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Did the LHC rule out SUSY as a solution to the hierarchy problem ? What's the common belief among theorists regarding the possibility of discovering SUSY in the 2015 run of the LHC ? Did the absence of a SUSY signal so far depress the enthusiasm that SUSY is an important element of our universe ?

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Related: physics.stackexchange.com/q/6438/2451 –  Qmechanic Jun 30 '13 at 11:57
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A comment on the use of the past tense here. Unless something goes dreadfully wrong the LHC can be expected to run (in the on again off again cycle that accelerators use) for at least a decade. Probably longer. The previous record holder in this game (the Tevatron at Fermilab) ran for thirty years. The fact that some physics goal has not yet been met doesn't say much about the final reach of the machine. –  dmckee Jun 30 '13 at 13:03
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Well, I am a retired particle physics experimentalist. This means I remember the evolutions of experiments and the extensions of theories from the beginning 60's, when the eightfold way was the fashion.

When the J/Psi was discovered everybody "fell from the clouds" as we say in greek ( I suppose cloud cuckoo land in english). Nobody but nobody had expected it to be so narrow.

When QCD was mooted the great Feynman himself was skeptical , being partial to his parton model.

As for theories? The Regge poles that dominated hadronic physics of the seventies and fell out of fashion with QCD and all, are having a comeback with string theories.

So my experience tells me that nothing is decided yet. It could be possible that even with the existing data at LHC a clever young physicist will unscramble resonances that are being thrown out with the bathwater of such large backgrounds. Certainly I would wait for the next data crop from the LHC before thinking that super symmetry manifestation has to be pushed to higher energies. My experience also tells me that theoreticians are quite adept at this last.

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Let me try to answer your questions. Your first question relates to naturalness/the big hierarchy problem:

Why is the Planck scale $(\sim10^{19}\,\text{GeV})$ so much larger than the electroweak scale $(\sim10^{2}\,\text{GeV})$?

Even with supersymmetry, we don't know the answer. This hierarchy is pathological in the Standard Model. Our electroweak scale is dragged to the Planck scale by quadratic quantum corrections. For the electroweak scale to be as we see (with quantum corrections), it's bare value (without quantum corrections) must be extraordinarily fine-tuned.

Supersymmetry can solve this problem, because the quadratic quantum corrections sum to zero. There are residual logarithmic corrections, because supersymmetry must be broken. The null results of LHC searches for supersymmetry and the Higgs mass $m_H\sim125\,\text{GeV}$ mean that that the supersymmetry breaking scale must be $\gtrsim10^3\,\text{GeV}$. Even with quantum corrections at this scale, which is slightly higher than the electroweak scale, the big hierarchy problem is solved. We're fine-tuning numbers of order $10^2\,\text{GeV}$ and $10^3\,\text{GeV}$, which is nothing compared to fine-tuning with the Planck scale. Though, of course, the breaking scale shouldn't be much much bigger than the electroweak scale.

That's not the end of the story though. Whilst supersymmetry closes the big hierachy between the Planck and the electroweak scales, it opens a little hierarchy between the electroweak and supersymmetry breaking scales. This hierarchy is far less severe, because there are no quadratic corrections to either scale, but is still somewhat fine-tuned and puzzling. This little hierachy bugs theorists, and it has done since LEP some 15 years ago.

Are we optimistic about finding SUSY in LHC Run II?

Hopeful, I'd say, but not very optimistic. Though some theorists consider a light Higgs to be evidence for supersymmetry, because a light Higgs is a robust prediction in most supersymmetry models.

Has absence of supersymmetry depressed the enthusiasm that SUSY is an important element of our universe?

No, I wouldn't say so. It's still the best solution to a lot of problems, of exprimental and technical nature, including the big hierarchy. I would say that people are less sure about the supersymmetry breaking scale, and the form of supersymmetry.

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I am not an expert on this subject, but check out this article, which is about a physicist who put a bet of one thousand dollars on not finding SUSY.

Relevant to the article above, is also this blog.

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As he explains for example here, Lubos Motl has a still running bet against Jester (the author of the quite nice physics blog Resonaances) saying that he will obtain 10000 dollars if the LHC discovers SUSY in the first 30 inverse femtobarns of data accumulated, whereas he has to pay only 1000 dollars if this is not the case. This 100:1 bet means that Lumo estimates the propability of finding SUSY in the mentioned amount of data to be larger than 1%.

Since this amount of data has not yet been accumulated, the bet is indeed about the early 2015 run of the LHC. Due to the inicrease of the collision energy in 2015 to 13 TeV, new particles that are not easy to descover for the LHC when running at 8 TeV, could quickly be found in the first data of the 13 TeV run, so Lubos consinders his position in this 100:1 bet as still comfortable and the probability to detect SUSY (early in) 2015 to be still larger than 1 %.

As mentioned in the same TRF article too, Jaques Distler was less lucky with his bet against Tommaso Dorigo, which was only about the first 10 inverse femtobarns of data.

But as you can see, some bets about the 2015 run are still open ... so stay tuned ;-)

PS: The absence of convincing SUSY signals in the data so far does not depress rational and scientific thinking people, who know that SUSY may still be an important part of the laws of nature describing our universe, even if it were broken at much larger than the LHC accessible energy scales.

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@Downvoter what is wrong with this answer? Could you please point out the mistake from a phyics point of view? Votes on the main page of Physics SE should, conversely to meta, not be misused to disagreement for personal opinion but to point out errors in the physics and facilitate an improvement. –  Dilaton Jul 16 '13 at 13:45
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