Section 10.7 Interactions and Messenger Bosons
Before describing the weak interaction on a fundamental level, let's review how photons and gluons serve as the messengers for the electromagnetic and strong interactions between leptons and quarks. Messenger particles that transmit interactions, such as photons, gluons, and the \(W\)'s and \(Z^0\)'s, are also called intermediate bosons, because they mediate interactions and carry integer spin.
Consider first the most familiar lepton, an electron, emitting or absorbing a photon. The basic interaction occurs at a vertex in a Feynman diagram. See Figure 10.6. As the electron emits or absorbs a photon, its energy and momentum change, but it remains an electron.
Turn now to the description of a quark emitting or absorbing a gluon. See Figure 10.7. Notice that only gluons carrying red (\(R\overline R\text{,}\) \(R\overline B\text{,}\) or \(R\overline G\)) can be emitted by red quarks, while only gluons carrying antired (\(R\overline R\text{,}\) \(B\overline R\text{,}\) or \(G\overline R\)) can be absorbed by red quarks. Similar rules apply for the gluons emitted or absorbed by blue or green quarks. As the quarks in the diagram emit or absorb a gluon, their energy, momentum, and color may all change, but the flavor remains the same, i.e., a down quark remains a down quark, an up quark remains an up quark, etc.
The weak interaction, mediated by the \(W^\pm\) and \(Z^0\) bosons, is probably the hardest one to understand. You saw in Chapter 9 that the weak interaction violates strangeness conservation, and it is known that certain other symmetries are violated as well. We know that both quarks and leptons seem to “feel” the weak interaction, but it affects quarks and leptons somewhat differently. Since the \(W^\pm\) bosons carry electric charge, the particle emitting or absorbing a \(W\) boson must change its identity in a major way.
Consider first how \(W\) bosons interact with quarks. A \(W\) boson changes a quark's flavor. That is, if an up quark emits or absorbs a \(W\text{,}\) then it is no longer an up quark. In Figure 10.8, we see a red strange quark emitting or absorbing a W and becoming a red up quark. Its energy, momentum, charge and flavor change, but the quark color remains red.
While Figure 10.8 shows typical interactions at a quark-\(W\) vertex, we can derive several other versions based on the symmetry properties of Feynman diagrams. Look at Table 10.9. Each operation is based on the standard version. Also, any combination of these operations yields a valid quark-\(W\) interaction.
| standard version | \(s \to u + W^-\) |
| reverse arrow | \(u + W^- \to s\) |
| particle out \(=\) anti-particle in | \(\overline u + s \to W^-\) |
| change to antiparticles | \(\overline s \to \overline u + W^+\) |
| replace \(s\) with \(d\) | \(d \to u + W^-\) |
Finally, let's look at how \(W\)'s interact with leptons. A \(W\) boson changes a lepton's “family membership.” We saw earlier that there are three types or families of leptons: electron, muon, and tauon. Each family contains a negative particle, a positive antiparticle, and a neutrino and antineutrino. The basic interaction is that a lepton emits a \(W^+\) or \(W^-\) and changes into a different lepton of the same family. This process of changing to a different lepton of the same family is what we mean by the phrase “change of family membership.” As Figure 10.10 illustrates, the electron emits a \(W^-\) or absorbs a \(W^+\) and changes its charge and family membership, becoming an electron neutrino. But, it maintains its lepton number, \(L_e = +1\text{.}\)
As with the quark interactions, we can derive several versions of the lepton-\(W\) interaction. These are listed in Table 10.11. Each operation is based on the standard version. Again, any combination of these operations yields a valid lepton-\(W\) interaction.
| standard version | \(e^- \to \nu_e + W^-\) |
| reverse arrow | \(\nu_e + W^- \to e^-\) |
| particle in \(=\) antiparticle out | \(\overline\nu_e + e^- \to W^-\) |
| change to antiparticles | \(e^+ \to \overline\nu_e + W^+\) |
| replace \(e\) with \(\mu\) or \(\tau\) | \(\mu^- \to \nu_\mu + W^-\) |
An important thing to note here is the equivalence in these processes and in the diagrams between a particle “going forward in time” and an antiparticle “going backward in time.” 1 In Figure 10.10, for instance, an electron is changed into a \(\nu_e\) neutrino either by emitting a \(W^-\) or by absorbing a \(W^+\text{.}\) This can result in some ambiguity: a process in which particle \(A\) emits a \(W^-\text{,}\) which is then absorbed by particle \(B\text{,}\) could just as easily be re-written as a process in which particle \(B\) emits a \(W^+\text{,}\) which is then absorbed by particle \(A\text{.}\)