Warped Passages - Lisa Randall [131]
Figure 65. In a supersymmetry theory, the Higgs particle’s mass gets contributions from both particles and supersymmetry particles (in this case, a virtual top quark and virtual antitop quark in one diagram, and a virtual stop quark and virtual antitop quark in the other). The two diagrams look different because the interactions of the fermions and bosons are different. Nonetheless, the contributions to the Higgs particle’s mass from the two diagrams cancel when added together.
In a non-supersymmetric theory, huge quantum contributions to the mass of the Higgs particle would destroy low-energy electroweak symmetry breaking unless a huge and unlikely fudge made all the large contributions to the particle’s mass add up to a very small number. But a supersymmetric extension of the Standard Model guarantees that any potentially destabilizing influences, such as the ones shown in these diagrams, will add up to zero. A small value for the classical mass of the Higgs particle guarantees that the true mass—which includes the quantum contributions—will also be small.
Supersymmetry is like a flexible, stable foundation for the Standard Model. If you imagine the Standard Model’s fine-tuning as the balancing required to make a pencil stand on end then supersymmetry is like a fine wire holding the pencil in place. Alternatively, if you think of the hierarchy problem as the INS officers overstepping their jurisdiction and delaying too many letters, supersymmetric partners are like civil liberty advocates who restrain the immigration officers and let most of the letters pass right through.
Because ordinary virtual particles’ contributions together with the supersymmetric partners’ contributions add up to zero, supersymmetry guarantees that quantum mechanical contributions from virtual particles do not eliminate low-mass particles from the theory. In a supersymmetric theory, a particle that is supposed to be light, such as the Higgs particle, will remain light, even when we take virtual contributions into account.
Broken Supersymmetry
Although supersymmetry potentially resolves the problem of large virtual contributions to the Higgs particle’s mass, there is a serious problem with supersymmetry as I have presented it so far. The world is manifestly not supersymmetric. How could it be? If there existed superpartners with identical masses and charges to those of the known particles, they too would already have been seen. Yet no one has discovered a selectron or a photino.
This doesn’t mean that we have to abandon the idea of supersymmetry. But it does mean that supersymmetry, should it exist in nature, cannot be an exact symmetry. Like the local symmetry that accompanies the electroweak force, supersymmetry must be broken.
Theoretical reasoning shows that supersymmetry can be broken by particles and their superpartners not having identical masses; small supersymmetry-breaking effects can distinguish them. The difference between a particle’s mass and that of its corresponding superpartner would be controlled by the degree to which supersymmetry is broken. If supersymmetry is broken only a little, the mass difference will be small, whereas if it is badly broken, the difference will be large. In fact, the difference in mass between particles and their superpartners is one way to describe how badly supersymmetry is broken.
In almost all models of supersymmetry breaking, the superpartners’ masses are greater than the masses of the known particles. This is fortunate, since superpartners being heavier than their Standard Model counterparts is critical to the consistency of supersymmetry with experimental observations. It would explain why we haven’t yet seen them. Heavier particles can be produced only at higher energies, and, if supersymmetry exists, colliders have presumably not yet achieved sufficiently high energy to produce them. Because experiments have explored energies up to a few hundred GeV, the fact that superpartners have not yet been seen tells us that if they exist, they must have masses that