I am writing these few lines while the conference “Higgs and beyond” is still going on at Tohoku University (Sendai) in Japan. Talks can be found here. Both ATLAS and CMS presented a lot of results about Higgs particle and the most relevant of them is the combination of the data from the two experiments (see here). I am following the excellent recount by Richard Ruiz on twitter (@bravelittlemuon) that also takes care of CERN’s blog. Some interesting point is that there seems to be a bump in channel that is persistent also in other channels. About decay rates, improvements confirm yet nearly Standard Model behavior of the Higgs particle but with the rates of WW and ZZ going down with a too large error bars yet (see my preceding post). Hopes are that CMS and ATLAS could combine also these data reducing error bars. No other Standard Model heavy Higgs particle is seen. Both CMS and ATLAS are looking for evidence of more Higgs particles to no avail yet. Of course, my view is that these excitations should be searched with somewhat different rates from Standard Model expectations. In any case, Standard Model confirms itself as one of the most successful theories in the history of physics. As said by one of ATLAS speakers: “There is overwhelming evidence for a new boson; there is overwhelming evidence for nothing else.” Both experiments plan to complete the analysis of data at 8 TeV for the summer conferences. My personal expectations are that just improvements in the precision of the measurements of the decay rates could eventually give hints of new physics. To fulfill other hopes, we need LHC upgrade that will restart operations on the spring of 2015, hopefully.
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
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
Note that Standard Model is alive and kicking yet but looking at the production mode of WW you will read
in close agreement with results given in my paper and improved respect to Moriond that was . The reason could be that: Higgs model is a conformal one. Data from ZZ yield
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 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
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.
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
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
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