Something to say but not yet…


Last week I have been in Montpellier to attend QCD 17 Conference hosted at the CNRS and whose mainly organizer is Stephan Narison. At this conference participates a lot of people from CERN presenting new results very nearly to the main summer conferences. This year, QCD 17 was in conjuction with EPSHEP 2017 were the new results coming from LHC were firstly presented. This means that the contents of the talks in the two conferences just superposed in a matter of few hours.

On Friday, the last day of conference, I posted the following twitter after attending the talk by Shunsuke Honda on behalf of ATLAS at QCD 17:

and the reason was this slide

The title of the talk was “Cross sections and couplings of the Higgs Boson from ATLAS”. As you can read from it, there is a deviation of about 2 sigmas from the Standard Model for the Higgs decaying to ZZ(4l) for VBF. Indeed, they can claim agreement yet but it is interesting anyway (maybe are we missing anything?). The previous day at EPSHEP 2017, Ruchi Gupta on behalf of ATLAS presented an identical talk with the title “Measurement of the Higgs boson couplings and properties in the diphoton, ZZ and WW decay channels using the ATLAS detector” and the slide was the following:

The result is still there but with a somewhat sober presentation. What does this mean? Presently, this amounts to very few. We are still within the Standard Model even if something seems to peep out. In order to claim a discovery, this effect should be seen with a lower error and at CMS too. The implications would be that there could be a more complex spectrum of the Higgs sector with a possible new understanding of naturalness if such a spectrum would not have a formal upper bound. People at CERN promised more data coming in the next weeks. Let us see what will happen to this small effect.

In the aftermath of ICHEP 2016



ATLAS and CMS nuked our illusions on that bump. More than 500 papers were written on it and some of them went through Physical Review Letters. Now, we are contemplating the ruins of that house of cards. This says a lot about the situation in hep in these days. It should be emphasized that people at CERN warned that that data were not enough to draw a conclusion and if they fix the threshold at 5\sigma a reason must exist. But carelessness acts are common today if you are a theorist and no input from experiment is coming for long.

It should be said that the fact that LHC could confirm the Standard Model and nothing else is one of the possibilities. We should hope that a larger accelerator could be built, after LHC decommissioning, as there is a long way to the Planck energy that we do not know how to probe yet.

What does it remain? I think there is a lot yet. My analysis of the Higgs sector is still there to be checked as I will explain in a moment but this is just another way to treat the equations of the Standard Model, not beyond it. Besides, for the end of the year they will reach 30\ fb^{-1}, almost triplicating the actual integrated luminosity and something interesting could ever pop out. There are a lot of years of results ahead and there is no need to despair. Just to wait. This is one of the most important activities of a theorist. Impatience does not work in physics and mostly for hep.

About the signal strength, things seem yet too far to be settled. I hope to see better figures for the end of the year. ATLAS is off the mark, going well beyond unity for WW, as happened before. CMS claimed 0.3\pm 0.5 for WW decay, worsening their excellent measurement of 0.72^{+0.20}_{-0.18} reached in Run I. CMS agrees fairly well with my computations but I should warn that the error bar is yet too large and now is even worse. I remember that the signal strength is obtained by the ratio of the measured cross section to the one obtained from the Standard Model. The fact that is smaller does not necessarily mean that we are beyond the Standard Model but that we are just solving the Higgs sector in a different way than standard perturbation theory. This solution entails higher excitations of the Higgs field but they are strongly depressed and very difficult to observe now. The only mark could be the signal strength for the observed Higgs particle. Finally, the ZZ channel is significantly less sensible and error bars are so large that one can accommodate whatever she likes yet. Overproduction seen by ATLAS is just a fluctuation that will go away in the future.

The final sentence to this post is what we have largely heard in these days: Standard Model rules.

Higgs or not Higgs, that is the question


LHCP2016 is running yet with further analysis on 2015 data by people at CERN. We all have seen the history unfolding since the epochal event on 4 July 2012 where the announcement of the great discovery happened. Since then, also Kibble passed away. What is still there is our need of a deep understanding of the Higgs sector of the Standard Model. Quite recently, LHC restarted operations at the top achievable and data are gathered and analysed in view of the summer conferences.

The scalar particle observed at CERN has a mass of about 125 GeV. Data gathered on 2015 seem to indicate a further state at 750 GeV but this is yet to be confirmed. Anyway, both ATLAS and CMS see this bump in the \gamma\gamma data and this seems to follow the story of the discovery of the Higgs particle. But we have not a fully understanding of the Higgs sector  yet. The reason is that, in run I, gathered data were not enough to reduce the error bars to such small values to decide if Standard Model wins or not. Besides, as shown by run II, further excitations seem to pop up. So, several theoretical proposals for the Higgs sector still stand up and could be also confirmed already in August this year.

Indeed, there are great news already in the data presented at LHCP2016. As I pointed out here, there is a curious behavior of the strengths of the signals of Higgs decay in WW,\ ZZ and some tension, even if small, appeared between ATLAS and CMS results. Indeed, ATLAS seemed to have seen more events than CMS moving these contributions well beyond the unit value but, as CMS had them somewhat below, the average was the expected unity agreeing with expectations from the Standard Model. The strength of the signals is essential to understand if the propagator of the Higgs field is the usual free particle one or has some factor reducing it significantly with contributions from higher states summing up to unity. In this case, the observed state at 125 GeV would be just the ground state of a tower of particles being its excited states. As I showed recently, this is not physics beyond the Standard Model, rather is obtained by solving exactly the quantum equations of motion of the Higgs sector (see here). This is done considering the other fields interacting with the Higgs field just a perturbation.

So, let us do a recap of what was the situation for the strength of the signals for the WW\, ZZ decays of the Higgs particle. At LHCP2015 the data were given in the following slide

Signal strengths at LHCP2015

From the table one can see that the signal strengths for WW,\ ZZ decays in ATLAS are somewhat beyond unity while in CMS these are practically unity for ZZ but, more interestingly, 0.85 for WW. But we know that data gathered for WW decay are largely more than for ZZ decay. The error bars are large enough to be not a concern here. The value 0.85 is really in agreement with the already cited exact computations from the Higgs sector but, within the error, in overall agreement with the Standard Model. This seems to point toward on overestimated number of events in ATLAS but a somewhat reduced number of events in CMS, at least for WW decay.

At LHCP2016 new data have been presented from the two collaborations, at least for the ZZ decay. The results are striking. In order to see if the scenario provided from the exact solution of the Higgs sector is in agreement with data, these should be confirmed from run II and those from ATLAS should go down significantly. This is indeed what is going on! This is the corresponding slide

CMS data LHCP2016

This result is striking per se as shows a tendency toward a decreasing value when, in precedence, it was around unity. Now it is aligned with the value seen at CMS for the WW decay! The value seen is again in agreement with that given in the exact solution of the Higgs sector. And ATLAS? This is the most shocking result: They see a significant reduced set of events and the signal strength they obtain is now aligned to the one of CMS (see Strandberg’s talk at page 11).

What should one conclude from this? If the state at 750 GeV should be confirmed, as the spectrum given by the exact solution of the Higgs sector is given by an integer multiplied by a mass, this would be at n=6. Together with the production strengths, if further data will confirm them, the proper scenario for the breaking of electroweak symmetry is exactly the one described by the exact solution. Of course, this should be obviously true but an experimental confirmation is essential for a lot of reasons, last but not least the form of the Higgs potential that, if the numbers are these, the one postulated in the sixties would be the correct one. An other important reason is that coupling with other matter does not change the spectrum of the theory in a significant way.

So, to answer to the question of the title remains to wait a few weeks. Then, summer conferences will start and, paraphrasing Coleman: God knows, I know and by the end of the summer we all know.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model Eur. Phys. J. Plus (2016) 131: 199 arXiv: 1504.02299v3

News from CERN


Two days ago, CERN presented their new results at 13 TeV to the World. Of course, collected data so far are not enough for conclusive results but the these are exciting anyway. The reason is that both the collaborations, CMS and ATLAS, see a bump at around 750 GeV in the \gamma\gamma decay. Summing up the results of the two collaborations, they are around 4\sigma without look elsewhere effect, not yet a discovery but, probably, at the summer conferences they will have something more conclusive to say. This could be an unlucky fluctuation but this situation remember us the story of the discovery of the Higgs boson more than three years ago. The question if this is beyond Standard Model physics is what I will try to answer in these few lines.ATLAS diphoton reults at 13 TeV

Firstly, if this particle is real, it decays with two photons exactly as the Higgs boson. Secondly, with a final state like this it can have only spin 0 or 2. We will be conservative and assume that this is not a graviton. Rather, it is a sibling of the Higgs particle. Besides, it was not observed in run I but is not inconsistent with data from there. It appears like the increased luminosity favored its appearance. We want to be more conservative and we take for granted just the Lagrangian of the Standard Model. So, what is this beast?

My answer is that this could be an excited state of the Higgs boson that, having a production rate lower than its ground state seen at run I, needed more luminosity to be observed. You do not need to change the Lagrangian of the Standard Model for this and it is not BSM physics yet. You do not even need a technicolor theory to describe it. The reason is that the Higgs part of the Standard Model can be treated mathematically yielding exact solutions. The quantum field theory can be exactly solved and the spectrum of the theory says exactly what I stated above (see here, and here). The Higgs model per se is exactly solvable. So, Jester’s idea to add another scalar field to the Lagrangian model is useless, it is all just inside and you will get a two photon final state as well.

Of course, it is too early to draw a final conclusion and a wealth of papers with a prompt explanation flooded arxiv in these two days. With the restart of LHC on spring and the collecting of more data, things will be clearer than now. For the moment, this hint is enough to keep us excited for the next few months.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v2

Marco Frasca (2015). Quantum Yang-Mills field theory arxiv arXiv: 1509.05292v1

Higgs even more standard


LHCP 2015 is going on at St. Peterburg and new results were presented by the two main collaborations at CERN. CMS and ATLAS combined the results from run 1 and improved the quality of the measured data of the Higgs particle discovered on 2012. CERN press release is here. I show you the main picture about the couplings between the Higgs field and the other particles in the Standard Model widely exposed in all the social networks

Combined couplings for the Higgs by ATLAS and CMS

What makes this plot so striking is the very precise agreement with the Standard Model. Anyhow, the ellipses are somewhat large yet to grant new physics creeping in at run 2. My view is that the couplings, determining the masses of the particles in the Standard Model, are less sensible to new physics than the strength of the signal at various decays. Also this plot is available (hat tip to Adam Falkowski)

Combined strengths at various decays by ATLAS and CMS

In this plot you can see that the Standard Model, represented by a star, is somewhat at the border of the areas of the ZZ and WW decays and that of the WW decay is making smaller. This does not imply that in the future deviations from the Standard Model will be seen here but leave the impression that this could happen in run 2 with the increasing precision expected for these measurements.

The strengths are so interesting because the Higgs sector of the Standard Model can be solved exactly with the propagator providing the values of them (see here). These generally disagree from those obtained by standard perturbation theory even if by a small extent. Besides, Higgs particle should have internal degrees of freedom living also in higher excited states. All of this to be seen at run 2 as the production rate of these states appears to be smaller as higher is their mass.

Run 2 is currently ongoing even if the expected luminosity will not be reached for this year. For sure, the next year summer conferences could provide a wealth of shocking new results. Hints are already seen by both the main collaborations and LHCb. Something new is just behind the corner.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v1

That Higgs is trivial!


Notwithstanding LHC has seen the particle, the Higgs sector of the Standard Model has some serious problems. This fact yielded more than one headache to physicists. One of these difficulties is called technically “triviality“. Michael AizenmanThe scalar field theory, that is so well defined classically, does not exist as a quantum field theory unless is non-interacting. There is a wonderful paper by Michael Aizenman that shows that this is true for dimensions 5 and higher. So, one should think that, as we live in four dimensions, there is no reason to worry. The point is that Michael Aizenman left the question in four dimensions open. So, does Higgs particle exist or not and how does it yield mass if it will not interact? CERN said to us that Higgs particle is there and so, in some way, the scalar sector of the Standard Model must properly work. Aizenman’s proof was on 1981 but what is the situation now? An answer is in this article on Scholarpedia. As stated by the author Ulli Wolff

Triviality of lattice phi^4 theory in this sense has been rigorously proven for D>4 while for the most interesting borderline case D=4 we have only partial results but very strong evidence from numerical simulations.

While there is another great expert on quantum field theory, Franco Strocchi, in his really worth to read book saying

The recent proof of triviality of phi^4 in 3 + 1 spacetime dimensions indicates that the situation becomes worse in the real world, and in particular the renormalized perturbative series of the phi^4 model seems to have little to do with the non-perturbative solution.

We see that experts do not completely agree about the fact that a proof exists or not but, for sure, the scalar theory in four dimensions cannot interact and the Standard Model appears in serious troubles.

Before to enter more in details about this matter, let me say that, even if Strocchi makes no citation about where the proof is, he is the one being right. We have proof about this, the matter is now well understood and again we are waiting for the scientific community to wake up. Also, the Standard Model is surely secured and there is no serious risk about the recent discovery by CERN of the Higgs particle.

The proof has been completed recently by Renata Jora with this paper on arxiv. Renata extended the proof an all the energy range. I met her in Montpellier (France) at this workshop organized by Stephan Narison. We have converging interests in research. Renata’s work is based on a preceding proof, due to me and Igor Suslov, showing that, at large coupling, the four dimensional theory is indeed trivial. You can find the main results here and here. Combining these works together, we can conclude that Strocchi’s statement is correct but there is no harm for the Standard Model as we will discuss in a moment. Also the fact that the perturbation solution of the model is not properly describing the situation can be seen from the strictly non-analytical behaviours seen at strong coupling that makes impossible to extend what one gets at small coupling to that regime.

The fact that CERN has indeed seen the Higgs particle and that the Higgs sector of the Standard Model is behaving properly, unless a better understanding will emerge after the restart of the LHC, has been seen with the studies of the propagators of the Yang-Mills theory in the Landau gauge. The key paper is this where the behaviour of the running coupling of the theory was obtained on all the energy range from lattice computations.

Running Coupling

This behaviour shows that, while the theory is trivial at both the extremes of the energy range, there is an intermediate regime where we can trust the theory and treat it as an effective one. There the coupling does not run to zero but moves around some finite non-null value. Of course, all this is just saying that this theory must be superseded by an extended one going to higher energies (supersymmetry? Technicolor?) but it is reasonable to manage the theory as if all this just works at current energies. Indeed, LHC has shown that a Higgs particle is there.

So, triviality is saying that the LHC will find something new for sure. Today, beams moved again inside the accelerator. We are eager to see what will come out form this wonderful enterprise.

Aizenman, M. (1981). Proof of the Triviality of Field Theory and Some Mean-Field Features of Ising Models for Physical Review Letters, 47 (12), 886-886 DOI: 10.1103/PhysRevLett.47.886

Renata Jora (2015). $Φ^4$ theory is trivial arXiv arXiv: 1503.07298v1

Marco Frasca (2006). Proof of triviality of $λφ^4$ theory Int.J.Mod.Phys.A22:2433-2439,2007 arXiv: hep-th/0611276v5

Igor M. Suslov (2010). Asymptotic Behavior of the \Beta Function in the Φ^4 Theory: A Scheme
Without Complex Parameters J.Exp.Theor.Phys.111:450-465,2010 arXiv: 1010.4317v1

I. L. Bogolubsky, E. -M. Ilgenfritz, M. Müller-Preussker, & A. Sternbeck (2009). Lattice gluodynamics computation of Landau-gauge Green’s functions in the deep infrared Phys.Lett.B676:69-73,2009 arXiv: 0901.0736v3

Is Higgs alone?


I am back after the announcement by CERN of the restart of LHC. On May this year we will have also the first collisions. This is great news and we hope for the best and the best here is just the breaking of the Standard Model.

The Higgs in the title is not Professor Higgs but rather the particle carrying his name. The question is a recurring one since the first hints of existence made their appearance at the LHC. The point I would like to make is that the equations of the theory are always solved perturbatively, even if exact solutions exist that provide a mass also if the theory is massless or has a mass term with a wrong sign (Higgs model). All you need is a finite self-interaction term in the equation. So, you will have bad times to recover such exact solutions with perturbation techniques and one keeps on living in the ignorance. If you would like to see the technicalities involved just take a cursory look at Dispersive Wiki.

What is the point? The matter is rather simple. The classical theory has exact massive solutions for the potential in the form V(\phi)=a\phi^2+b\phi^4 and this is a general result implying that a scalar self-interacting field gets always a mass (see here and here). Are we entitled to ignore this? Of course no. But today exact solutions have lost their charm and we can get along with them.

For the quantum field theory side what could we say? The theory can be quantized starting with these solutions and I have shown that one gets in this way that these massive particles have higher excited states. These are not bound states (maybe could be correctly interpreted in string theory or in a proper technicolor formulation after bosonization) but rather internal degrees of freedom. It is always the same Higgs particle but with the capability to live in higher excited states. These states are very difficult to observe because higher excited states are also highly depressed and even more hard to see. In the first LHC run they could not be seen for sure. In a sense, it is like Higgs is alone but with the capability to get fatter and present himself in an infinite number of different ways. This is exactly the same for the formulation of the scalar field as originally proposed by Higgs, Englert, Brout, Kibble, Guralnik and Hagen. We just note that this formulation has the advantage to be exactly what one knows from second order phase transitions used by Anderson in his non-relativistic proposal of this same mechanism. The existence of these states appears inescapable whatever is your best choice for the quartic potential of the scalar field.

It is interesting to note that this is also true for the Yang-Mills field theory. The classical equations of this theory display similar solutions that are massive (see here) and whatever is the way you develop your quantum filed theory with such solutions the mass gap is there. The theory entails the existence of massive excitations exactly as the scalar field does. This have been seen in lattice computations (see here). Can we ignore them? Of course no but exact solutions are not our best choice as said above even if we will have hard time to recover them with perturbation theory. Better to wait.

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

Marco Frasca (2013). Scalar field theory in the strong self-interaction limit Eur. Phys. J. C (2014) 74:2929 arXiv: 1306.6530v5

Marco Frasca (2014). Exact solutions for classical Yang-Mills fields arXiv arXiv: 1409.2351v2

Biagio Lucini, & Marco Panero (2012). SU(N) gauge theories at large N Physics Reports 526 (2013) 93-163 arXiv: 1210.4997v2

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