Warped Passages - Lisa Randall [127]
This chapter introduces supersymmetry, a strange new symmetry transformation that interchanges bosons and fermions. Physicists can now construct theories that incorporate supersymmetry. However, supersymmetry as a symmetry of nature is still hypothetical, since no one has yet discovered supersymmetry in the world around us. Nonetheless, physicits have two major reasons to think that it might exist in the world:
One reason is the superstring, which will be more thoroughly investigated in the chapter that follows. Superstring theory, which incorporates supersymmetry, is the only known version of string theory that has the potential to reproduce the particles of the Standard Model. String theory without supersymmetry doesn’t look as if it could possibly describe our universe.
The second reason is that supersymmetric theories have the potential to solve the hierarchy problem. Supersymmetry doesn’t necessarily explain the origin of the large ratio of the weak scale mass to the Planck scale mass, but it does eliminate the problematic enormous quantum contributions to the Higgs particle’s mass. The hierarchy problem is a serious conundrum for which very few suggestions have survived experimental and theoretical scrutiny. Before extra-dimensional theories were introduced as potential alternatives, supersymmetry was the lone candidate solution.
Because no one yet knows whether or not supersymmetry exists in the external world, all we can do at this point is evaluate candidate theories and their consequences. This way, when experiments reach higher energy, we’ll be prepared to figure out what the physical theory underlying the Standard Model really is. So let’s take a look at what could lie in store.
Fermions and Bosons: An Unlikely Match
In a supersymmetric world every known particle is paired with another—its supersymmetric partner, also known as a superpartner—with which it is interchanged by a supersymmetry transformation. A supersymmetry transformation turns a fermion into its partner boson and a boson into its partner fermion. We saw in Chapter 6 that fermions and bosons are particle types that are distinguished in quantum mechanical theories by their spin. Fermionic particles have half-integer spin, while bosonic particles have integer spin. Integer spin values are those numbers that ordinary objects spinning in space could take, whereas half-integer values are a peculiar feature of quantum mechanics.
All fermions in a supersymmetric theory can be transformed into their partner bosons and the bosons can all be transformed into their partner fermions. Supersymmetry is a feature of the theoretical description of these particles. If you muck around with the equations that describe how particles behave by making a supersymmetry transformation that interchanges bosons and fermions, the equations will all end up looking the same. The predictions would all be identical to those you made before you did the transformation.
At first glance, such a symmetry defies logic. Symmetry transformations are supposed to leave systems unchanged. But supersymmetry transformations interchange particles that are manifestly different: fermions and bosons.
Although one would not expect a symmetry to mix things that are so different, several groups of physicists nevertheless proved that it could. In the 1970s, European and Russian physicists* showed that a symmetry could interchange such different particles, and that the laws of physics could be the same before and after bosons and fermions were interchanged.
This symmetry is a little different from previous symmetries we have considered because the objects that it interchanges clearly have different properties. But the symmetry can nonetheless exist if bosons and fermions are present in equal numbers. As an analogy, imagine an equal number