## 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.

## Cracks in the Witten’s index theorem?

18/06/2019

In these days, a rather interesting paper (see here for the preprint) appeared on Physical Review Letters. These authors study a Wess-Zumino model for ${\cal N}=1$, the prototype of any further SUSY model, and show that there exists an anomaly at one loop in perturbation theory that breaks supersymmetry. This is rather shocking as the model is supersymmetric at the classical level and, in agreement with Witten’s index theorem, no breaking of supersymmetry should ever be observed. Indeed, the authors, in the conclusions, correctly ask how the Witten’s theorem copes with this rather strange behavior. Of course, Witten’s theorem is correct and the question comes out naturally and is very much interesting for further studies.

This result is important as I have incurred in a similar situation for the Wess-Zumino model in a couple of papers. The first one (see here and here)  went published and shows how the classical Wess-Zumino model, in a strong coupling regime, breaks supersymmetry. Therefore, I asked a similar question as for the aforementioned case: How quantum corrections recover the Witten’s theorem? The second one is remained a preprint (see here). I tried to send it to Physics Letters B but the referee, without any check of mathematics, just claimed that there was the Witten’s theorem to forbid my conclusions. The Editor asked me to withdraw the paper in view of this identical reason. This was a very strong one. So, I never submited this paper again and just checked the classical case where I was more lucky.

So, my question is still alive: Has supersymmetry in itself the seeds of its breaking?

This is really important in view of the fact that the Minimal Supersymmetric Standard Model (MSSM), now in disgrace after LHC results, can have a dark side in its soft supersymmetry breaking sector. This, in turn, could entail a wrong understanding of where the superpartners could be after the breaking. Anyway, it is really something exciting already at the theoretical level. We are just stressing Witten’s index theorem in search for answers.

## Is it possible to get rid of exotic matter in warp drive?

12/05/2019

On 1994, Miguel Alcubierre proposed a solution of the Einstein equations (see here) describing a space-time bubble moving at arbitrary speed. It is important to notice that no violation of the light speed limit happens because is the space-time moving and inside the bubble everything goes as expected. This kind of solutions of the Einstein equations have a fundamental drawback: they violate Weak Energy Condition (WEC) and, in order to exist, some exotic matter with negative energy density must exist. Useless to say, nobody has ever seen such kind of matter. There seems to exist some clue in the way Casimir effect works but this just relies on the way one interprets quantum fields rather than an evidence of existence. Besides, since the initial proposal, a great number of studies have been published showing how pathological the Alcubierre’s solution can be, also recurring to quantum field theory (e.g. Hawking radiation). So, we have to turn to dream of a possible interstellar travel hoping that some smart guy will one day come out with a better solution.

Of course, Alcubierre’s solution is rather interesting from a physical point of view as it belongs to a number of older solutions, like wormholes, time machines and like that, yielded by very famous authors as Kip Thorne, that arise when one impose a solution and then check the conditions of its existence. This turns out to be a determination of the energy-momentum tensor and, unavoidably, is negative. Then, they violate whatever energy condition of the Einstein equations granting pathological behaviour. On the other side, they appear the most palatable for science fiction of possible futures of space and time travels. In these times where this kind of technologies are largely employed by the film industry, moving the fantasy of millions, we would hope that such futures should also be possible.

It is interesting to note the procedure to obtain these particular solutions. One engineers it on a desk and then substitute them into the Einstein equations to see when are really a solution. One fixes in this way the energy requirements. On the other side, it is difficult to come out from the blue with a solution of the Einstein equations that provides such a particular behaviour, moving the other way around. It is also possible that such solutions are not possible and imply always a violation of the energy conditions. Some theorems have been proved in the course of time that seem to prohibit them (e.g. see here). Of course, I am convinced that the energy conditions must be respected if we want to have the physics that describes our universe. They cannot be evaded.

So, turning at the question of the title, could we think of a possible warp drive solution of the Einstein equations without exotic matter? The answer can be yes of course provided we are able to recover the York time, or warp factor, in the way Alcubierre obtained it with its pathological solution. At first, this seems an impossible mission. But the space-time bubble we are considering is a very small perturbation and perturbation theory can come to rescue. Particularly, when this perturbation can be locally very strong. On 2005, I proposed such a solution (see here) together with a technique to solve the Einstein equations when the metric is strongly perturbed. My intent at that time was to give a proof of the BKL conjecture. A smart referee suggested to me to give an example of application of the method. The metric I have obtained in this way, perturbing a Schwarzaschild metric, yields a solution that has an identical York time (warp factor) as for the Alcubierre’s metric. Of course, I am respecting energy conditions as I am directly solving the Einstein equations that do.

The identity between the York times can be obtained provided the form factor proposed by Alcubierre is taken to be 1 but this is just the simplest case. Here is an animation of my warp factor.

It seen the bubble moving as expected along the x direction.

My personal hope is that this will go beyond a mathematical curiosity. On the other side, it should be understood how to provide such kind of perturbations to a given metric. I can think to the Einstein-Maxwell equations solved using perturbation theory. There is a lot of literature about and a lot of great contributions on this argument.

Finally, this could give a meaning to the following video by NASA.

## 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.

## Paper with a proof of confinement has been accepted

28/03/2018

Recently, I wrote a paper together with Masud Chaichian (see here) containing a mathematical proof of confinement of a non-Abelian gauge theory based on Kugo-Ojima criterion. This paper underwent an extended review by several colleagues well before its submission. One of them has been Taichiro Kugo, one of the discoverers of the confinement criterion, that helped a lot to improve the paper and clarify some points. Then, after a review round of about two months, the paper has been accepted in Physics Letters B, one of the most important journals in particle physics.

This paper contains the exact beta function of a Yang-Mills theory. This confirms that confinement arises by the combination of the running coupling and the propagator. This idea was around in some papers in these latter years. It emerged as soon as people realized that the propagator by itself was not enough to grant confinement, after extended studies on the lattice.

It is interesting to point out that confinement is rooted in the BRST invariance and asymptotic freedom. The Kugo-Ojima confinement criterion permits to close the argument in a rigorous way yielding the exact beta funtion of the theory.

## 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.

## Something to say but not yet…

12/07/2017

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: