## Where we are now?

13/08/2019

Summer conferences passed by, we have more precise data on the Higgs particle and some new results were announced. So far, this particle appears more and more in agreement with the Standard Model expectations without no surprise in view. Several measurements were performed with the full dataset at 140 ${\rm fb}^{-1}$. Most commentators avoid to tell about this because it does not warrant click-bait anymore. At EPS-HEP 2019 in Ghent (Belgium), the following slide was presented by Hulin Wang on behalf of the ATLAS Collaboration

There appears to be an excess at 250 GeV and another at 700 GeV but we are talking of about 2 sigma, nothing relevant. Besides, ATLAS keeps on seeing an excess in the vector boson fusion for ZZ decay, again about 2 sigma, but CMS sees nothing, rather they are somewhat on the missing side!

No evidence of supersymmetry whatsoever, neither the multiplet of Higgs nor charged Higgs are seen that could hint to supersymmetry. I would like to remember that some researchers were able to obtain the minimal supersymmetric standard model from string theory and so, this is a diriment aspect of the experimental search. Is the Higgs particle just the first one of an extended sector of electroweak (soft) supersymmetry breaking?

So, why could the slide I just posted be so important? The interesting fact is the factor 2 between the mass of this presumed new resonance and that of the Higgs particle. The Higgs sector of the Standard Model can be removed from it and treated independently. Then, one can solve it exactly and the spectrum is given by an integer multiple of the mass of the Higgs particle. This is exactly the spectrum of a Kaluza-Klein particle and it would represents an indirect proof of the existence of another dimension in space. So, if confirmed, we would move from a desolating scenario with no new (beyond standard model) physics in view to a completely overturned situation! We could send all the critics back to sleep wishing them a better luck for the next tentative.

Back to reality, the slide yields the result for the dataset of 36.1 ${\rm fb}^{-1}$ and no confirmation from CMS has ever arrived. We can just hope that the dreaming scenario takes life.

## ICHEP 2018

08/07/2018

The great high-energy physics conference ICHEP 2018 is over and, as usual, I spend some words about it. The big collaborations of CERN presented their last results. I think the most relevant of this is about the evidence ($3\sigma$) that the Standard Model is at odds with the measurement of spin correlation between top-antitop pair of quarks. More is given in the ATLAS communicate. As expected, increasing precision proves to be rewarding.

About the Higgs particle, after the important announcement about the existence of the ttH process, both ATLAS and CMS are pursuing further their improvement of precision. About the signal strength they give the following results. For ATLAS (see here)

$\mu=1.13\pm 0.05({\rm stat.})\pm 0.05({\rm exp.})^{+0.05}_{-0.04}({\rm sig. th.})\pm 0.03({\rm bkg. th})$

and CMS (see here)

$\mu=1.17\pm 0.06({\rm stat.})^{+0.06}_{-0.05}({\rm sig. th.})\pm 0.06({\rm other syst.}).$

The news is that the error is diminished and both agrees. They show a small tension, 13% and 17% respectively, but the overall result is consistent with the Standard Model.

When the different contributions are unpacked in the respective contributions due to different processes, CMS claims some tensions in the WW decay that should be taken under scrutiny in the future (see here). They presented the results from $35.9{\rm fb}^{-1}$ data and so, there is no significant improvement, for the moment, with respect to Moriond conference this year. The situation is rather better for the ZZ decay where no tension appears and the agreement with the Standard Model is there in all its glory (see here). Things are quite different, but not too much, for ATLAS as in this case they observe some tensions but these are all below $2\sigma$ (see here). For the WW decay, ATLAS does not see anything above $1\sigma$ (see here).

So, although there is something to take under attention with the increase of data, that will reach $100 {\rm fb}^{-1}$ this year, but the Standard Model is in good health with respect to the Higgs sector even if there is a lot to be answered yet and precision measurements are the main tool. The correlation in the tt pair is absolutely promising and we should hope this will be confirmed a discovery.

## Good news from Moriond

20/03/2018

Some days ago, Rencontres of Moriond 2018 ended with the CERN presenting a wealth of results also about the Higgs particle. The direction that the two great experiments, ATLAS and CMS, took is that of improving the measurements on the Standard Model as no evidence has been seen so far of possible new particles. Also, the studies of the properties of the Higgs particle have been refined as promised and the news are really striking.

In a communicate to the public (see here), CERN finally acknowledge, for the first time, a significant discrepancy between data from CMS and Standard Model for the signal strengths in the Higgs decay channels. They claim a 17% difference. This is what I advocated for some years and I have published in reputable journals. I will discuss this below. I would like only to show you the CMS results in the figure below.

ATLAS, by its side, is seeing significant discrepancy in the ZZ channel ($2\sigma$) and a $1\sigma$ compatibility for the WW channel. Here are their results.

On the left the WW channel is shown and on the right there are the combined $\gamma\gamma$ and ZZ channels.

The reason of the discrepancy is due, as I have shown in some papers (see here, here and here), to the improper use of perturbation theory to evaluate the Higgs sector. The true propagator of the theory is a sum of Yukawa-like propagators with a harmonic oscillator spectrum. I solved exactly this sector of the Standard Model. So, when the full propagator is taken into account, the discrepancy is toward an increase of the signal strength. Is it worth a try?

This means that this is not physics beyond the Standard Model but, rather, the Standard Model in its full glory that is teaching something new to us about quantum field theory. Now, we are eager to see the improvements in the data to come with the new run of LHC starting now. In the summer conferences we will have reasons to be excited.

## In the aftermath of ICHEP 2016

06/08/2016

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

16/06/2016

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

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

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

17/12/2015

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.

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

02/09/2015

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

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)

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!

05/04/2015

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“. The 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.

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

## That’s a Higgs but how many?

17/11/2014

CMS and ATLAS collaborations are yet up to work producing results from the datasets obtained in the first phase of activity of LHC. The restart is really near the corner and, maybe already the next summer, things can change considerably. Anyway what they get from the old data can be really promising and rather intriguing. This is the case for the recent paper by CMS (see here). The aim of this work is to see if a heavier state of Higgs particle exists and the kind of decay they study is $Zh\rightarrow l^+l^-bb$. That is, one has a signature with two leptons moving in opposite directions, arising from the dacy of the $Z$, and two bottom quarks arising from the decay of the Higgs particle. The analysis of this decay aims to get hints of existence of a heavier pseudoscalar Higgs state. This can be greatly important for SUSY extensions of the Standard Model that foresee more than one Higgs particle.

Often CMS presents its results with some intriguing open questions and also this is the case and so, it is worth this blog entry. Here is the main result

The evidence, as said in the paper, is that there is a 2.6-2.9 sigma evidence at 560 GeV and a smaller one at around 300 GeV. Look elsewhere effect reduces the former at 1.1 sigma and the latter is practically negligible. Overall, this is pretty negligible but, as always, with more data at the restart, could become something real or just fade away. It should be appreciated the fact that a door is left open anyway and a possible effect is pointed out.

My personal interpretation is that such higher excitations do exist but their production rates are heavily suppressed with the respect to the observed ground state at 126 GeV and so, negligible with the present datasets. I am also convinced that the current understanding of the breaking of SUSY, currently adopted in MSSM-like to go beyond the Standard Model, is not the correct one provoking the early death of such models. I have explained this in a coupled of papers of mine (see here and here). It is my firm conviction that the restart will yield exciting results and we should be really happy to have such a powerful machine in our hands to grasp them.

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

Marco Frasca (2012). Classical solutions of a massless Wess-Zumino model J.Nonlin.Math.Phys. 20:4, 464-468 (2013) arXiv: 1212.1822v2

## Higgs what?

06/09/2014

In these days it has been announced the new version of Review of Particle Physics by the Particle Data Group (PDG). This is the bread and butter of any particle physicist and contains all the relevant data about this area of research. It is quite common for us to search the on-line version or using the booklet to know a mass or a decay rate. After the first run of LHC data gathering about Higgs particle, this edition contains a bunch of fundamental informations about it and I post a part of them.

It is Standard Model Higgs! No, not so fast. Take a look at the WW final state. It is somewhat low but yes, it is perfectly consistent with the Standard Model. Also, error bars are somewhat large to conclude something definitive. So, let us take a look nearer at these strengths.

We discover that the strengths measured by CMS are really low and takes down this value. Indeed, this is consistent with my proposal here. I get 0.68 for both channels WW and ZZ. On the other side, ATLAS moves all upward consistently and there is this strange behaviour compensating each other. So, let us also take a look at the ZZ strength. PDG yields

again CMS agrees with my conclusions and ATLAS moves all upward to compensate. But both these results, due to the large error bars, agree rather well with the Standard Model. So, I looked for the publication by CMS  that were produced till today if one or both these analyses were improved. The result was that CMS improved the measure of the strength in the WW channel to leptons (see here). What they measure is

$\frac{\sigma}{\sigma_{SM}}=0.72^{+0.20}_{-0.18}.$

The error is significantly smaller and the result striking. It is bending in the “wrong” turn loosing higgsness. It would be interesting to understand why CMS appear to get results downward for these strengths and ATLAS more upward compensating each other toward the Standard Model. On the other side, I should admire the more aggressive approach by CMS with their results more and more similar to my expectations. I am just curious to see with the restart of LHC what will happen to these data that CMS sharpened to such a point.

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

CMS Collaboration (2013). Measurement of Higgs boson production and properties in the WW decay
channel with leptonic final states JHEP 01 (2014) 096 arXiv: 1312.1129v2