō calculus to consider fractional powers of a Wiener process. I posted my paper on arxiv and performed both experimental and numerical computations. All this confirms my theorem that the square root of a Wiener process has as a diffusion equation the Schrödinger equation. You can easily take the square root of a natural noise (I did it) or compute this on your preferred math software. It is just interesting that mathematicians never decided to cope with this and still claim that all this evidence does not exist, basing their claims on a theory that can be easily amended.

We have just thrown a seed in the earth. This is our main work. And we feel sure that very good fruits will come out. Thank you very much Alfonso and Matteo!

Farina, A., Frasca, M., & Sedehi, M. (2013). Solving Schrödinger equation via Tartaglia/Pascal triangle: a possible link between stochastic processing and quantum mechanics Signal, Image and Video Processing DOI: 10.1007/s11760-013-0473-y

Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2

Farina, A., Giompapa, S., Graziano, A., Liburdi, A., Ravanelli, M., & Zirilli, F. (2011). Tartaglia-Pascal’s triangle: a historical perspective with applications Signal, Image and Video Processing, 7 (1), 173-188 DOI: 10.1007/s11760-011-0228-6

## Conformal Standard Model is consistent with the observed Higgs particle

12/04/2013

Robert Garisto is an Editor of Physical Review Letters, the flagship journal of American Physical Society and the one with the highest impact factor in physics. I follow him on twitter (@RobertGaristo) and he points out interesting papers that appear in the journal he works in. This time I read the following

and turned immediately my attention to the linked paper: This one (if you have not a subscription you can find it at arxiv) by Tom Steele and Zhi-Wei Wang showing, with the technique of Padè approximants and an average method how to compute the exact mass of Higgs particle from Coleman-Weinberg mechanism arriving to estimate the ninth order contribution. This is so beacuse they need a stronger coupling with respect to the original Higgs mechanism. They reach an upper bound of 141 GeV for the mass and 0.352 for the self-coupling while they get the mass of 124 GeV for a self-coupling of 0.23. This shows unequivocally that the quadratic term, the one generating the hierarchy problem, is absolutely not needed and the Standard Model, in its conformal formulation, is able to predict the mass of the Higgs particle. Besides, the production rates are identical to the original model but differ for the production of Higgs pairs and this is where one could tell which way nature has chosen. This implies that, at the moment, one has no way to be sure this is the right solution but we have to wait till 2015 after LHC upgrade. So, once again, the precise measurements of these decay rates are essential to tell if we are coping with the original Higgs mechanism or something different or if we need two more years to answer this question. In any case, it is possible that Nobel committee has to wait yet before to take a decision. However, in the sixties that formulation was the only possible and any other solution would have been impossible to discover for the lack of knowledge. They did a great job even if we will prove a different mechanism at work as they provided credibility to the Standard Model and people could trust it.

Finally, I would like to note how the value of the coupling is consistent with my recent estimation where I get 0.36 for the self-interaction. I get different production rates and I would be just curious to see how pictures from ATLAS and CMS would change comparing differently from the Standard Model in order to claim no other Higgs-like particle is seen.

What we can conclude is that the conformal Standard Model is in even more better shape than before and just a single Higgs particle would be needed. An astonishing result.

Steele, T., & Wang, Z. (2013). Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass? Physical Review Letters, 110 (15) DOI: 10.1103/PhysRevLett.110.151601

Marco Frasca (2013). Revisiting the Higgs sector of the Standard Model arXiv arXiv: 1303.3158v1

## Much closer to the Standard Model

18/03/2013

Today, the daily from arxiv yields a contribution from John Ellis and Tevong You analyzing new data presented at Aspen and Moriond the last two weeks by CMS and ATLAS about Higgs particle (see here). Their result can be summarized in the following figure

that is really impressive. This means that the updated data coming out from LHC constraints even more the Higgs particle found so far to be the Standard Model one. Another impressive conclusion they are able to draw is that the couplings appear to be proportional to the masses as it should be expected from a well-behaved Higgs particle. But they emphasize that this is “a” Higgs particle and the scenario is well consistent with supersymmetry. Citing them:

The data now impose severe constraints on composite alternatives to the elementary Higgs boson of the Standard Model. However, they do not yet challenge the predictions of supersymmetric models, which typically make predictions much closer to the Standard Model values. We therefore infer that the Higgs coupling measurements, as well as its mass, provide circumstantial support to supersymmetry as opposed to these minimal composite alternatives, though this inference is not conclusive.

They say that further progress on the understanding of this particle could be granted after the upgraded LHC will run and, indeed, nobody is expecting some dramatic change into this scenario from the data at hand.

John Ellis, & Tevong You (2013). Updated Global Analysis of Higgs Couplings arXiv arXiv: 1303.3879v1

## A Higgs particle but which one?

14/03/2013

After Moriond conference last week, and while Moriond QCD and Aspen conferences are running yet, an important conclusion can be drawn and it is the one given in this CERN press release. The particle announced on 4th July last year is for certain a Higgs particle as it has spin 0, positive parity and couples almost like the Standard Model Higgs particle to all others. The agreement with Standard Model is embarrassingly increasing as cumulated data since last year are analyzed. Today, CMS will also update their results for the decay $H\rightarrow\gamma\gamma$ and we will know if the small deviation observed by ATLAS will be confirmed. It is true that they see such a deviation with a larger dataset but, rather to increase, it has slightly diminished and this is not really encouraging.

So far, no other particle has been seen and no new physics beyond the Standard Model is seen at the horizon. There is some people pushing for a conclusive assignment of the nature of this boson to the vanilla Higgs particle postulated in the sixties. But it is really too early yet to draw such a conclusion and I have explained why in a paper of mine appeared today on arxiv (see here). Indeed, a formulation of the Higgs field is possible such that, at the tree level, coincides with the original Higgs field (a Higgs impostor). This is due to the existence of exact solutions of the equations of motion of such a field (see here). The relevant point to tell which one is realized in nature is through the decay rate in WW and ZZ and, with the current data, there is agreement for both yet. But, being amplitudes exponentially damped, higher excited states of the Higgs boson cannot be easily seen presently and their eventual observation appears as a statistical fluctuation yet. This can be evaluated quantitatively. It is important because the ZZ decay is sensible to higher masses and displays some peaks that reveal themselves as statistical fluctuations. Increasing the number of events could turn these peaks into real observations.

The interesting point here is that we are moving form the discovery moment to the study phase with a lot of room for improving measurements on this Higgs particle. But the analysis for the existence of higher excited states, Higgs’ brothers, is just at its infancy.

Update: This the analogous figure from ATLAS while the figure for $H\rightarrow\gamma\gamma$ from CMS agrees quite well with the Standard Model: $0.8\pm 0.3$.

Marco Frasca (2013). Revisiting the Higgs sector of the Standard Model arXiv arXiv: 1303.3158v1

Marco Frasca (2009). Exact solutions of classical scalar field equations J.Nonlin.Math.Phys.18:291-297,2011 arXiv: 0907.4053v2