Higgs boson and conformal symmetry

30/08/2012

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

Higgs: Tevatron confirms CERN findings

07/03/2012

In these days, at Moriond (La Thuile indeed, a great ski station) on Italian Alps, a conference is held (see here). Today is the Higgs day and people at Tevatron confirmed the clues found by CERN and announced last December. Higgs particle mass should be around 125 GeV. This has being reverberated on the media (see here). The evidence found at Tevatron is about two sigma (one percent probability that is not a fluctuation in the data) and so, one cannot claim a discovery and well below the three sigma evidence from CERN. For a final word we will have to wait summer conferences and new data from the restart of LHC at April.

Update: Here is Fermilab press release.

Update: Matt Strassler is pointing out in his blog that ATLAS has now a lower evidence for the Higgs particle than in last December. This seems something like the fluctuation of the last summer. Evidence for this would be now 10%.

News on the Higgs

11/11/2011

The end of this year is approaching, LHC gathered data at higher luminosity but it is since the end of August that no news is around about the status of the search of the Higgs particle. Of course, a frenzy of activity is going around at CERN and finally, something seems to move. On Monday a new conference will begin in Paris (see here). No relevant novelties are expected with respect to this talk but DG of CERN asked for updates in the mid of December (see here for other information). Besides, rumors are spreading around blogosphere that a group at CERN asked at the conference organizers a further slot to give an announcement. All this is giving the flavor that, for the end of this year, some relevant news about Higgs will come out. It could be possibly a matter of days.

I would like to resume here the situation. Latest measurements seem to exclude a standard model Higgs for almost all the range from the LEP limit of 114 GeV to near 600 GeV. At about 600 GeV ATLAS is seeing an excess. Similarly, it is possible that Higgs particle is hiding at around 140 GeV but all the excesses seen so far are no more high than $2\sigma$ so that, a no Higgs scenario is gaining support. Tevatron appears to confirm this situation. The excess at 600 GeV, if confirmed, will imply a relevant re-analysis of the standard model as, in this case, we will enter into the realm of a strongly coupled quantum field theory. I provided mathematics for this (see here and here) but it is not widely accepted by the scientific community and, in general, other methods to work with this case are not known and most of our understanding relies on lattice computations. A heavy Higgs has also been forecast by Paolo Cea and Leonardo Cosmai (see here and here) having approximately the mass near the ATLAS excess. This would make the situation quite dramatic but really exciting and will provide a strong evidence for the existence of supersymmetry. Besides, in this case, a whole spectrum of excited states of this heavy and strongly coupled Higgs will also be observed.

In view of this near approaching dates, we wish the best of luck to people at CERN and thank them for their excellent work.

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

Marco Frasca (2010). Mapping theorem and Green functions in Yang-Mills theory PoS FacesQCD:039,2010 arXiv: 1011.3643v3

P. Cea, & L. Cosmai (2011). The trivial Higgs boson: first evidences from LHC arXiv arXiv: 1106.4178v1

P. Cea, & L. Cosmai (2011). The Trivial Higgs at LHC arXiv arXiv: 1109.5922v1

What’s going on with Higgs particle?

03/08/2011

The aftermath of the EPS Conference is quite exciting on a side. Higgs hunting points to an unexpected direction even if some residuals of an old expectation are still there. I just want to show you the graphs of this conference from Tevatron and LHC

From these it is very clear that the excluded range of mass is become significantly large restricting the possibilities to the intervals of a mass around 140 GeV or to a massive Higgs implying a strongly coupled theory. The evidence for a 140 GeV Higgs particle is yet small, about two sigmas, and we cannot exclude that this is a fluke but, to support this clue, it appears both at Tevatron and LHC. A small peak at around 250 GeV is seen only by ATLAS and could disappear in the future.

What I would like to emphasize here is that the possibility of a strongly coupled Higgs is well alive and this can have deep implications for the model and physics at large. There are several reasons for this. First of all, a strongly coupled Higgs field implies supersymmetry (see here). This result is inescapable and some breaking pattern of supersymmetry must be devised to get the right mass spectrum of the Standard Model. But this is already old and well-acquired matter. The most important point is that there will be a completely new way to approach quantum field theory. So far, quantum field theory has been managed just using weak perturbation theory but a strongly coupled Higgs would mean that we will also have to devise a perturbative technique the other way round, i.e. with a coupling increasingly large.

So, I will keep on support this view of a heavy Higgs as, being a theoretical physicist, consequences will be devastating and largely more exciting of any other possibility. We will be eager to see the improvement in the next months from the measurement datasets. Certainly, on 2012 all the curtains will be definitely down.

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

CDF bump at 4.8 sigma!

01/06/2011

In these days I am exceeding with exclamation marks but let me say that there are sound reasons for this. I will keep on staying on a prudence line as my more renowned colleagues are doing but there is a talk by Giovanni Punzi, the spokesman of CDF Collaboration at Tevatron, (see here), presenting the following picture

They increased the number of events and the bump is still there. They have consistently found $147\pm 5 GeV$ for the mass of this presumed particle. Of course, we have to wait for D0 and LHC to confirm this finding but this is becoming more and more a real discovery. But since the first inception, theoretical physicists have come out with possible explanations, the most reasonable of these seems a new U(1) interaction with Z’ leptophobic boson, where leptophobic just means that this particle has essentially strong decay modes. People at CDF has discarded several possible mundane explanations that emerged at the dawn of the first announcement but, as my readers know, it should be stated that our current understanding of low-energy QCD is somewhat in development and some modeling used by people at CERN or Tevatron can be not so accurate. My personal view is that is time to wait yet notwithstanding the good news.

For more relevant posts see here, here and here.

Kingman Cheung, & Jeonghyeon Song (2011). Baryonic Z’ Explanation for the CDF Wjj Excess arXiv arXiv: 1104.1375v3

A simpler explanation for the CDF bump

20/04/2011

A lot of fuss arose about the recent almost finding of a new particle at Tevatron (see here). Several exotic hypotheses were put forward mostly looking for physics beyond Standard Model. Of course, being there such a bump at about $3\sigma$, we cannot yet cry out for a discovery and more mundane explanations could exist.

Indeed, this is the content of this paper appeared on arXiv. These authors point out some weak points in the analysis done by CDF that amount in the end at an imperfect estimation of the background. This is also my claim as strong interactions are not completely under control. I give here authors’ conclusions for your considerations:

In conclusion, we observe that the dijet invariant mass peak seen in the recent CDF Wjj cross section is completely consistent with the excess observed in the CDF single-top-quark analysis. Both may be explained by an upward fluctuation in the CDF data set of s-channel single-top-quark production, and t-channel production accompanied by an additional low-energy jet. The latter process is poorly modeled by Monte Carlo, and the apparent t-channel excess could simply be an artifact of theoretical uncertainty. Given the modest excess observed by the D0 Collaboration in their single-top-quark data set , we predict the D0 Collaboration would not see a significant dijet invariant mass peak if they follow the CDF procedure.

So, Standard Model strikes back again.

CDF Collaboration, & T. Aaltonen (2011). Invariant Mass Distribution of Jet Pairs Produced in Association with a
W boson in ppbar Collisions at sqrt(s) = 1.96 TeV arXiv arXiv: 1104.0699v1

Zack Sullivan, & Arjun Menon (2011). A standard model explanation of a CDF dijet excess in Wjj arXiv arXiv: 1104.3790v1

A new particle at Fermilab?

06/04/2011

I am a registered reader at New York Times and subscribed Dennis Overbye‘s articles. So, this morning I received the mail from the journal with a new writing from Dennis. The title is “At Particle Lab, a Tantalizing Glimpse Has Physicists Holding Their Breaths”. I just jumped on my chair and then, eagerly, read the article. Indeed, CDF Collaboration posted a paper on arXiv last night (see here). The kind of process that they studied is the one with a final diboson (WW or WZ) from a lepton plus jets. They analyzed the invariant mass for masses higher than $100\ GeV/c^2$. They get a $3\sigma$ excess in the region $120-160\ GeV/c^2$ that, if confirmed, should correspond to a new particle. Some tests seem  to point toward a non-Standard Model particle having a mass of $150\ GeV/c^2$ that cannot be identified with Higgs.

As always, it is important to emphasize the this is a $3\sigma$ evidence and further analysis is needed to confirm or disprove the discovery. But it is important to emphasize that Tevatron is paving the way to a large number of discoveries to be seen soon at LHC.

Update: CDF will present these results at a seminar. We can follow it on the web here.

Another update: A post by Tommaso Dorigo, one of the authors of the CDF paper, is here.

CDF Collaboration, & T. Aaltonen (2011). Invariant Mass Distribution of Jet Pairs Produced in Association with a
W boson in ppbar Collisions at sqrt(s) = 1.96 TeV arXiv arXiv: 1104.0699v1

The Tevatron affair and the “fat” gluon

25/01/2011

Tevatron is again at the forefront of the blogosphere mostly due to Jester and Lubos. Top quark seems the main suspect to put an end to the domain of the Standard Model in particle physics. Indeed, years and years of confirmations cannot last forever and somewhere some odd behavior must appear. But this is again an effect at 3.4 sigma and so all could reveal to be a fluke and the Standard Model will escape again to its end. But in the comment area of the post in the Lubos’ blog there is a person that pointed out my proposal for a “fat” gluon. “Fat” here stays just for massive and now I will explain this idea and its possible problems.

The starting point is the spectrum of Yang-Mills theory that I have obtained recently (see here and here). I have shown that, at very low energies, the gluon field has a propagator proportional to

$G(p)=\sum_{n=0}^\infty(2n+1)\frac{\pi^2}{K^2(i)}\frac{(-1)^{n+1}e^{-(n+\frac{1}{2})\pi}}{1+e^{-(2n+1)\pi}}\frac{1}{p^2-m_n^2+i\epsilon}$

with the spectrum given by

$m_n=\left(n+\frac{1}{2}\right)\frac{\pi}{K(i)}\sqrt{\sigma}$

being $\sigma$ the string tension being about $(440\ MeV)^2$. If we go beyond the leading order of such a strong coupling expansion one gets that the masses run with momenta. This has been confirmed on the lattice quite recently by Orlando Oliveira and Pedro Bicudo (see here). The interesting point about such a spectrum is that is not bounded from above and, in principle, one could take n large enough to reach TeV energies. These glueballs are very fat indeed and could explain CDF’s results if these should be confirmed by them, their colleagues at D0 and LHC.

It should be emphasized that these excitations of the glue field have spin zero and so will produce t-tbar pairs in a singlet state possibly explaining the charge asymmetry through the production rate of such very massive glueballs.

A problem can be seen immediately from the form of the propagator that has each contribution in the sum exponentially smaller as n increases. Indeed, this has a physical meaning as this is also what appears in the decay constants of such highly massive gluons (see here). Decay constants are fundamental in the computation of cross sections and if they are very near zero so could be the corresponding cross sections. But Oliveira and Bicudo also showed that these terms in the propagator depend on the momenta too, evading the problem at higher energies. Besides, I am working starting from the low energy part of the theory and assuming that such a spectrum will not change too much at such high energies where asymptotic freedom sets in and gluons seem to behave like massless particles. But we know from the classical theory that a small self-interaction in the equations is enough to get masses for the field and massless gluons are due to the very high energies we are working with. For very high massive excitations this cannot possibly apply. The message I would like to convey with this analysis is that if we do not know the right low-energy behavior of QCD we could miss important physics also at high-energies. We cannot live forever assuming we can forget about the behavior of Yang-Mills theory in the infrared mostly if the mass spectrum is not bounded from above.

Finally, my humble personal conviction, also because I like the idea behind Randall-Sundrum scenario, is that KK gluons are a more acceptable explanation if these CDF’s results will prove not to be flukes. The main reason to believe this is that we would obtain for the first time in the history of mankind a proof of existence for other dimensions and it would be an epochal moment indeed. And all this just forgetting what would imply for me to be right…

Frasca, M. (2008). Infrared gluon and ghost propagators Physics Letters B, 670 (1), 73-77 DOI: 10.1016/j.physletb.2008.10.022

Frasca, M. (2009). Mapping a Massless Scalar Field Theory on a Yang–Mills Theory: Classical Case Modern Physics Letters A, 24 (30) DOI: 10.1142/S021773230903165X

P. Bicudo, & O. Oliveira (2010). Gluon Mass in Landau Gauge QCD arxiv arXiv: 1010.1975v1

Frasca, M. (2010). Glueball spectrum and hadronic processes in low-energy QCD Nuclear Physics B – Proceedings Supplements, 207-208, 196-199 DOI: 10.1016/j.nuclphysbps.2010.10.051

A more prosaic explanation

09/01/2011

The aftermath of some blogosphere activity about CDF possible finding at Tevatron left no possible satisfactory explanation beyond a massive octet of gluons that was already known in the literature and used by people at Fermilab. In the end we need some exceedingly massive gluons to explain this asymmetry. If you look around in the net, you will find other explanations that go beyond ordinary known physics of QCD. Of course, speaking about known physics of QCD we leave aside what should have been known so far about Yang-Mills theory and mass gap. As far as one can tell, no generally accepted truth is known about otherwise all the trumpets around the World would have already sung.

But let us do some educated guesses using our recent papers (here and here) and a theorem proved by Alexander Dynin (see here). These papers show that the spectrum of a Yang-Mills theory is discrete and the particles have an internal spectrum that is bounded below (the mass gap) but not from above. I can add to this description that there exists a set of spin 0 excitations making the ground state of the theory and ranging to infinite energy. So, if we suppose that the annihilation of a couple of quarks can generate a particle of this with a small chance, having enough energy to decay in a pair t-tbar in a singlet state, we can observe an asymmetry just arising from QCD.

I can understand that this is a really prosaic explanation but it is also true that we cannot live happily forgetting what is going on after a fully understanding of a Yang-Mills theory and that we are not caring too much about. So, before entering into  the framework of very exotic explanations just we have to be sure to have fully understood all the physics of the process and that we have not forgotten anything.

Marco Frasca (2007). Infrared Gluon and Ghost Propagators Phys.Lett.B670:73-77,2008 arXiv: 0709.2042v6

Marco Frasca (2009). Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical
Case Mod. Phys. Lett. A 24, 2425-2432 (2009) arXiv: 0903.2357v4

Alexander Dynin (2009). Energy-mass spectrum of Yang-Mills bosons is infinite and discrete arxiv arXiv: 0903.4727v2

Rumors on Higgs at Tevatron

10/07/2010

It is not my habit to put rumors about as my readers know, but the news is really sensational. Tommaso Dorigo in his blog told  that rumors are leaking about a light Higgs seen in one of the two collaborations at Tevatron. Tommaso is working there too.

Rumors say of a Higgs particle having a mass of 115 GeV, very near the limit identified at LEP and so a reason to regret for CERN. This will support the view of a supersymmetric particle. Supersymmetry, for consistency reasons, requires Higgs to be light. On the other side, we know that the Standard Model cannot hold with a superheavy Higgs particle. This implies that a similar identification at LHC should be near and this machine should work out supersymmetry in all its glory.

Finally, let me point out a similar post by the Czech guy.

Update: Fermilab denied rumors about Higgs finding at Tevatron (see here).