Knocking on Heaven's Door (47 page)

Supersymmetric models posit that every fundamental particle of the Standard Model—electrons, quarks, and so on—has a partner in the form of a particle with similar interactions but different quantum mechanical properties. If the world is supersymmetric, then there exist many unknown particles that could soon be found—a supersymmetric partner for every known particle. (See Figure 57.)

Supersymmetric models could help solve the hierarchy problem and, if so, would do it in a remarkable fashion. In an exactly supersymmetric model, the virtual contributions from particles and their superpartners cancel exactly. That is, if you add together all the quantum mechanical contributions from every particle in the supersymmetric model and tally their effect on the Higgs boson mass, you would find they all add up to zero. In a supersymmetric model, the Higgs boson would be massless or light, even in the presence of quantum mechanical virtual corrections. In a true supersymmetric theory, the sum of the contributions of both types of particles exactly cancel. (See Figure 58.)

[
FIGURE 57
]
In a supersymmetric theory, every Standard Model particle would have a supersymmetric partner. The Higgs sector is also enhanced beyond that of the Standard Model.

This sounds miraculous perhaps but is guaranteed because supersymmetry is a very special type of symmetry. It’s a symmetry of space and time—like the symmetries you are familiar with such as rotations and translations—but it extends them into the quantum regime.

[
FIGURE 58
]
In a supersymmetric model, contributions from virtual supersymmetric particles exactly cancel the Standard Model particles’ contributions to the Higgs boson mass. For example, the sum of the contributions from the two diagrams above is zero.

Quantum mechanics divides matter into two very different categories—bosons and fermions. Fermions are particles that have half-integer
spin
, where spin is a quantum number that essentially tells us something like how much the particle acts as if it is spinning. Half-integer means values like 1/2, 3/2, 5/2, and so on. The quarks and leptons of the Standard Model are examples of fermions and have spin -1/2. Bosons are particles such as the force-carrying gauge bosons or perhaps the yet-to-be-discovered Higgs boson that have integral spin, indicated by whole numbers such as 0, 1, 2, and so on.

Fermions and bosons are distinguished not only by their spins. They behave very differently when there are two or more of them of the same type. For example, identical fermions with the same properties can never be found in the same place. This is what the
Pauli exclusion principle
, named after the Austrian physicist Wolfgang Pauli, tells us. This fact about fermions accounts for the structure of the periodic table that tells us that electrons, unless distinguished by some quantum number, have to orbit around the nucleus differently from each other. It is also the reason why my chair isn’t falling to the center of the Earth, since the fermions in my chair can’t be in the same place as the material of the Earth.

Bosons, on the other hand, behave in exactly the opposite manner. They are actually more likely to be found in the same place. Bosons can pile on top of each other—kind of like crocodiles, which is why phenomena like Bose condensates that require many particles to pile up in the same quantum mechanical state can exist. Lasers, too, rely on bosonic photons’ affinity for each other. The intense beam is created by the many identical photons that shoot off together.

Remarkably, in a supersymmetric model, particles that we take to be very different—bosons and fermions—can be exchanged in such a way that the result in the end is the same as the theory you started with. Each particle has a partner particle of the opposite quantum mechanical type, but with exactly the same mass and charges. The nomenclature for the new particles is a bit funny—it never fails to elicit giggles when I speak on this topic in public. For example, the fermionic electron is paired with a bosonic
selectron
. A bosonic photon is paired with a fermionic
photino
, and a W is paired with a
Wino
. The new particles have related interactions to the Standard Model particles with which they are paired. But they have opposite quantum mechanical properties.

In a supersymmetric theory, the properties of each boson are related to the properties of its superpartnered fermion and vice versa. Since each particle has a partner and the interactions are carefully aligned, the theory permits this bizarre symmetry that interchanges fermions and bosons.

One way to understand the apparently miraculous cancellation of virtual contributions to the Higgs mass is that supersymmetry relates any boson to a partner fermion. In particular, supersymmetry partners the Higgs boson with a Higgs fermion, the Higgsino. Even though quantum mechanical contributions radically influence the mass of a boson, the mass of a fermion will never be much bigger than the classical mass, which is the mass before you account for quantum contributions you started out with—even when quantum mechanical corrections are included.

The logic is subtle, but large corrections don’t occur because fermion masses involve both left-handed and right-handed particles. Mass terms allow them to convert back and forth into each other. If there were no classical mass term and they couldn’t convert into each other before quantum mechanical virtual effects were included, they couldn’t do so even with quantum mechanical effects taken into account. If a fermion has no mass to begin with (no classical mass), it will still have zero mass after quantum mechanical contributions are included.

No such argument applies to bosons. The Higgs boson, for example, has zero spin. So there is no sense in which we can talk about a Higgs boson spinning to the left or to the right. But supersymmetry tells us that boson masses are the same as fermion masses. So if the Higgsino mass is zero (or small), so too must be the mass of the partnered Higgs boson in a supersymmetric theory—even when quantum mechanical corrections are taken into account.

We don’t yet know if this rather elegant explanation for the stability of the hierarchy and cancellation of large corrections to the Higgs mass is correct. But if supersymmetry does address the hierarchy problem, then we know a lot about what we would expect to find at the LHC. That’s because we know what new particles should exist, since every known particle should have a partner. On top of that, we can estimate what the masses of the new supersymmetric particles should be.

Of course, if supersymmetry were exactly preserved in nature, we would know precisely the masses for all the superpartners. They would be identical to the mass of the particle they were paired with. However, none of the superpartners have been observed. That tells us that even if supersymmetry applies in nature, it cannot be exact. If it were, we would have already discovered the selectron and the squark and all the other supersymmetric particles a supersymmetric theory would predict.

So supersymmetry has to be
broken
, meaning the relationships that are predicted in a supersymmetric theory—though possibly approximate—cannot be exact. In a broken supersymmetric theory, every particle would still have a superpartner, but those superpartners would have different masses than their partner Standard Model particles.

However, if supersymmetry were too badly broken, it wouldn’t help with the hierarchy problem, since the world would then look as if supersymmetry didn’t apply to nature at all. Supersymmetry has to be broken in just such a way that we wouldn’t have yet discovered evidence of supersymmetry, while the Higgs mass is nonetheless protected from large quantum mechanical contributions that would give it too big a mass.

This tells us that supersymmetric particles should have weak scale masses. Any lighter and they would have been seen, and any heavier and we would expect the Higgs mass to be heavier as well. We don’t know precisely the masses since we only know the Higgs mass approximately. But we do know that if the masses were overly heavy, the hierarchy problem would persist.

So we conclude that if supersymmetry exists in nature and addresses the hierarchy problem, lots of new particles with masses in the range of a few hundred GeV to a few TeV should exist. This is precisely the range of masses the LHC is positioned to search for. The LHC, with 14 TeV of energy, should be able to produce these particles even if only a fraction of the protons’ energy goes into quarks and gluons colliding together and making new particles.

The easiest particles to produce at the LHC would be the supersymmetric particles that are charged under the strong nuclear force. These particles could be made in abundance when protons collide (or more specifically the quarks and gluons within them). When these collisions happen, new supersymmetric particles that interact via the strong force can be produced. If so, they will leave very distinctive and characteristic evidence in the detectors.

These
signatures
—the experimental pieces of evidence they leave—depend on what happens to the particle after its creation. Most supersymmetric particles will decay. That’s because, in general, lighter particles (such as those in the Standard Model) exist for which the total charge is the same as the heavy supersymmetric particle. If that’s the case, the heavy supersymmetric particle will decay into lighter Standard Model particles in a way that conserves the initial charge. Experiments will then detect the Standard Model particles.

That’s probably not sufficient to identify supersymmetry. But in almost all supersymmetric models, a supersymmetric particle won’t decay solely into Standard Model particles. Another (lighter) supersymmetric particle remains at the end of the decay. That’s because supersymmetric particles appear (or disappear) only in pairs. Therefore, a supersymmetric particle has to remain at the end after a supersymmetric particle has decayed—one supersymmetric particle cannot turn into none. Consequently, the lightest such particle must be stable. This lightest particle, which has nothing to decay into, is known to physicists as the lightest supersymmetric particle, the LSP.

Supersymmetric particle decays are distinctive from an experimental vantage point in that the lightest of the neutral supersymmetric particles will remain, even after the decay is complete. Cosmological constraints tell us that the LSP carries no charges, so it won’t interact with any elements of the detector. This means that whenever a supersymmetric particle is produced and decays, momentum and energy will appear to be lost. The LSP will disappear from the detector and carry away momentum and energy to where it can’t be recorded, leaving as its signature missing energy. Missing energy isn’t specific to supersymmetry alone, but since we already know a good deal about the supersymmetric spectrum, we know both what we should and shouldn’t see.

For example, suppose a squark, the supersymmetric partner of a quark, is produced. Which particles it can decay into will depend on which of the particles are lighter. One possible mode of decay will always be a squark turning into a quark and the lightest supersymmetric particle. (See Figure 59.) Recall that because decays can occur essentially immediately, the detector records only the decay products. If such a squark decay occurred, detectors would record the passage of the quark in the tracker and in the hadronic calorimeter that measures energy deposited by a strongly interacting particle. But the experiment will also measure that energy and momentum are missing. Experimenters should be able to tell that momentum is missing in the same way they can when neutrinos are produced. They would measure momentum perpendicular to the beam and find that it doesn’t add to zero. One of the biggest challenges the experimenters face will be to unambiguously identify this missing momentum. After all, anything that is not detected appears to be missing. If something is wrong or mismeasured and even small amounts of energy go undetected, the missing momentum could add up to mimic an escaping supersymmetric particle’s signal, even though nothing exotic was produced.