## Back to Earth

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

### 2 Responses to Back to Earth

1. X says:

I’m sure you well know that perturbation theory is not “the only technique known so far to manage a quantum field theory”. What a peculiar thing to say!

• mfrasca says:

Hi X,

Well, this is a matter I discussed widely here and elsewhere. The point is that whatever we are going to make, also when we talk about non-perturbative techniques like renormalization group, it is modeled on small perturbation theory. Indeed, all the difficulties we meet to answer to questions like: Is $\phi^4$ theory trivial in four dimensions? Has Yang-Mills theory a mass gap in the infrared? originate from our impossibility to manage theories, also classically, with a (bare) coupling increasingly large. Of course, this fact can be seen also for their classical counterparts.

A blatant example of this typical cultural attitude is the Landau pole. Whoever works with perturbation theory is well aware that relying on the first terms of a perturbative series to draw global conclusions on the solutions of an equation is rather dumb, producing all kind of possible mistakes. But, notwithstanding this elementary fact learned from our undergraduate courses, you will find a lot of textbooks on QFT talking about the Landau pole like a deep truth about the theory that seems to possess it.

AdS/CFT is another question and, so far, has not yet a sound mathematical ground. I find really satisfactory that this approach seems to reproduce several of the features seen on the lattice and from other theoretical approaches (let me say like mine). But this technique is not yet in its full maturity like the old fashioned perturbation theory.

So, try an experiment. Take any textbook on QFT, also the most cherished one, and cite to me some pages where the results do not rely somewhere on those got from small perturbation theory. I think you will be disappointed at the end of this to see how much all our culture on QFT is deeply rooted on this method.

I am a supporter of this approach so that I have extended it to the case of very large (bare) coupling ($1/\lambda$ instead than just $\lambda$). Now, I have (published) answers on the aforementioned questions. Have you the same with the methods you claim to already exist?

Cheers,

Marco