Warped Passages - Lisa Randall [83]
So we now know that weak interactions act only on left-handed particles, and can change particle type. But to truly understand the weak force we need a theory that predicts the interactions of the weak gauge bosons that communicate the force. Physicists initially found that constructing that theory was not simple. They needed to make a major theoretical advance before they could truly understand the weak force and its consequences.
The problem was the final bizarre feature of the weak force: it falls away precipitously over a very short distance, one ten thousand trillionth (10-16) of a centimeter. That makes it quite unlike gravity and electromagnetism, for both of which, as we saw in Chapter 2, strength decreases with distance in proportion to the inverse square of the separation. Although gravity and electromagnetism become weaker as you go further out, they don’t drop off nearly as quickly as the weak force. The photon conveys the electromagnetic force to large distances. Why does the weak force behave so differently?
It was clear that physicists needed to find a new type of interaction to account for nuclear processes such as beta decay, but it was not clear what this new interaction could possibly be. Before Glashow, Weinberg, and Salam developed their theory of the weak force, Fermi made a stab at it with a theory that included new types of interaction involving four particles, such as the proton, neutron, electron, and neutrino. This Fermi interaction directly produced beta decay without invoking an intermediate weak gauge boson. In other words, the interaction permitted a proton to turn directly into its decay products—the neutron, electron, and neutrino.
However, it was clear, even at the time, that the Fermi theory could not be the true theory that would work at all energies. Although its predictions were correct for low energies, they were obviously completely wrong for high energies, at which particle interactions became much too strong. In fact, if you incorrectly assumed that you could apply the Fermi theory when the particles were highly energetic, you would get nonsensical predictions, such as particles that should interact with a probability greater than one. That’s impossible, since nothing can happen more often than always.
Although the theory based on the Fermi interaction was a fine effective theory for explaining interactions at low energies and between sufficiently distant particles, physicists saw that they needed a more fundamental explanation of processes such as beta decay if they were to know what happened at high energies. A theory based on forces communicated by weak gauge bosons looked as if it would work much better at high energies—but no one knew how to account for the weak force’s short range.
That short range turns out to be a consequence of nonzero masses for the weak gauge bosons. In particle physics the relationships implied by the uncertainty principle and special relativity have noticeable consequences. At the end of Chapter 6 I discussed the smallest distances at which a particle of a particular energy, such as the weak scale energy or the Planck scale energy, can be affected by forces. Because of the special relativity relation between energy and mass (E = mc2), massive particles, such as the weak gauge bosons, automatically incorporate similar relationships between mass and distance.
In particular, the force communicated by the exchange of a particle with a given mass dies away over a larger distance when the mass is smaller. (That distance is also proportional to Planck’s constant and inversely proportional to the speed of light.*) The relationship between mass and distance given in Chapter 6 tells us that the weak gauge boson, whose mass is about 100 GeV, automatically transmits the weak force only to particles that lie within one ten thousand trillionth of a centimeter. Beyond this distance, the force conveyed by the particle becomes extremely small, too small to do anything