Warped Passages - Lisa Randall [134]
On the theoretical side, supersymmetry is not completely compelling because big questions remain about how it is broken. We know that it must be broken spontaneously, but, as in the case of the Standard Model and weak force symmetry, we don’t yet know which particles are responsible. Many fascinating ideas have been suggested, but a completely satisfactory four-dimensional theory has yet to be proposed.
When I first learned about supersymmetry, it almost seemed too easy from a model building perspective. It looked as though supersymmetric theories could contain random unrelated masses, since quantum contributions were absent. Even if we didn’t know why very disparate masses should appear, they wouldn’t cause any trouble. This was very disappointing from a model building perspective because nothing seemed to give any clue about the as yet undetermined underlying theory. And it also was pretty boring, since building models didn’t seem to present any challenges.
Figure 66. The upper plot represents the strengths of the electromagnetic, weak, and strong forces as a function of energy in the Standard Model. The curves approach one another, but do not meet in a single point. The lower plot represents the strengths of the same three forces as a function of energy in the supersymmetric extension of the Standard Model. The strength of the three forces is the same at high energy, indicating that the three forces might actually unify into a single force.
But then I learned about the supersymmetry flavor problem, which tells us that this isn’t true; in fact, it’s very difficult to make the concrete details of a theory with broken supersymmetry work. The problem is a bit subtle, but it’s important nonetheless. The flavor problem is the major obstacle to a simple theory of supersymmetry breaking. All new theories of supersymmetry breaking focus on this problem, and Chapter 17 will show why supersymmetry breaking in extra dimensions is a potential solution.
Recall that the flavors of Standard Model fermions are the three different fermions of the three different generations that have identical charges but different masses: the up, charm, and top quarks, or the electron, muon, and tau, for example. In the Standard Model, the identities of these particles do not change. For example, muons never directly interact with electrons: they interact only indirectly through the exchange of a weak gauge boson. Although muons can decay into electrons, that is only because the decay produces a muon neutrino and an electron antineutrino as well (see Figure 53, Chapter 7). The muon never converts to an electron directly without the emission of the associated neutrinos.
A physicist’s way of expressing this definite identity of a particular lepton type is to say that electron or muon number is conserved. We assign positive electron number to an electron and an electron neutrino, and a negative electron number to a positron and an electron antineutrino. And we assign a positive muon number to a muon and a muon neutrino, and a negative muon number to an antimuon and a muon antineutrino. If muon and electron numbers are preserved, a muon could never decay into an electron and a photon, since we would start with a positive muon number and a zero electron number and end up with a positive electron number and a zero muon number. And in fact, no one has ever seen such a decay. So far as we can tell, electron and muon number are preserved by all particle interactions.
In a supersymmetric theory, electron and muon