by Jim Baggott
This is a bit of a nightmare. As Columbia University mathematical physicist Peter Woit puts it:
Since one doesn’t understand the supersymmetry breaking, to define the MSSM one must include not only an unobserved super-partner for each known particle, but also all possible terms that could arise from any kind of supersymmetry breaking. The end result is that the MSSM has at least 105 extra undetermined parameters that were not in the standard model. Instead of helping to understand some of the eighteen experimentally known but undetermined parameters of the standard model, the use of supersymmetry has added in 105 more.8
With so many parameters undetermined by the theory, it becomes impossible to use it to make any predictions. So, there are no real predictions for the masses of the sparticles, for example, other than that some must lie in the range from a few hundred up to a thousand GeV in order to provide a natural fix for the hierarchy problem. As we have seen, there is much riding on the role of the LSP as a candidate dark matter particle, but no SUSY theorist can tell you the identity of the LSP.
I’m afraid there’s more. Whenever we establish symmetry relationships between particles, there is always the risk that we get more than we bargained for. Specifically, identities that appear from experiment to be conserved (and, whether by default or not, are conserved in the standard model) become transient. The seemingly impossible becomes possible. And this is the case in SUSY.
As far as we can tell, a muon cannot decay into an electron and a photon. This transformation is not forbidden on energy grounds, but it simply does not happen — it is a process that has never been observed in an accelerator or particle collider. In the context of the standard model, this kind of fact is rationalized in terms of the conservation of muon and electron number. We assign a muon (or electron) a muon (electron) number of +1. The anti-muon (positron) is assigned a muon (electron) number of -1. In particle collisions involving muons and electrons we find that muon or electron number is conserved. The total numbers of muons and electrons coming out of such a collision are the same as the numbers of muons and electrons going in.
This situation is maintained in SUSY, until we break the supersymmetry. The large masses of smuons and selectrons cause their identities to blur somewhat, and interactions between muons and electrons and smuons and selectrons can provide a convoluted path in which a muon transforms into an electron. In other words, in a broken SUSY theory, transformations become possible which are not observed experimentally.
There are other problems which need not detain us. It is sufficient at this stage for us to note that SUSY has some uncomfortable consequences. For every standard model problem that it resolves, another problem arises that needs a fix.
Of course, the promise of SUSY is that it provides an important stepping stone on the path towards grand unification. And indeed, a supersymmetric SU(5) theory of the subatomic forces predicts rates of proton decay much more in line with observation. But yet again we get more than we bargained for. A supersymmetric GUT requires a pair of Higgs particles associated with the SU(2) component of the broken theory. It also requires a triplet of colour Higgs particles associated with SU(3). Now, in order to be consistent with our experience of the forces involved, the masses of the Higgs doublet must come out relatively small (about 100 GeV), consistent with the electro-weak energy scale. But the Higgs triplet must have large masses, consistent with the energy scale of grand unification.
There is no obvious way to fix the mass difference of the Higgs doublet and Higgs triplet naturally from within the theory. But if it isn’t fixed, the Higgs triplet can mediate proton decay and we’re back at square one: with protons decaying faster than we observe. This is generally known as the doublet—triplet splitting problem.
It is the hierarchy problem all over again.
Weighing the evidence
So, where do we stand? There can be little doubting the value of SUSY in terms of the logic of the approach and its promised resolution of some of the fundamental problems of the standard model. Our reality check may cause us some discomfort, but nobody ever said this was going to be easy.
Is nature supersymmetric? Of course, our seemingly protracted debates are immediately ended the moment we find unambiguous evidence for sparticles. Gordon Kane again:
If the superpartners are found, it will confirm that supersymmetry is part of our description of nature. If superpartners are not observed, it will show that nature is not supersymmetric.9
Now, it would be asking too much of a theory with 105 additional parameters to come up with hard-and-fast predictions for the masses of the sparticles, but it’s enough for us to know that at least some of them should have masses of the order of hundreds of GeV. The theory stands or falls on its prediction of sparticles, at whatever masses they can be shown to possess. For this reason, although generally sceptical, I tend to regard SUSY as a legitimate theory of physics. It is at least testable, in the sense of the Testability Principle, although it does have a fairy-tale tendency, as we will see.
Kane’s book on supersymmetry from which I have quoted was published in 2000, and at this time there were plenty of reasons for optimism. The lighter sparticles were thought to be in range of CERN’s Large Electron-Positron (LEP) Collider and Fermilab’s Tevatron. If these colliders came up empty, there was the promise of the LHC, CERN’s successor to the LEP, which would be designed to achieve total proton—proton collision energies of 14 TeV.
This sounds perfect, but don’t be misled. Not all of the headline collision energy can be utilized. Protons consist of quarks and gluons, and the energy of a 7 TeV proton travelling very near the speed of light around a collider is distributed over these components. Proton—proton collisions are actually quark—quark, gluon—gluon or quark—gluon collisions, and the energies of these can be a lot less than the headline collision energy.
Nevertheless, when the LEP and the Tevatron did indeed come up empty, the LHC became the gaming house in which the SUSY gamble would either pay out, or not. American theorist Lisa Randall put it this way:
… if supersymmetry solves the hierarchy problem, it will be an experimental windfall. A particle accelerator that explores energies of about a TeV (1,000 GeV) will find, in addition to the Higgs particle, a host of supersymmetric partners of standard model particles. We should see gluinos and squarks, as well as sleptons, winos … a zino and a photino … With sufficient energy, these particles would be hard to miss. If supersymmetry is right, we will soon see it confirmed.10
It’s a simple fact that in order for the stop (meaning the stop squark) to stabilize the Higgs mass and provide a natural resolution of the hierarchy problem, it would need to possess a mass not very different from the electro-weak energy scale — a few hundred GeV. This is well within the range of the LHC, even though, at the time of writing (July 2012), the collider had not yet reached its design collision energy of 14 TeV.
If they exist, there are several ways in which stop squarks might be produced in proton—proton collisions in the LHC. They can in theory be produced directly from proton—proton (actually, gluon—gluon) collisions, but the rate of production by this route is thought to be rather limited. A more productive route is possible indirectly via gluinos. A proton—proton collision produces two gluinos, each of which goes on to decay into a top—stop pair.
According to the MSSM, the stop is expected ultimately to decay into a top quark plus the LSP. So, if the collision produces two gluinos, these decay first into two top quarks and two stop squarks and the two stops decay further to give two more top quarks and two LSPs. The end result is a collision producing four top quarks and lots of ‘missing’ energy, as the LSP behaves like a neutrino and escapes undetected. There are few standard model processes that can give rise to four top quarks, so this gluino-mediated route is an attractive candidate in the search for the stop, as there should be little contribution from ‘background’ processes.
Alternatively, the stop could decay into a W particle and a sbottom squark, with the sbott
om going on to decay into a bottom quark plus the LSP. Irrespective of the actual decay paths, the end result is a number of top and/or bottom quarks, and lots of missing energy.
From the beginnings of proton physics at the LHC in March 2010, the principal focus of attention for the two general-purpose detector collaborations, ATLAS and CMS, has been the search for the Higgs boson. Nevertheless, both collaborations have periodically reported on the search for sparticles and other kinds of’new physics’. In all cases, no significant excess of events over and above the expected background from standard model processes has been observed.
Absence of evidence cannot necessarily be taken in this case as evidence of absence. At the time of writing, both ATLAS and CMS have yet to analyse all the data gathered from some 350 trillion 7 TeV proton—proton collisions in 2011 and substantially more data at 8 TeV gathered in 2012. However, the signs are not good. The data that have been analysed are not producing the telltale signatures of stop or sbottom squarks, and exclusion limits are being pushed to higher and higher mass ranges. The exclusion limits are starting to become incompatible with a natural resolution of the hierarchy problem.
It is looking increasingly likely that the gamble will be lost. And soon.
The search for WIMPs
Where does this leave us on the question of dark matter? Of course, if nature turns out not to be supersymmetric, then there is no LSP and no SUSY dark matter candidate. This does not mean that there are no WIMPs, however. If we could ever identify a WIMP, its properties might give us important clues to the nature of physics beyond the standard model.
Physicists need relatively little motivation to start a search if the technology (and, more importantly, the funding) is available to support it. The Cryogenic Dark Matter Search (CDMS) experiment is located half a mile underground at the Soudan mine in northern Minnesota. It consists of thirty detectors cooled to temperatures very near absolute zero. Signals generated by a particle interacting inside one of the detectors allow the experimenters to tell whether this is a conventional standard model particle or a WIMP.
On 17 December 2009, the CDMS collaboration announced that it had found just two decay events that were potential candidates involving WIMPs. Two events are insufficient to discriminate positive results from false positives, and further results released in 2011 showed no evidence for WIMPs with a mass below 9 GeV.
A search by the XENON100 experiment at the Gran Sasso National Laboratory in Italy reported similar results in April 2011. This experiment looks for telltale signals from WIMPs interacting with liquid xenon. Data gathered from 100 days of operation between January and June 2010 turned up three candidate events. This would sound promising were it not for the fact that the number of background events (false positives) in this period was predicted to be nearly two.
On 18 July 2012, the XENON100 experiment reported the results of a further 225 days of data-taking during 2011 and 2012, with even higher instrument sensitivity. Once again, the two observed candidate WIMP events could not be distinguished from the background (predicted to be one event). Instead, the experiment was able to extend the mass range for which WIMPs can be confidently excluded, pushing the hypothetical particles up to higher and higher masses.
It seems we cannot look to WIMPs to provide us with guidance just yet.
The end of SUSY?
It is a mistake to think that scientific progress is driven solely on the basis of scientific evidence. Theorists who have become enamoured of a particular theoretical structure may argue in its favour long after unambiguous evidence against it has been published and broadly accepted. In his famous dissection of the structure of scientific revolutions, Thomas Kuhn drew analogies with the process and aftermath of political revolution. Long after a revolution has sealed the fate of a failed political system, it will always be possible to find dissidents who will argue that things were better in the ‘old days’.
It is this attitude among some theorists that is beginning to edge SUSY in the direction of fairy-tale physics. Instead of accepting the evidence at face value and acknowledging that nature might not, after all, be supersymmetric, they work to develop alternative interpretations or extensions to the theory which explain why the absence of light sparticles and WIMPs is not inconsistent.
For example, split supersymmetry, first proposed in 2003, pushes the sparticle masses to higher energies, above a TeV, and so out of reach of our ability to detect them at the LHC. In this form, SUSY is spared the embarrassment of failing the current experimental tests by making the tests no longer relevant. But in relaxing the requirements of ‘naturalness’, such theories no longer provide a solution to the hierarchy problem.
There is obviously a limit to the number of times that theorists can play this game. But such argumentation doesn’t necessarily end even when the evidence is overwhelming. I’ve been struck by the enduring popularity of Fritjof Capra’s book The Tao of Physics, which still makes an occasional appearance on the shelves of my local bookstore 37 years after it was first published.
The Tao of Physics extols the virtues of the ‘bootstrap’ theory, which was very popular in the 1960s. This theory argued in favour of a kind of ‘nuclear democracy’, in which there are no ‘elementary’ particles as such. Instead, all of the particles known to physicists are supposedly formed from combinations of each other. This model quickly went out of fashion when evidence for quarks — the ‘elementary’ constituents of protons, neutrons and mesons — began to emerge in the late 1960s.
Despite the fact that the theory has long since ceased to be regarded as having anything to do with the current version of reality, it appears there is still a readership for a popular book about it. No doubt this has something to do with the parallels that Capra draws between the bootstrap theory and aspects of Eastern religious philosophies.
Is this the ultimate fate of SUSY? It is perhaps a little too early to tell, but further proton—proton collision data collected at the LHC in 2012 should in principle prove decisive. My belief is that many theorists will continue to declare that the writing of obituaries for SUSY is premature, finding ever more convoluted and elaborate ways of keeping the theory alive. Like Darth Vader’s journey to the dark side, SUSY’s journey to fairy-tale physics will then be complete.
There is a simple reason for this: there is now far too much at stake. The post-standard model structure that has dominated theoretical particle physics for more than thirty years is, of course, superstring theory.
And what, precisely, is it that makes superstrings ‘super’?
SUSY, of course.
* They should not be confused with the predictions of theories such as superstring theory (which we will examine in the next chapter), which suggest that there are more spacetime dimensions than the four with which we are already familiar.
* Strictly speaking, SU(5) is 15—dimensional, but acts on a complex 5—dimensional space …
* I actually can’t write such words without hearing Star Trek’s McCoy in my head: ‘It’s life, Jim, but not as we know it.’
** To illustrate what this means, suppose the probability of proton decay is 1 per cent (it is actually much, much smaller than this). We re—write 1 per cent as 0.01 and raise this to the fourth power: 0.014 = 0.01 × 0.01 × 0.01 × 0.01 = 0.00000001, which is a million times smaller than 1 per cent.
* Each water molecule — H2O — contains 18 protons, 16 in the oxygen atom nucleus and one in each of the two hydrogen nuclei.
** Readers concerned that such elaborate (and, no doubt, expensive) facilities appear to have been dedicated to an ultimately fruitless search should draw some comfort from the fact that they are also engaged in other experiments. For example, Super—Kamiokande is an exquisite neutrino observatory and has contributed precise measurements of neutrino oscillation.
* As is typical, the history is a little more complicated than this, with several theorists discovering and then rediscovering the basic principles.
* Yet again, t
he historical development of the MSSM is more complicated that this simple statement implies. See http://cerncourier.eom/cws/article/28388/2 for more details. Thanks to Peter Woit for bringing this article to my attention.
* Pronounced ‘weenos’. Presumably to avoid confusion.
* White ambassardinos of morning?
* In fact, to make this mechanism work, the MSSM actually needs five Higgs particles, each with a different mass. Three of these are neutral and two carry electric charge.
* The super—partners of neutrinos are sneutnnos.
* Actually, a supersymmetry transformation is equivalent to the square root of an infinitesimal translation in space.
8
In the Cemetery of Disappointed Hopes
Superstrings, M-theory and the Search for the Theory of Everything
I’m still working, passionately, though most of my intellectual off-spring are ending up prematurely in the cemetery of disappointed hopes.
Albert Einstein1
Soon after his triumphant presentation of the general theory of relativity to the Prussian Academy of Sciences in 1915, Einstein began searching for a way to unify gravity and electromagnetism. At this stage the quantum was much more than a hypothesis but it was not yet a fully fledged theory. The development of quantum theory still awaited the intellectual energies of Bohr, Heisenberg, Pauli, Schrödinger, Dirac and Born, and many others.
And yet Einstein was already acknowledging that such a unification would require that the general theory of relativity should somehow be ‘reconciled’ with quantum theory.
In truth, as the discomforting consequences of quantum theory began to emerge, bringing problems such as quantum probability, the collapse of the wavefunction and ‘spooky’ action-at-a-distance, Einstein came to believe that a proper unified theory would actually serve to eliminate these problems, a belief that would shape the nature of his intellectual pursuit over the later stages of his life. This despite the fact that experimental science of the 1930s and 1940s established beyond any real doubt the supremacy of the quantum and the importance of two further forces — the strong and weak nuclear forces — which would need to be accommodated in any theory purporting to be a unified theory of everything.