Warped Passages - Lisa Randall [102]
Therefore, according to quantum field theory, the short range of the weak force could mean only one thing: the weak gauge bosons communicating the force had to have nonzero mass. However, the theory of forces I described in the previous chapter works only for gauge bosons such as the photon, which communicates a force over large distances and has zero mass. According to the original theory of forces, the existence of nonzero masses was strange and problematic—the theory’s high-energy predictions when gauge bosons have mass make no sense. For example, the theory would predict that very energetic, massive gauge bosons would interact much too strongly—so strongly in fact that particles would appear to be interacting more than 100% of the time. This naive theory is clearly wrong.
Furthermore, the masses for weak gauge bosons, quarks, and leptons (all of which we know to have nonzero mass) do not preserve the internal symmetry which, as we saw in the previous chapter, is a key ingredient in the theory of forces. Physicists who hoped to construct a theory with massive particles clearly needed a new idea.
Physicists have shown that the only way to make a theory that avoids nonsensical predictions about energetic, massive gauge bosons is to have the weak force symmetry break spontaneously through the process known as the Higgs mechanism. Here’s why.
You might recall from the previous chapter that one of the reasons we wanted to include an internal symmetry that eliminates one of the three possible polarizations of a gauge boson was that a theory without the symmetry makes the same sort of nonsensical predictions I’ve just mentioned. The simplest theory of forces without an internal symmetry predicts that any energetic gauge boson, with or without a mass, interacts with other gauge bosons far too often.
The successful theory of forces eliminates this bad high-energy behavior by forbidding the polarization that is responsible for the incorrect predictions and doesn’t actually exist in nature. Spurious polarizations are the source of the problematic predictions for high-energy scattering, so the symmetry allows only physical polarizations—the ones that really exist and are consistent with the symmetry—to remain. The symmetry, which rids the theory of nonexistent polarizations, also eliminates the incorrect predictions they would otherwise induce.
Although I didn’t say so explicitly at the time, this idea works as stated only for massless gauge bosons. The weak gauge bosons, unlike the photon, have nonzero masses. Weak gauge bosons travel at less than the speed of light. And that puts a wrench in the works.
Whereas massless gauge bosons have only two polarizations that exist in nature, massive gauge bosons have three. One way to understand this distinction is that massless gauge bosons always travel at the speed of light, which tells us that they are never at rest. They therefore always single out their direction of motion, so you can always distinguish the perpendicular directions from the remaining polarization along the direction of travel. And it turns out that for massless gauge bosons, physical polarizations oscillate only in the two perpendicular directions
Massive gauge bosons, on the other hand, are different. Like all familiar objects, they can sit still. But when a massive gauge boson isn’t