Knocking on Heaven's Door - Lisa Randall [147]
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