Waiting for EPS HEP 2013: Some thoughts

13/07/2013

ResearchBlogging.org

On 18th July the first summer HEP Conference will start in Stockholm. We do not expect great announcements from CMS and ATLAS as most of the main results from 2011-2012 data were just unraveled. The conclusions is that the particle announced on 4th July last year is a Higgs boson. It decays in all the modes foreseen by the Standard Model and important hints favor spin 0. No other resonance is seen at higher energies behaving this way. It is a single yet. There are a lot of reasons to be happy: We have likely seen the guilty for the breaking of the symmetry in the Standard Model and, absolutely for the first time, we have a fundamental particle behaving like a scalar. Both of these properties were looked upon for a long time and now this search is finally ended. On the bad side, no hint of new physics is seen anywhere and probably we will have to wait the restart of LHC on 2015. The long sought SUSY is at large yet.

Notwithstanding this hopeless situation for theoretical physics, my personal view is that there is something that gives important clues to great novelties that possibly will transmute into something of concrete at the restart. It is important to note that there seem to exist some differences between CMS and ATLAS  and this small disagreement can hide interesting news for the future. I cannot say if, due to the different conception of this two detectors, something different should be seen but is there. Anyway, they should agree in the end of the story and possibly this will happen in the near future.

The first essential point, that is often overlooked due to the overall figure, is the decay of the Higgs particle in a couple of W or Z. WW decay has a significantly large number of events and what CMS claims is indeed worth some deepening. This number is significantly below one. There is  a strange situation here because CMS gives 0.76\pm 0.21 and in the overall picture just write 0.68\pm 0.20 and so, I cannot say what is the right one. But they are consistent each other so not a real problem here. Similarly, ZZ decay yields 0.91^{+0.30}_{-0.24}. ATLAS, on the other side, yields for WW decay 0.99^{+0.31}_{-0.28} and for ZZ decay 1.43^{+0.40}_{-0.35}. Error bars are large yet and fluctuations can change these values. The interesting point here, but this has the value of a clue as these data agree with Standard Model at 2\sigma, is that the lower values for the WW decay can be an indication that this Higgs particle could be a conformal one. This would mean room for new physics. For ZZ decay apparently ATLAS seems to have a lower number of events as this figure is somewhat larger and the error bar as well. Anyway, a steady decrease has been seen for the WW decay as a larger dataset was considered. This decrease, if confirmed at the restart, would mean a major finding after the discovery of the Higgs particle. It should be said that ATLAS already published updated results with the full dataset (see here). I would like to emphasize that a conformal Standard Model can imply SUSY.

The second point is a bump found by CMS in the \gamma\gamma channel (see here).  This is what they see

CMS Another Higgs

but ATLAS sees nothing there and this is possibly a fluke. Anyway, this is about 3\sigma and so CMS reported about on a publication of them.

Finally, it is also possible that heavier Higgs particles could have depressed production rates and so are very rare. This also would be consistent with a conformal Standard Model. My personal view is that all hopes to see new physics at LHC are essentially untouched and maybe this delay to unveil it is just due to the unlucky start of the LHC on 2008. Meantime, we have to use the main virtue of a theoretical physicist: keeping calm and being patient.

Update: Here is the press release from CERN.

ATLAS Collaboration (2013). Measurements of Higgs boson production and couplings in diboson final
states with the ATLAS detector at the LHC arXiv arXiv: 1307.1427v1


Higgs and beyond

06/06/2013

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 Z\gamma 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.


CMS harbors new physics beyond the Standard Model

17/05/2013

ResearchBlogging.org

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

CMS at LHCP2013

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.

ATLAS at LHCP2013

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


Conformal Standard Model is consistent with the observed Higgs particle

12/04/2013

ResearchBlogging.org

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

Tweets from Garisto

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

ResearchBlogging.org

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

Ellis & You: agreement with Standard Modelthat 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

ResearchBlogging.org

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. H->ZZ decay at CMSBut, 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.

ATLAS ZZ->4l

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


Fabiola Gianotti at Accademia dei Lincei

11/01/2013

On November 7th last year, Fabiola Gianotti, spokesperson of ATLAS experiment at CERN and one of the discoverers of the Higgs-like boson, has been nominated fellow of the Accademia dei Lincei. This is one of the oldest and most prestigious scientific societies that held fellows like Galileo Galilei and Enrico Fermi. Today, she held a public conference with fellows both of moral and scientific classes about “The Higgs boson and our life”. Fabiola Gianotti at Accademia dei Lincei Of course, I was there to see and listen to her personally. As I entered the room, I asked “excuse me” to three people blocking my passage to the chair. When I sat, I looked at them and I realized who were: Carlo di Castro, Francesco de Martini and Giovanni Jona-Lasinio. They were all my former professors. Also Giorgio Parisi was there and later Luciano Maiani entered the audience. Undoubtedly, the audience was truly remarkable.

Lamberto Maffei, president of the Accademia, introduced Gianotti through her main achievements and awards. I would like to remember that she gave the money of the Fundamental Physics Prize for student grants.

The aim of this conference was to convey to all fellows of the Accademia and public at large what was behind the discovery of the Higgs-like particle announced on July 4th last year. For me has been a good chance to hear, from one of the persons mastering this matter, a talk addressed to everybody without the use of technical jargon and using several nice images. Gianotti has shown a very fine gift for this. I would like to reassure my readers that she used comic sans.Fabiola Gianotti on TIME cover

By my side, I was proud to hear that 1400 scientists working at CERN are Italians and that an Italian company, Ansaldo Superconduttori Genova, is responsible for one third of the realization of the superconductors at LHC and are also installed in ATLAS detector. At CERN it is working  a great majority of young people. Gianotti said that it does not matter if you are a graduate student just entered the team. If your idea is good it is taken and applied. This is what makes scientific enterprise quite different from other realities and renders it so effective. Ideas count more than any authority.

Gianotti pointed out how difficult the situation is for Italy as we have a lot of young people leaving the country for academic positions at foreign universities while there are very few students coming in Italy to do research. Also, reduced budgets from our government with nonsensical cuts can produce a gap between generations of a line that produced excellent people. Recovering would be difficult then.

Turning attention to the discovery, I would like to emphasize that Gianotti repeated more and more times that the only certainty is that Standard Model, a beautiful theory, is verified with very high precision without no hint of breaking so far. But she warned the audience that we know that it must be overcome motivating this mostly from evidence of dark matter. The new particle, she said “Higgs-like”, resemble more and more the one originally postulated by Peter Higgs et al. but they have a lot of data to analyse yet and cannot be certain it is that one yet. They hope to clarify this matter with these other data (Moriond?).Fabiola Gianotti announces the new particle. She used an interesting image to describe the Higgs field to common people and then turned to the technical one to recover with respect to the formidable physicists were present there. Who speaks Italian can appreciate this video: Gianotti, Tonelli and Bertolucci explain Higgs field with children on similar lines.

The reason why she referred to our life is that most people generally ask “Why?”. Why all this effort to catch such a particle? She gave the beautiful example of J. J. Thompson and the discovery of the electron. When this happened both Thompson’s life and that of his neighbourhood did not change at all. But with the discovery of electronics and its application we all know now what all that has meant. For the Higgs particle can happen the same. From the discovery to its possible applications can pass some time and we need fundamental physics as a priori we cannot foresee the consequences but when they appear can be devastating and change our life definitely and forever for better. Gianotti said that without fundamental research, applied research dries up and eventually dies causing serious troubles to the economy of a country. I completely share her view. She also showed how hadron therapy and pet imaging were by-products of such endeavour.

Questions took more time than expected as the talk was really exciting and several people asked questions. She took this chance to recognize her debt with Ettore Fiorini, in the audience, that introduced her to particle physics and taught her a lot about it. Also Giorgio Salvini was present and asked for beyond LHC. Gianotti said that they hope to have LHC running for more than twenty years as also happened to other accelerator facilities. Salvini participated to most of the history of particle physics since Fermi’s time. He was in the experiment at CERN that produced W and Z particles for the first time with Carlo Rubbia. Francesco de Martini asked a technical question: Has Higgs particle cosmological implications? He was referring to a paper by Lee Smolin that claims that, due to this field, geometry should change from a Riemann to a Weyl one. Fabiola Gianotti and LHCGianotti answered immediately that the cosmological implications for the Higgs particle are enormous. The reason is that this is the first scalar particle ever discovered and inflation, the main mechanism in the Standard Model of cosmology to solve the problem of the homogeneity of the universe, has as a basic ingredient a scalar field. CERN discovery shows once again that the idea of inflation is in the right direction. de Martini was not satisfied with the answer turning back to the Smolin’s paper. Then Gianotti asked support to Giorgio Parisi, Parisi is one of the greatest Italian theoretical physicist, that confirmed Gianotti’s answer and said that, even if he is not an expert in the field of general relativity, people working in this research area have devised everything but the kitchen sink and so he would not be surprised if something like this was conceived.

In the end, a very beautiful talk from a great physicist. I would like to paraphrase what Gianotti said about Higgs and its light mass: Thanks Nature for giving us Gianotti!


Where does mass come from?

16/12/2012

ResearchBlogging.org

After CERN’s updates (well recounted here, here and here) producing no real news but just some concern about possible Higgs cloning, I would like to discuss here some mathematical facts about what one should expect about mass generation and why we should not be happy with these results, now coming out on a quarterly basis.

The scenario we are facing so far is one with a boson particle resembling more and more the Higgs particle appearing in the original formulation of the Standard Model. No trace is seen of anything else at higher energies, no evidence of supersymmetry. It appears like no new physics is hiding here rather for it we will have to wait eventually the upgrade of LHC that will start its runs on 2015.

I cannot agree with all of this and this is not the truth at all. The reason to not believe all this is strictly based on theoretical arguments and properties of partial differential equations. We are aware that physicists can be skeptical also about mathematics even if this is unacceptable as mathematics has no other way than being true or false. There is nothing like a half truth but there are a lot of theoretical physicists trusting on it. I have always thought that being skeptical on mathematics is just an excuse to avoid to enter into other work. There could always be the risk that one discovers it is correct and then has to support it.

The point is the scalar field. A strong limitation we have to face when working in quantum field theory is that only small coupling can be managed. No conclusive analysis can be drawn when a coupling is just finite and also lattice computations produce confusion. It seems like small coupling only can exist and all the theory we build are in the hope that nature is benign and yields nothing else than that. For the Higgs field is the same. All our analysis are based on this, the hierarchy problem comes out from this. Just take any of your textbook on which you built your knowledge of this matter and you will promptly realize that nothing else is there. Peschin and Schroeder, in their really excellent book, conclude that strong coupling cannot exist in quantum field theory and the foundation of this argument arises from renormalization group. Nature has only small couplings.

Mathematics, a product of nature, has not just small couplings and nobody can impede a mathematician to take these equations and try to analyze them with a coupling running to infinity. Of course, I did it and somebody else tried to understand this situation and the results make the situation rather embarrassing.

These reflections sprang from a paper appeared yesterday on arxiv (see here). In a de Sitter space there is a natural constant having the dimension of energy and this is the Hubble constant (in natural units). It is an emerging result that a massless scalar field with a quartic interaction in such a space develops a mass. This mass goes like m^2\propto \sqrt{\lambda}H^2 being \lambda the coupling coming from the self-interaction and H the Hubble constant. But the authors of this paper are forced to turn to the usual small coupling expansion just singling out the zero mode producing the mass. So, great news but back to the normal.

A self-interacting scalar field has the property to get mass by itself. Generally, such a self-interacting field has a potential in the form \frac{1}{2}\mu^2\phi^2+\frac{\lambda}{4}\phi^4 and we can have three cases \mu^2>0, \mu^2=0 and \mu^2<0. In all of them the classical equations of motion have an exact massive free solution (see here and Tao’s Dispersive Wiki) when \lambda is finite. These solutions cannot be recovered by any small coupling expansion unless one is able to resum the infinite terms in the series. The cases with \mu^2\ne 0 are interesting in that this term gets a correction depending on \lambda and for the case \mu^2<0 one can recover a spectrum with a Goldstone excitation and the exact solution is an oscillating one around a finite value different from zero (it never crosses the zero) as it should be for spontaneous breaking of symmetry. But the mass is going like \sqrt{\lambda}\Lambda^2 where now \Lambda is just an integration constant. The same happens in the massless case as one recovers a mass going like m^2\propto\sqrt{\lambda}\Lambda^2.  We see the deep analogy with the scalar field in a de Sitter space and these authors are correct in their conclusions.

The point here is that the Higgs mechanism, as has been devised in the sixties, entails all the philosophy of “small coupling and nothing else” and so it incurs in all the possible difficulties, not last the hierarchy problem. A modern view about this matter implies that, also admitting \mu^2<0 makes sense, we have to expand around a solution for \lambda finite being this physically meaningful rather than try an expansion for a free field. We are not granted that the latter makes sense at all but is just an educated guess.

What does all this imply for LHC results? Indeed, if we limit all the analysis to the coupling of the Higgs field with the other fields in the Standard Model, this is not the best way to say we have observed a true Higgs particle as the one postulated in the sixties. It is just curious that no other excitation is seen beyond the (eventually cloned) 126 GeV boson seen so far but we have a big desert to very high energies. Because the very nature of the scalar field is to have massive solutions as soon as the self-interaction is taken to be finite, this also means that other excited states must be seen. This simply cannot be the Higgs particle, mathematics is saying no.

M. Beneke, & P. Moch (2012). On “dynamical mass” generation in Euclidean de Sitter space arXiv arXiv: 1212.3058v1

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


Breaking of a symmetry

05/11/2012

ResearchBlogging.org

This week-end has been somewhat longer in Italy due to November 1st holiday and I have had the opportunity to read a very fine book by Ian Aitchison: Supersymmetry in Particle Physics – An Elementary Introduction. This book gives a very clear introduction to SUSY with all the computations clearly stated and going into the details of the Minimal Supersymmetric Standard Model (MSSM). This model was originally proposed by Howard Georgi and Savas Dimopolous (see here) and today does not seem to be in good shape due to recent results from LHC. Authors introduce a concept of a “softly” broken supersymmetry to accomodate the Higgs mechanism in the low-energy phenomenology.  A “soflty” broken supersymmetry is when the symmetry is explicitly broken using mass terms but keeping renormalizability and invariance under the electroweak symmetry group. The idea is that, in this way, the low-energy phenomenology will display a standard Higgs mechanism with a vacuum expectation value different from zero. This fact is really interesting as we know that in a standard electroweak theory the symmetry cannot be explicitly broken as we lose immediately renormalizability but a supersymmetric theory leaves us more freedom. But why do we need to introduce explicit breaking terms into the Lagrangian of the MSSM? The reason is that SUSY is conveying a fundamental message:

There is no such a thing as a Higgs mechanism.

Indeed, one can introduce a massive contribution to a scalar field, the \mu-term, but this has just the wrong sign and, indeed, a spontaneously broken supersymmetry is somewhat of a pain. There are some proposed mechanisms, as F or D breaking fields or some dynamical symmetry breaking, but nothing viable for the MSSM. Given the “softly” breaking terms, then the argument runs smoothly and one recovers two doublets and \tan\beta parameter that some authors are fond of.

The question at the root of the matter is that a really working supersymmetry breaking mechanism is yet to be found and should be taken for granted as we do not observe superpartners at accessible energies and LHC has yet to find one if ever. This mechanism also drives the electroweak symmetry breaking. Indeed, supersymmetry properly recovers a quartic self-interaction term but the awkward quadratic term with a wrong sign gives serious difficulties. Of course, the presence of a quartic term into a scalar field interacting with a fermion field, e.g. a Wess-Zumino model, provides the essential element to have a breaking of supersymmetry at lower energies: This model is reducible to a Nambu-Jona-Lasinio model and the gap equation will provide a different mass to the fermion field much in the same way this happens to chiral symmetry in QCD. No explicit mass term is needed but just a chiral model.

This means that the MSSM can be vindicated once one gets rid of an explicit breaking of the supersymmetry and works out in a proper way the infrared limit. There is a fundamental lesson we can learn here: SUSY gives rise to self-interaction and this is all you need to get masses. Higgs mechanism is not a fundamental one.

Dimopoulos, S., & Georgi, H. (1981). Softly broken supersymmetry and SU(5) Nuclear Physics B, 193 (1), 150-162 DOI: 10.1016/0550-3213(81)90522-8

Marco Frasca (2011). Chiral symmetry in the low-energy limit of QCD at finite temperature Phys. Rev. C 84, 055208 (2011) arXiv: 1105.5274v4


Higgs boson and conformal symmetry

30/08/2012

ResearchBlogging.org

So far, I believed to be the only man on Earth to trust a complete absence of mass terms in the Standar Model (we call this conformal symmetry). I was wrong.  Krzysztof Meissner and Hermann Nicolai anticipated this idea. Indeed, in a model where mass is generally banned, there is no reason to believe that also the field that is the source of mass should keep a mass term (imaginary or real). We have one more reason to believe in such a scenario and it is the hierarchy problem as the quadratic term in the Higgs field just produces that awkward dependence on the square of the cut-off, the reason why people immediately thought that something else must be in that sector of the model. Meissner and Nicolai obtained their paper published on Physics Letters B and can be found here. As they point out in the article, the problem is to get a meaningful mass for the Higgs field, provided one leaves the self-coupling to be small. I do not agree  at all with the reasons for this, the Landau pole, as I have already widely said in this blog. One cannot built general results starting from perturbation theory. But assuming that this is indeed the case, the only mechanism at our disposal to get a mass is the Coleman-Weinberg mechanism. In this case, radiative corrections produce an effective potential that has a non-trivial minimum. The problem again is that this is obtained using small perturbation theory and so, the mass one gets is too small to be physically meaningful. The authors circumvent the problem adding a further scalar field. In this case the model appears to be consistent and all is properly working. What I would like to emphasize is that, if one assumes conformal symmetry to hold for the Standard Model, a single Higgs is not enough. So, I like this paper a lot and I will explain the reasons in a moment. I am convinced that these authors are on the right track.

Two days ago these authors come out with another paper (see here). They claim that the second Higgs has been already seen at CDF (Tevatron), at about 325 GeV, while we know there is just a hint (possibly a fluke) from CMS and nothing from ATLAS for that mass. Of course, there is always the possibility that this resonance escaped due to its really small width.

My personal view was already presented here. At that time, I was not aware of the work by Meissner and Nicolai otherwise I would have used it as a support. The only point I would like to question is the effective generation of mass. There is no generally accepted quantum field theory for a large coupling, neglecting for the moment attempts arising from string theory. Before to say that string theory grants a general approach for strongly coupled problems I would like to see it to give a solution to the scalar massless quartic field theory in such a case. This is the workhorse for this kind of problems and both the communities of physicists and mathematicians were just convinced that perturbation theory has only one side. As I showed here, this is not true. One can do perturbation theory also when a perturbation is taken to go to infinity. This means that we do not need a Coleman-Weinberg mechanism in a conformal Standard Model but we can do perturbation theory assuming a finite self-interaction: An asymptotic perturbation series can be also obtained in this case. But the fundamental conclusions one can draw from this analysis are the following:

  • The theory must be supersymmetric.
  • The theory has a harmonic oscillator spectrum for a free particle given by m_n=(2n+1)(\pi/2K(i))v, being K(i) an elliptic integral and v an integration constant with the dimension of energy.

Now, let us look at the last point. One can prove that the decays for the higher excited states are increasingly difficult to observe as their decay constants become exponentially smaller with n (see here, eq. 11). But, if the observed Higgs boson has a mass of  about 125 GeV, one has v=105\ GeV and the next excitation is at about 375 GeV, very near the one postulated by Meissner and Nicolai and also near to the bump seen at CDF. This would be an exciting evidence of existence for supersymmetry: The particle seen at CERN would be supersymmetric!

So, what I am saying here is that a conformal Standard Model, not only solves the hierarchy problem, but it is also compelling for the existence of supersymmetry. I think it would be worthy further studies.

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

Krzysztof A. Meissner, & Hermann Nicolai (2012). A 325 GeV scalar resonance seen at CDF? arXiv arXiv: 1208.5653v1

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

Marco Frasca (2010). Glueball spectrum and hadronic processes in low-energy QCD Nucl.Phys.Proc.Suppl.207-208:196-199,2010 arXiv: 1007.4479v2


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