Quantum Diaries

This is the last part of a series of three on supersymmetry, the theory many believe could go beyond the Standard Model. First I explained what is the Standard Model and show its limitations. Then I introduced supersymmetry and explained how it would fix the main flaws of the Standard Model. I now review how experimental physicists are trying to discover “superparticles” at the Large Hadron Collider (LHC) at CERN.

If Supersymmetry (or SUSY for short) is as good as it looks, why has none of the new SUSY particles been found yet? There could be many reasons, the simplest being that this theory is wrong and supersymmetric particles do not exist. If that were the case, one would still need another way to fix the Standard Model.

SUSY can still be the right solution if supersymmetric particles have eluded us for some reasons: we might have been looking in the wrong place, or in the wrong way or they could still be out of the reach of current accelerators.

So how does one go looking for supersymmetric particles? One good place to start is at CERN with the Large Hadron Collider or LHC. The 27-km long accelerator is the most powerful in the world. It brings protons into collisions at nearly the speed of light, generating huge amounts of energy in the tiniest points in space.  Since energy and matter are two forms of the same essence, like water and ice, the released energy materializes in the form of fundamental particles. The hope is to create some of the SUSY particles.

One major problem is that nobody knows the mass of all these new particles. And without the mass, it is very much like looking for someone in a large city without knowing the person’s address. All one can do then is comb the city trying to spot that person. But imagine the task if you don’t even know what the person looks like, how she behaves or even in which city, let alone which country she lives in.

Supersymmetry is in fact a very loosely defined theory with a huge number of free parameters. These free parameters are quantities like the masses of the supersymmetric particles, or their couplings, i.e. quantities defining how often they will decay into other particles. Supersymmetry does not specify which value all these quantities can take.

Hence, theorists have to make educated guesses to reduce the zone where one should search for SUSY particles. This is how various models of supersymmetry have appeared. Each one is an attempt at circumscribing the search zone based on different assumptions.

One common starting point is to assume that a certain property called R-parity is conserved. This leads to a model called Minimal SUSY but this model still has 105 free parameters. But with this simple assumption, one SUSY particle ends up having the characteristics of dark matter. Here is how it works: R-parity conservation states that all supersymmetric particles must decay into other, lighter supersymmetric particles. Therefore, the lightest supersymmetric particle or LSP cannot decay into anything else. It remains stable and lives forever, just like dark matter particles do. Hence the LSP could be the much sought-after dark matter particle.

Credit: Fermilab

How can the Large Hadron Collider help? Around the accelerator, large detectors act like giant cameras, recording how the newly created and highly unstable particles break apart like miniature fireworks. By taking a snapshot of it, one can record the origin, direction and energy of each fragment and reconstruct the initial particle.

Heavy and unstable SUSY particles would decay in cascade, producing various Standard Model particles along the way. The LSP would be the last possible step for any decay chain. Generally, the LSP is one of the mixed SUSY states with no electric charge called neutralino. Hence, each of these events contains a particle that is stable but does not interact with our detectors. In the end, there would be a certain amount of energy imbalance in all these events, indicating that a particle has escaped the detector without leaving any signal.

At the LHC, both the CMS and ATLAS experiments have searched billions of events looking for such events but to no avail. Dozens of different approaches have been tested and new possibilities are constantly being explored. Each one corresponds to a different hypothesis, but nothing has been found so far.

Two events with jets as seen in the ATLAS detector. (Left) A very common event containing two jets of particles. The event is balanced, all fragments were recorded, no energy is missing. (Right) A simulation of a mono-jet event where a single jet recoils against something unrecorded by the detector. The imbalance in energy could be the signature of a dark matter particle like the lightest supersymmetric particle (LSP), something that carries energy away but does not interact with the detector, i.e. something we would not see.

One reason might be that all supersymmetric particles are too heavy to have been produced by the LHC. A particle can be created only if enough energy is available. You cannot buy something that costs more money than you have in your pocket. To create heavy particles, one needs more energy. It is still possible all SUSY particles exist but were out of the current accelerator reach. This point will be settled in 2015 when the LHC resumes operation at higher energy, going from 8 TeV to at least 13 TeV.

If the SUSY particles are light enough to be created at 13 TeV, the chances of producing them will also be decupled, making them even easier to find. And if we still do not find them, new limits will be reached, which will also greatly help focus on the remaining possible models.

SUSY has not said its last word yet. The chances are good supersymmetric particles will show up when the LHC resumes. And that would be like discovering a whole new continent.

Pauline Gagnon

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This is the second part of a series of three on supersymmetry, the theory many believe could go beyond the Standard Model. First I explained what is the Standard Model and showed its limitations. I now introduce supersymmetry and explain how it would fix the main flaws of the Standard Model. Finally, I will review how experimental physicists are trying to discover “superparticles” at the Large Hadron Collider (LHC) at CERN.

Theorists often have to wait for decades to see their ideas confirmed by experimental findings. This was the case for François Englert, Robert Brout and Peter Higgs whose theory, elaborated in 1964, only got confirmed in 2012 with the discovery of the Higgs boson by the LHC experiments.

Today, many theorists who participated in the elaboration of what is now known as supersymmetry, are waiting to see what the LHC will reveal.

Supersymmetry is a theory that first appeared as a mathematical symmetry in string theory in early 1970s. Over time, several people contributed new elements that eventually led to a theory that is now one of the most promising successors to the Standard Model. Among the pioneers, the names of two Russian theorists, D. V. Volkov and V. P Akulov, stand out. In 1973, Julius Wess and Bruno Zumino wrote the first supersymmetric model in four dimensions, paving the way to future developments. The following year, Pierre Fayet generalized the Brout-Englert-Higgs mechanism to supersymmetry and introduced superpartners of Standard Model particles for the first time.

All this work would have remained a pure mathematical exercise unless people had noticed that supersymmetry could help fix some of the flaws of the Standard Model.

As we saw, the Standard Model has two types of fundamental particles: the grains of matter, the fermions with spin ½, and the force carriers, the bosons with integer values of spin.

The mere fact that bosons and fermions have different values of spin makes them behave differently. Each class follows different statistical laws. For example, two identical fermions cannot exist in the same quantum state, that is, something -one of their quantum numbers – must be different. Quantum numbers refer to various properties: their position, their charge, their spin or their “colour” charge for quarks. Since everything else is identical, two electrons orbiting on the same atomic shell must have different direction for their spin. One must point up, the other down. This means at most two electrons can cohabit on an atomic shell since there are only two possible orientations for their spins. Hence, atoms have several atomic shells to accommodate all their electrons.

On the contrary, there are no limitations on the number of bosons allowed in the same state. This property is behind the phenomenon called superconductivity. A pair of electrons forms a boson since adding two half spins gives a combined state with a spin of 0 or 1, depending if they are aligned or not. In a superconductor, all pairs of electrons can be identical, with exactly the same quantum numbers since this is allowed for combined spin values of 0 or 1. Hence, one can interchange two pairs freely, just like two grains of sand of identical size can swap position in quick sand, which makes it so unstable. Likewise, in a superconductor, all pairs of electrons can swap position with others, leaving no friction. An electric current can then flow without encountering any resistance.

Supersymmetry builds on the Standard Model and associates a “superpartner” to each fundamental particle. Fermions get bosons as superpartners, and bosons get associated with fermions. This unifies the building blocks of matter with the force carriers. Everything becomes more harmonious and symmetric.

Supersymmetry builds on the Standard Model and comes with many new supersymmetric particles, represented here with a tilde (~) on them. (Diagram taken from the movie “Particle fever” reproduced with permission from Mark Levinson)

But there are other important consequences. The number of existing fundamental particles doubles. Supersymmetry gives a superpartner to each Standard Model particle. In addition, many of these partners can mix, giving combined states such as charginos and neutralinos

This fact has many implications. First major consequence: the two superpartners to the top quark, called the stops, can cancel out the large contribution from the top quark to the mass of the Higgs boson. Second implication: the lightest supersymmetric particle (in general one of the mixed states with no electric charge called neutralino) has just the properties one thinks dark matter should have.

Not only supersymmetry would fix the flaws of the Standard Model, but it would also solve the dark matter problem. Killing two huge birds with one simple stone. There is just one tiny problem: if these supersymmetric particles exist, why have we not found any yet? I will address this question in the next part in this series.

Pauline Gagnon

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