Subatomic Physics

11.3. The Current–Current Interaction of the Standard Model 341
Figure 11.5: Leptonic decays of K 0 and K + and quark analogue; the decay shown for the K 0 is
forbidden.
For the rest of this chapter we denote four-vectors with ordinary letters. The scalar
product of two four-vectors is defined by Eq. (1.10); the product Jw · J † w is
and the weak Hamiltonian becomes
gµ νJwJ † w = c2 ρwρ † w − J w·J † w ,
Hw = GF
√
2 c2 �
d 3 xJw(x) · J † w (x). (11.25)
This equation makes it obvious that Hw is a Lorentz invariant. So far, we
have taken the weak current Jw and the intermediate boson W to be charged, as
shown in Fig. 11.4. This assumption was generally held to be true until about
1979 and was based on experimental data. It was known, for instance, that the
decay K0 → µ + µ − , shown in Fig. 11.5a, was absent or greatly suppressed relative
to the primary decay mode of the K + ,K + → µ + νµ, shown in Fig. 11.5b. Such
two-body weak decay modes can be understood more readily in terms of quarks,
as illustrated in Fig. 11.5c. The composition of the K + is (u¯s) and that of the
K0 is (d¯s). The analogy to Fig. 11.3 now becomes apparent, even more so if the
initial ¯s leg is turned into an s in the final state, as shown in Fig. 11.5c. A neutral
weak current, mediated by a neutral intermediate vector boson Z0 would allow
processes such as K0 → µ + µ − and the elastic scattering of neutrinos on leptons and
protons, νµe → νµe, νµp → νµp, illustrated in Fig. 11.6. Around 1968, Weinberg (6)
and Salam (7) independently predicted the existence of weak neutral currents in a
theory that unified the weak and electromagnetic interactions. The absence of the
decay K0 → µ + µ − was a major hurdle in the acceptance of the Weinberg–Salam
theory until 1970 when Glashow, Iliopoulos, and Maiani (8) (GIM) showed that the
absence of the missing K0 decay could be understood by postulating the existence
of charmed quarks (Sections 7.6 and 13.2), which permitted a cancelation to occur.
6S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967), 27, 1688 (1977); Phys. Rev. D5, 1962 (1972).
7A. Salam, in Elementary Particle Theory, (N. Swartholm ed.) Almqvist and Wiksells, Stockholm,
1969, p. 367.
8S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285 (1970).