Farewell to Reality (28 page)

The MSSM resolves this problem, too. The effects of interactions with virtual sparticles change the extrapolation such that the strengths of the forces smoothly converge on a near—single point, as shown in Figure 7(b). This is much more like it. Now the extrapolation is strongly suggestive of a time and an energy regime where a single electro-nuclear force dominated.

If we are prepared to draw conclusions from such calculations, then it does seem that something significant is missing from the standard model, and that something could be SUSY.

SUSY, the LSP and the problem of dark matter

The problem of dark matter demands a solution that lies beyond the current standard model of particle physics. By definition, dark matter must consist of a particle or particles that are not to be found among the known families of quarks, leptons and force carriers. Dark matter candidates can only be found among new particles predicted by theories that extend the standard model in some way.

It probably won't come as much of a surprise to learn that SUSY predicts the existence of particles with precisely the right kinds of properties.

Figure 7
(a) Extrapolating the strengths of the forces in the standard model of particle physics implies an energy (and a time after the big bang) at which the forces have the same strength and are unified. However, the forces do not quite converge on a single point. (b) In the Minimum Supersymmetric Standard Model (MSSM) the additional quantum fields change this extrapolation, and the forces more nearly converge.

Remember, there is a category of candidate for cold dark matter particles known as WIMPs. These are neutrino-like (neutral, not subject to the strong force or electromagnetism) but much, much heavier. By design, the MSSM predicts superpartners that must be heavy (as they haven't been observed yet) and several of these are neutral. To take an example, the photino — the heavy superpartner of the photon — readily fits the bill.

But many potential candidate superpartners are believed to be relatively unstable. They will decay rapidly into other sparticles. We can conclude, with some sense of justification, that the cold dark matter responsible for governing the shapes, structures and rotation speeds of whole galaxies is likely to be much more enduring than this. The attentions of theorists have therefore turned to the sparticle most likely to lie at the end of the chain of decays. This is referred to as the Lightest Superpartner, or LSP. Simply put, once the sparticles have decayed into the LSP, there's nowhere else for it to go. The LSP is stable.

Now, the
neutralino
is not, as might first be thought, the superpartner of the neutrino.
^*
In the MSSM, neutralinos are formed through the quantum superposition of the zino, the photino and a couple of electrically neutral Higgsinos. This mixing occurs because these particles have similar properties (such as charge and spin), and there is an unwritten law in quantum theory that if particles with mass cannot be distinguished by their other quantum properties, then they are likely to suffer an identity crisis and combine in a superposition. The mixing produces four neutralino states, the lightest of which is a candidate for the LSP and therefore a candidate WIMP.

Calculations suggest that if the MSSM is right and neutralinos do exist, then their ‘relic density' — the density of neutralinos left over after the big bang — is consistent with the observed density of cold dark matter in the ACDM model.

Supergravity

It does seem as though we're getting quite a lot in return for our willingness to suspend disbelief and embrace the idea of heavy
superpartners. We solve the hierarchy problem. We enable convergence between the fundamental forces that operate at atomic and subatomic levels. We gain some candidates for cold dark matter particles.

There is yet more.

In SUSY, a spacetime symmetry transformation acting on a fermion or boson changes the spin of the particle by ½. Fermions become sfermions, with spin zero. Bosons become bosinos, with spin ½. This kind of change affects the spacetime properties of the particle that is transformed, such that it is slightly displaced.
^*
Conventional standard model forces such as electromagnetism cannot displace particles in this way. They can change the direction of motion, momentum and energy of the particle but they cannot displace it in spacetime. In fact, this displacement is equivalent to a transformation characteristic of the
gravitational
force.

It is possible to conceive a supersymmetry theory that is also therefore a theory of gravity. This is actually quite remarkable. The standard model itself does not accommodate gravity at all, and attempts to create a quantum field theory of gravity have led to little more than a hundred years of frustration. By extending the standard model to include supersymmetry, it seems that we open the door to gravity.

Such theories are collectively called
supergravity.
They introduce the gravitino, the superpartner of the graviton, the notional force carrier of quantum gravitation. It seems that supersymmetry not only offers the promise of illuminating the path to a grand unified theory, but may also be a key ingredient in any theory purporting to be a theory of everything.

One of the first theories of supergravity was developed in 1976 by American Daniel Freedman, Dutch physicist Peter van Nieuwenhuizen and Italian Sergio Ferrara. They discovered that some of the problems associated with renormalizing a quantum field theory of gravity were somewhat relieved if supersymmetry was assumed. It seemed that the contributions from terms in the equations that had mushroomed to infinity could be partly offset by terms derived from the gravitino. There was indeed some cancellation, but the problem didn't go away completely.

For a relatively short time, excitement built up around a version of supergravity based on eight different kinds of supersymmetry. Such theories include not only the particles of the standard model and their superpartners, but many others as well. But these theories could not be renormalized, and by 1984, interest in them was waning.

The reality check

Obviously, SUSY has a lot going for it, and many contemporary theoretical physicists are convinced that nature must be supersymmetric. Of course, the theory will stand or fall on whether or not sparticles are observed in high-energy particle collisions, or supersymmetric WIMPs are detected.

The big problem with SUSY is that the supersymmetry must be broken, and it is not at all obvious how this is supposed to happen. Using a Higgs-like mechanism which ties symmetry-breaking to a real scalar field and a real scalar boson gives incorrect particle masses. Mechanisms for ‘soft' supersymmetry-breaking have been devised, but these tend to introduce yet more fields and yet more particles.

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: