Knocking on Heaven's Door - Lisa Randall [148]
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)