That strange behavior of supersymmetry…

07/12/2013

ResearchBlogging.org

I am a careful reader of scientific literature and an avid searcher for already published material in peer reviewed journals. Of course, arxiv is essential to accomplish this task and to satisfy my needs for reading. In these days, I am working on Dyson-Schwinger equations. I have written on this a paper (see here) a few years ago but this work is in strong need to be revised. Maybe, some of these days I will take the challenge. Googling around and looking for the Dyson-Schwinger equations applied to the well-known supersymmetric model due to Wess and Zumino, I have uncovered a very exciting track of research that uses Dyson-Schwinger equations to produce exact results in quantum field theory. The paper I have got was authored by Marc Bellon, Gustavo Lozano and Fidel Schaposnik and can be found here. These authors get the Dyson-Schwinger equations for the Wess-Zumino model at one loop and manage to compute the self-energies of the involved fields: A scalar, a fermion and an auxiliary bosonic field. Their equations are yielded for three different self-energies, different for each field. Self-energies are essential in quantum field theory as they introduce corrections to masses in a propagator and so enters into the physical part of an object that is not an observable.

Now, if you are in a symmetric theory like the Wess-Zumino model, such a symmetry, if it is not broken, will yield equal masses to all the components of the multiplet entering into the theory. This means that if you start with the assumption that in this case all the self-energies are equal, you are doing a consistent approximation. This is what Bellon, Lozano and Schaposnik just did. They assumed from the start that all the self-energies are equal for the Dyson Schwinger equations they get and go on with their computations. This choice leaves an open question: What if do I choose different self-energies from the start? Will the Dyson-Schwiner equations drive the solution toward the symmetric one?

This question is really interesting as the model considered is not exactly the one that Witten analysed in his famous paper  on 1982 on breaking of a supersymmetry (you can download his paper here). Supersymmetric model generates non-linear terms and could be amenable to spontaneous symmetry breaking, provided the Witten index has the proper values. The question I asked is strongly related to the idea of a supersymmetry breaking at the bootstrap: Supersymmetry is responsible for its breaking.

So, I managed to numerically solve Dyson-Schwinger equations for the Wess-Zumino model as yielded by Bellon, Lozano and Schaposnik and presented the results in a paper (see here). If you solve them assuming from the start all the self-energies are equal you get the following figure for coupling running from 0.25 to 100 (weak to strong):

All equal self-energies for the Wess-Zumino model

It does not matter the way you modify your parameters in the Dyson-Schwinger equations. Choosing them all equal from the start makes them equal forever. This is a consistent choice and this solution exists. But now, try to choose all different self-energies. You will get the following figure for the same couplings:

Not all equal self-energies for the Wess-Zumino model

This is really nice. You see that exist also solutions with all different self-energies and supersymmetry may be broken in this model. This kind of solutions has been missed by the authors. What one can see here is that supersymmetry is preserved for small couplings, even if we started with all different self-energies, but is broken as the coupling becomes stronger. This result is really striking and unexpected. It is in agreement with the results presented here.

I hope to extend this analysis to more mundane theories to analyse behaviours that are currently discussed in literature but never checked for. For these aims there are very powerful tools developed for Mathematica by Markus Huber, Jens Braun and Mario Mitter to get and numerically solve Dyson-Schwinger equations: DoFun anc CrasyDSE (thanks to Markus Huber for help). I suggest to play with them for numerical explorations.

Marc Bellon, Gustavo S. Lozano, & Fidel A. Schaposnik (2007). Higher loop renormalization of a supersymmetric field theory Phys.Lett.B650:293-297,2007 arXiv: hep-th/0703185v1

Edward Witten (1982). Constraints on Supersymmetry Breaking Nuclear Physics B, 202, 253-316 DOI: 10.1016/0550-3213(82)90071-2

Marco Frasca (2013). Numerical study of the Dyson-Schwinger equations for the Wess-Zumino
model arXiv arXiv: 1311.7376v1

Marco Frasca (2012). Chiral Wess-Zumino model and breaking of supersymmetry arXiv arXiv: 1211.1039v1

Markus Q. Huber, & Jens Braun (2011). Algorithmic derivation of functional renormalization group equations and
Dyson-Schwinger equations Computer Physics Communications, 183 (6), 1290-1320 arXiv: 1102.5307v2

Markus Q. Huber, & Mario Mitter (2011). CrasyDSE: A framework for solving Dyson-Schwinger equations arXiv arXiv: 1112.5622v2


Living dangerously

05/11/2013

ResearchBlogging.org

Today, I read an interesting article on New York Times by Dennis Overbye (see here). Of course, for researchers, a discovery that does not open new puzzles is not really a discovery but just the end of the story. But the content of the article is intriguing and is related to the question of the stability of our universe. This matter was already discussed in blogs (e.g. see here) and is linked to a paper by Giuseppe Degrassi, Stefano Di Vita, Joan Elias-Miró, José R. Espinosa, Gian F. Giudice, Gino Isidori, Alessandro Strumia (see here)  with the most famous picture

Stability and Higgs

Our universe, with its habitants, lives in that small square at the border between stability and meta-stability. So, it takes not too much to “live dangerously” as the authors say. Just a better measurement of the mass of the top quark can throw us there and this is in our reach at the restart of LHC. Anyhow, their estimation of the tunnel time is really reassuring as the required time is bigger than any reasonable cosmological age. Our universe, given the data coming from LHC, seems to live in a metastable state. This is further confirmed in a more recent paper by the same authors (see here). This means that the discovery of the Higgs boson with the given mass does not appear satisfactory from a theoretical standpoint and, besides the missing new physics, we are left with open questions that naturalness and supersymmetry would have properly assessed. The light mass of the Higgs boson, 125 GeV, in the framewrok of the Higgs mechanism, recently awarded with a richly deserved Nobel prize to Englert and Higgs, with an extensive use of weak perturbation theory is looking weary.

The question to be answered is: Is there any point in this logical chain where we can intervene to put all this matter on a proper track? Or is this the situation with the Standard Model to hold down to the Planck energy?

In all this matter there is a curious question that arises when you work with a conformal Standard Model. In this case, there is no mass term for the Higgs potential but rather, the potential gets modified by quantum corrections (Coleman-Weinberg mechanism) and a non-null vacuum expectation value comes out. But one has to grant that higher order quantum corrections cannot spoil conformal invariance. This happens if one uses dimensional regularization rather than other renormalization schemes. This grants that no quadratic correction arises and the Higgs boson is “natural”. This is a rather strange situation. Dimensional regularization works. It was invented by ‘t Hooft and Veltman and largely used by Wilson and others in their successful application of the renormalization group to phase transitions. So, why does it seem to behave differently (better!) in this situation? To decide we need a measurement of the Higgs potential that presently is out of discussion.

But there is a fundamental point that is more important than “naturalness” for which a hot debate is going on. With the pioneering work of Nambu and Goldstone we have learned a fundamental lesson: All the laws of physics are highly symmetric but nature enjoys a lot to hide all these symmetries. A lot of effort was required by very smart people to uncover them being very well hidden (do you remember the lesson from Lorentz invariance?). In the Standard Model there is a notable exception: Conformal invariance appears to be broken by hand by the Higgs potential. Why? Conformal invariance is really fundamental as all two-dimensional theories enjoy it. A typical conformal theory is string theory and we can build up all our supersymmetric models with such a property then broken down by whatever mechanism. Any conceivable more fundamental theory has conformal invariance and we would like this to be there also in the low-energy limit with a proper mechanism to break it. But not by hand.

Finally, we observe that all our theories seem to be really lucky: the coupling is always small and we can work out small perturbation theory. Also strong interactions, at high energies, become weakly interacting. In their papers, Gian Giudice et al. are able to show that the self-interaction of the Higgs potential is seen to decrease at higher energies and so, they satisfactorily apply perturbation theory. Indeed, they show that there will be an energy for which this coupling is zero and is due to change sign. As they work at high energies, the form of their potential just contains a quartic term. My question here is rather peculiar: What if exist exact solutions for finite (non-zero) quartic coupling that go like the inverse power of the coupling? We were not able to recover them with perturbation theory  but nature could have sat there. So, we would need to properly do perturbation theory around them to do the right physics. I have given some of there here and here but one cannot exclude that others exist. This also means that the mechanism of symmetry breaking can hide some surprises and the matter could not be completely settled. Never heard of breaking a symmetry by a zero mode?

So, maybe it is not our universe on the verge of showing a dangerous life but rather some of our views need a revision or a better understanding. Only then the next step will be easier to unveil. Let my bet on supersymmetry again.

Living Dangerously

Giuseppe Degrassi, Stefano Di Vita, Joan Elias-Miró, José R. Espinosa, Gian F. Giudice, Gino Isidori, & Alessandro Strumia (2012). Higgs mass and vacuum stability in the Standard Model at NNLO JHEP August 2012, 2012:98 arXiv: 1205.6497v2

Dario Buttazzo, Giuseppe Degrassi, Pier Paolo Giardino, Gian F. Giudice, Filippo Sala, Alberto Salvio, & Alessandro Strumia (2013). Investigating the near-criticality of the Higgs boson arXiv arXiv: 1307.3536v1

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

Marco Frasca (2013). Exact solutions and zero modes in scalar field theory arXiv arXiv: 1310.6630v1


The Witten’s paradox

17/08/2013

ResearchBlogging.org

Edward Witten is one of the greatest living physicists and also ranks high with mathematicians. He set the agenda for theoretical physics in several areas of research. He is mostly known for championing string theory and being one of few people that revolutionized the field. One of his major contributions to supersymmetry has been a deep understanding of its breaking. In a pair of famous papers (here and here) he put the foundations to our current understanding on the way supersymmetry can break and introduced the well-known Witten index. If a supersymmetric theory breaks supersymmetry then its Witten index is 0. This index is generally very difficult to compute and only perturbative or lattice computations can come to rescue. An important conclusion from Witten’s paper is that the well-known Wess-Zumino model in four dimensions does not break supersymmetry. Witten could rigorously justify this conclusion at small coupling but, at that time, an approach for strong coupling was missing and here Maldacena conjecture cannot help. Anyhow, he concluded that this should be true also for a strongly coupled Wess-Zumino model. Checks to this model in such a regime are rare. After I submitted a paper on arxiv last year (see here) I become aware of an attempt using Dyson-Schwinger equations that confirmed Witten conclusions for small coupling (see here). I have had an interesting mail exchange with one of the authors and this seems a promising approach, given authors’ truncation of Dyson-Schwinger hierarchy. Other approaches consider the Wess-Zumino model in two dimensions on the lattice. So, this appears a rather unexplored area , given the difficulties to cope with a strongly coupled theory, and Witten’s words appear like nails on a coffin to this theory.

I have worked out a lot of techniques to cope with strongly coupled theories and everywhere there is a perturbation going to infinity in a differential equation of any kind and so, I applied these ideas also to this famous model of supersymmetry. The idea is to prove that “supersymmetry has inside itself the seeds of its breaking“. The real issue at stake here is a correct understanding of the way supersymmetry breaks and recover in this way models that now appear to be defeated by data from LHC simply because the idea of symmetry breaking must be applied differently.

Of course, I do not aim to present a claim against the beautiful results given by Witten decades ago but just open up an interesting scientific question. So, considering that the Wess-Zumino model is just a theory of two scalar fields coupled to a Majorana spinor, its equations can be treated classically and so solved both for a strong and a weak coupling limit. I did this in a paper of mine (see here) and this paper has been accepted in these days in the Journal of Nonlinear Mathematical Physics as a letter. The classical solutions contradict the expectations giving a surviving of the supersymmetry at small coupling (as expected from Witten index for the quantum theory) while this does not happen for a strong coupling (formal limit of the coupling going to infinity). This is  a paradox, the Witten paradox, because classical solutions seem to break supersymmetry while the quantum theory does not.  So, we are left with a deep question: How is supersymmetry recovered by quantum corrections?

Marco Frasca (2012). Chiral Wess-Zumino model and breaking of supersymmetry arXiv arXiv: 1211.1039v1

A. Bashir, & J. Lorenzo Diaz-Cruz (1999). A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models J.Phys.G25:1797-1805,1999 arXiv: hep-ph/9906360v1

Marco Frasca (2012). Classical solutions of a massless Wess-Zumino model arXiv arXiv: 1212.1822v2


Unbreakable

14/11/2012

Today, at HCP2012, new results on Higgs boson search were made available by CMS and ATLAS. Of course, well aligned with preceding rumors, all in all these appear rather disappointing. Maybe, beyond the increasing agreement with Standard Model expectations, the most delusional result is that the particle announced on July 4th appears to be completely lonely on a desert ranging till almost 1 TeV, at least if one is looking for other Higgs particles behaving Standard Model-like. \tau\tau decay rate is now aligning with expectations even if there is some room for a different outcome. On the other side, both experiments did not update \gamma\gamma findings. The scenario that is emerging from these results is the theorist’s nightmare. Tomorrow, all this will be collected in single talks by CMS and ATLAS speakers.

In a retrospective we could say that people claiming for a prize to discoverers of the Higgs mechanism seem to be vindicated. There appears no sign of supersymmetry that is more and more relinquished in a nowhere land. But, I would like to point out that, if a supersymmetric theory is the right one, there is just one theory to be singled out exploring the parameter space. It is normal in any case to see such a vast epidemic death of theories. It is also possible that theorists should now do a significant effort for new proposals beyond those largely explored in these last thirty years.

Standard Model is even more resembling a perfect theory really unbreakable and mimicking the success of the Maxwell equations put forward 150 years ago.  But we know it must break…

Finally, I would like to conclude this rather fizzling out post by pointing out a rather funny side of this situation. Tommaso Dorigo has a bet on with Gordon Watts and Jacques Distler amounting to $1200 on the non-existence of SUSY partners. This bet has not been payed yet as Distler is claiming there are a lot of “juicy rumors” from CERN and the terms are not fulfilled yet (see comments here).  I do not know what rumors Distler is talking about but, unless CERN is not hiding data (that would appear a rather strange behavior at best), maybe it is time to do a check on who the winner could be.


Breaking of a symmetry: A paper

07/11/2012

ResearchBlogging.org

I have uploaded a paper on arXiv (see here), following my preceding post,  where I show that supersymmetry has inside itself the seeds for the breaking. I consider a Wess-Zumino model without masses (chiral) and I prove that, at lower momenta, it boils down to a Nambu-Jona-Lasinio model so, breaking supersymmetry through a gap equation that has a solution beyond a critical coupling. An essential assumption is that the coupling in the model is not increasingly smaller but rather increasingly greater. So, bosons and fermions get different masses.

This should open up a new way to see at supersymmetric theories that produce by themselves nonlinearities: It is enough to have such nonlinearities growing bigger. In this way, the large number of parameters that seems a need in the Minimal Supersymmetric Standard Model, arising from the introduction by hand of breaking terms, hopefully should reduce significantly.

Finally, I would like to point out a paper by Jamil Hetzel giving a nice introduction to these problematics (see here). This is a master thesis whose content appeared on JHEP.

Marco Frasca (2012). Chiral Wess-Zumino model and breaking of supersymmetry arXiv arXiv: 1211.1039v1

Jamil Hetzel (2012). Probing the supersymmetry breaking mechanism using renormalisation group
invariants arXiv arXiv: 1211.1157v1


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


Today great news!

18/11/2011

ResearchBlogging.org

A couple of fundamental great news, well one is just a rumor, is hitting scientific community today.

Higgs search

At Paris Conference, Gigi Rolandi addressed his talk on combination for LHC and Tevatron. This picture has been waited for a long time since the excellent work of Phil Gibbs at his blog (see here for an account of this). So far, this combination accounted just for a 2.3\ fb^{-1} luminosity and what is obtained is that no excess greater than 2\sigma is observed on all the range starting from 114 GeV to near 600 GeV. I give here, as done by other bloggers, the picture

Now, the most promising region seems to be at high mass but we are always around 2\sigma. The great news here, but it is an uncontrolled rumor, is given at Jester’s blog: Also with 5\ fb^{-1} no excess greater than 2\sigma is seen in the low mass region! Standard model Higgs seems to be ruled out and the physics here is somewhat different. My view is that if it is proven true that such a scalar particle exists and has a high mass, something unacceptable so far for the standard model, also supersymmetry will be proven true (see here).

OPERA

OPERA Collaboration confirmed their measurements on the speed of neutrinos. This is a major breakthrough in physics and a new version of their preprint is appeared on arXiv today (see here).  This will soon be published on JHEP. So, no more discussions whatsoever but the last word is left to other independent measurements. This is really a breaking news for physics and my personal view is that this should represent a first example of a measurement that could have some impact in the area of quantum gravity. For a fine account, as usual, you can read here.

These are the promises for exciting time ahead. Stay tuned!

Update: Dennis Overbye commented on OPERA new results on New York Times (see here). A few comments from reputable scientists are worth reading.

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

The OPERA Collaboraton: T. Adam, N. Agafonova, A. Aleksandrov, O. Altinok, P. Alvarez Sanchez, A. Anokhina, S. Aoki, A. Ariga, T. Ariga, D. Autiero, A. Badertscher, A. Ben Dhahbi, A. Bertolin, C. Bozza, T. Brugière, R. Brugnera, F. Brunet, G. Brunetti, S. Buontempo, B. Carlus, F. Cavanna, A. Cazes, L. Chaussard, M. Chernyavsky, V. Chiarella, A. Chukanov, G. Colosimo, M. Crespi, N. D’Ambrosio, G. De Lellis, M. De Serio, Y. Déclais, P. del Amo Sanchez, F. Di Capua, A. Di Crescenzo, D. Di Ferdinando, N. Di Marco, S. Dmitrievsky, M. Dracos, D. Duchesneau, S. Dusini, J. Ebert, I. Efthymiopoulos, O. Egorov, A. Ereditato, L. S. Esposito, J. Favier, T. Ferber, R. A. Fini, T. Fukuda, A. Garfagnini, G. Giacomelli, M. Giorgini, M. Giovannozzi, C. Girerd, J. Goldberg, C. Göllnitz, D. Golubkov, L. Goncharov, Y. Gornushkin, G. Grella, F. Grianti, E. Gschwendtner, C. Guerin, A. M. Guler, C. Gustavino, C. Hagner, K. Hamada, T. Hara, M. Hierholzer, A. Hollnagel, M. Ieva, H. Ishida, K. Ishiguro, K. Jakovcic, C. Jollet, M. Jones, F. Juget, M. Kamiscioglu, J. Kawada, S. H. Kim, M. Kimura, E. Kiritsis, N. Kitagawa, B. Klicek, J. Knuesel, K. Kodama, M. Komatsu, U. Kose, I. Kreslo, C. Lazzaro, J. Lenkeit, A. Ljubicic, A. Longhin, A. Malgin, G. Mandrioli, J. Marteau, T. Matsuo, N. Mauri, A. Mazzoni, E. Medinaceli, F. Meisel, A. Meregaglia, P. Migliozzi, S. Mikado, D. Missiaen, K. Morishima, U. Moser, M. T. Muciaccia, N. Naganawa, T. Naka, M. Nakamura, T. Nakano, Y. Nakatsuka, V. Nikitina, F. Nitti, S. Ogawa, N. Okateva, A. Olchevsky, O. Palamara, A. Paoloni, B. D. Park, I. G. Park, A. Pastore, L. Patrizii, E. Pennacchio, H. Pessard, C. Pistillo, N. Polukhina, M. Pozzato, K. Pretzl, F. Pupilli, R. Rescigno, F. Riguzzi, T. Roganova, H. Rokujo, G. Rosa, I. Rostovtseva, A. Rubbia, A. Russo, O. Sato, Y. Sato, J. Schuler, L. Scotto Lavina, J. Serrano, A. Sheshukov, H. Shibuya, G. Shoziyoev, S. Simone, M. Sioli, C. Sirignano, G. Sirri, J. S. Song, M. Spinetti, L. Stanco, N. Starkov, S. Stellacci, M. Stipcevic, T. Strauss, S. Takahashi, M. Tenti, F. Terranova, I. Tezuka, V. Tioukov, P. Tolun, N. T. Tran, S. Tufanli, P. Vilain, M. Vladimirov, L. Votano, J. -L. Vuilleumier, G. Wilquet, B. Wonsak, J. Wurtz, C. S. Yoon, J. Yoshida, Y. Zaitsev, S. Zemskova, & A. Zghiche (2011). Measurement of the neutrino velocity with the OPERA detector in the CNGS beam arXiv arXiv: 1109.4897v2


Back to Earth

01/03/2011

ResearchBlogging.org

Nature publishes, in the last issue, an article about SUSY and LHC (see here).  The question is really simple to state. SUSY (SUperSYmmetry) is a solution to some problems that plagued physics for some time. An important question is the Higgs particle. In order to have the Standard Model properly working, one needs to fine tune the Higgs mass. SUSY, at the price to double all the existing particles, removes this need. But this can be obtained only if a finite parameter space of the theory is considered. This parameter space is what is explored at accelerator facilities like Tevatron and LHC. Tevatron was not able to uncover any SUSY partner for the known particles restricting it. Of course, with LHC opportunities are much larger and, with the recent papers by ATLAS and CMS, the parameter space has become dangerously smaller making somehow more difficult to remove fine tuning for the Higgs mass without fine tuning of the parameters of the SUSY, a paradoxical situation that can be avoided just forgetting about supersymmetry.

But, as often discussed in this blog, there is another way out saving both Higgs and supersymmetry. All the analysis carried out so far about Higgs field are from small perturbation theory and small couplings: This is the only technique known so far to manage a quantum field theory. If the coupling of the Higgs field is large, the way mass generation could happen is different being with a Schwinger-like mechanism. This imposes supersymmetry on all the particles in the model. This was discussed here. But in this way there is no parameter space to be constrainted for fine tuning to be avoided and this is a nice result indeed.

Of course, situation is not so dramatic yet and there is other work to be carried on at CERN, at least till the end of 2012, to say that SUSY is ruled out. Since then, it is already clear to everybody that exciting time are ahead us.

The ATLAS Collaboration (2011). Search for supersymmetry using final states with one lepton, jets, and missing transverse momentum with the ATLAS detector in sqrt{s} = 7 TeV pp
arxiv arXiv: 1102.2357v1

CMS Collaboration (2011). Search for Supersymmetry in pp Collisions at 7 TeV in Events with Jets
and Missing Transverse Energy arxiv arXiv: 1101.1628v1

The ATLAS Collaboration (2011). Search for squarks and gluinos using final states with jets and missing
transverse momentum with the ATLAS detector in sqrt(s) = 7 TeV proton-proton
collisions arxiv arXiv: 1102.5290v1

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


Yang-Mills and string theory

09/12/2010

As I pointed out in a recent post, the question of the mass gap for Yang-Mills theory should be considered settled. This implies an understanding of the way mass arises in our world. It is seen that mass is a derived concept and not a fundamental one. I have given an explanation of this here. In a Yang-Mills theory, massive excitations appear due to the presence of a finite nonlinearity. The same effect is seen for a massless quartic scalar field and, indeed, these fields map each other at a classical level. It is interesting to note that a perturbation series with a coupling going to zero can miss this conclusion and we need a dual perturbation with the coupling going to infinity to uncover it. The question we would like to ask here is: What does all this mean for string theory?

As we know, string theory has been claimed not to have any single proposal for an experimental verification. But, of course, without entering into a neverending discussion, there are some important points that could give strong support to the view string theory entails. Indeed, so far there are two essential points that research on string theory produced and that should be confirmed as soon as possible: AdS/CFT correspondence and supersymmetry. Both these theoretical results are strongly supported by the research pursued by our community. For the first point, understanding of QCD spectrum, with or without quarks, through the use of AdS/CFT correspondence is a very active field of research with satisfactory results. I have discussed here this matter several times and I have pointed out the very good work of Stan Brodsky and Guy de Teramond as an example for this kind of research (e.g. see this). Soft-wall model discussed by these authors seems in a very good agreement with the current scenario that is arisen in our understanding of Yang-Mills theory that I emphasized several times in this blog.

About supersymmetry I should say that I am at the forefront since I have presented this paper. The mass gap obtained in Yang-Mills theory arising from nonlinearities has an interesting effect when considered for the quartic scalar field interecting with a gauge field and spinor fields. Taking a coupling for the self-interaction of the scalar field being very large, all the conditions for supersymmetry are fulfilled and all the interacting fields get identical masses and coupling. This implies that, if the mechanism that produces mass in QCD and Standard Model is the same, the Higgs field must be supersymmetric. I call this field Higgs, notwithstanding it has lost some important characteristics of a Higgs field, because is again a scalar field inducing masses to the other fields interacting with it. So, if current experiments should confirm this scenario this would be a big hit for physics ending with a complete understanding of the way mass arises in our world both for the macroscopic and the microscopic world.

So, we can conclude that our research area is producing some relevant conclusions that could address research in more fundamental areas as quantum gravity in a well-defined direction. I think we will get some great news in the near future. As for the present, I am happy to have given an important contribution to this research line.


Mass generation and supersymmetry

30/07/2010

I have uploaded a paper on arxiv with a new theorem of mine. I have already exposed the idea in this blog but, so far, I have had no much time to make it mathematically sound.  The point is that the mechanism I have found that gives mass to Yang-Mills and scalar fields implies supersymmetry. That is, if I try to apply it to the simplest gauge theory, in a limit of a strong self-interaction of a massless Higgs field, all the fields entering into the theory acquire identical masses  and the couplings settle down to the proper values for a supersymmetric model. Being this result so striking, I was forced to produce a theorem at the classical level, as generally done with the standard Higgs mechanism, and let it widely known. My next step is to improve the presentation and extend this result after a fully quantum treatment. This is possible as I have already shown in the case of a Yang-Mills theory.

My view is that just a mechanism could be seen in Nature to produce masses and I expect that this is the same already seen for QCD. So, supersymmetry is mandatory. This will imply a further effort for people at work to uncover Higgs particle as they should also say to us what kind of self-interaction is in action here and if it is a supersymmetric particle, as it should.

The interesting point is that all the burden of the spectrum of the standard model will rely, not on the mechanism that generates masses but on the part of the model that breaks supersymmetry.

Interesting developments are expected in the future. Higgs is always Higgs but a rather symmetric one. So, stay tuned!


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