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.

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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:

and the reason was this slide

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

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


Well below 1%

14/04/2017

ResearchBlogging.org

When a theory is too hard to solve people try to consider lower dimensional cases. This also happened for Yang-Mills theory. The four dimensional case is notoriously difficult to manage due to the large coupling and the three dimensional case has been treated both theoretically and by lattice computations. In this latter case, the ground state energy of the theory is known very precisely (see here). So, a sound theoretical approach from first principles should be able to get that number at the same level of precision. We know that this is the situation for Standard Model with respect to some experimental results but a pure Yang-Mills theory has not been seen in nature and we have to content ourselves with computer data. The reason is that a Yang-Mills theory is realized in nature just in interaction with other kind of fields being these scalars, fermions or vector-like.

In these days, I have received the news that my paper on three dimensional Yang-Mills theory has been accepted for publication in the European Physical Journal C. Here is tha table for the ground state for SU(N) at different values of N compared to lattice data

N Lattice     Theoretical Error

2 4.7367(55) 4.744262871 0.16%

3 4.3683(73) 4.357883714 0.2%

4 4.242(9)     4.243397712 0.03%

4.116(6)    4.108652166 0.18%

These results are strikingly good and the agreement is well below 1%. This in turn implies that the underlying theoretical derivation is sound. Besides, the approach proves to be successful both also in four dimensions (see here). My hope is that this means the beginning of the era of high precision theoretical computations in strong interactions.

Andreas Athenodorou, & Michael Teper (2017). SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions J. High Energ. Phys. (2017) 2017: 15 arXiv: 1609.03873v1

Marco Frasca (2016). Confinement in a three-dimensional Yang-Mills theory arXiv arXiv: 1611.08182v2

Marco Frasca (2015). Quantum Yang-Mills field theory Eur. Phys. J. Plus (2017) 132: 38 arXiv: 1509.05292v2


Quote of the day

09/03/2017

“Bad men need nothing more to compass their ends, than that good men should look on and do nothing.”

John Stuart Mill


Yang-Mills theory paper gets published!

30/12/2016

ResearchBlogging.org

Exact solutions of quantum field theories are very rare and, normally, refer to toy models and pathological cases. Quite recently, I put on arxiv a pair of papers presenting exact solutions both of the Higgs sector of the Standard Model and the Yang-Mills theory made just of gluons. The former appeared a few month ago (see here) while the latter has been accepted for publication a few days ago (see here). I have updated the latter just today and the accepted version will appear on arxiv on 2 January next year.

What does it mean to solve exactly a quantum field theory? A quantum field theory is exactly solved when we know all its correlation functions. From them, thanks to LSZ reduction formula, we are able to compute whatever observable in principle being these cross sections or decay times. The shortest way to correlation functions are the Dyson-Schwinger equations. These equations form a set with the former equation depending on the higher order correlators and so, they are generally very difficult to solve. They were largely used in studies of Yang-Mills theory provided some truncation scheme is given or by numerical studies. Their exact solutions are generally not known and expected too difficult to find.

The problem can be faced when some solutions to the classical equations of motion of a theory are known. In this way there is a possibility to treat the Dyson-Schwinger set. Anyhow, before to enter into their treatment, it should be emphasized that in literature the Dyson-Schwinger equations where managed just in one way: Carl BenderUsing their integral form and expressing all the correlation functions by momenta. It was an original view by Carl Bender that opened up the way (see here). The idea is to write the Dyson-Schwinger equations into their differential form in the coordinate space. So, when you have exact solutions of the classical theory, a possibility opens up to treat also the quantum case!

This shows unequivocally that a Yang-Mills theory can display a mass gap and an infinite spectrum of excitations. Of course, if nature would have chosen the particular ground state depicted by such classical solutions we would have made bingo. This is a possibility but the proof is strongly related to what is going on for the Higgs sector of the Standard Model that I solved exactly but without other matter interacting. If the decay rates of the Higgs particle should agree with our computations we will be on the right track also for Yang-Mills theory. Nature tends to repeat working mechanisms.

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

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

Carl M. Bender, Kimball A. Milton, & Van M. Savage (1999). Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory Phys.Rev.D62:085001,2000 arXiv: hep-th/9907045v1


NASA paper leaked!

05/11/2016

EmDrive is a possible propulsion system granting no apparent expulsion of propellent. It has been reason of hot debate with strong criticisms from the scientific community championed by Sean Carroll and John Baez. Harold "Sonny" WhiteNotwithstanding this, NASA went ahead performing in-depth experiments to test this technology. It was announced that, on December this year, a paper will appear in a reputable journal reporting on the last measurement campaign. But to today the paper leaked out on reddit. The results, at a first sight, appear to be striking confirming the effect, with all the possible mundane disturbing causes excluded. You can also find other material there as a small video.

I hope this will go properly evaluated by the scientific community moving to a more serious addressing of this effect.

Update: The links were removed from the subreddit’s moderator. I have copies of these files but I do not mean to publish them in any form.

Update: Here is the published paper.


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