Subatomic Physics

404 The Electroweak Theory of the Standard Model
Furthermore, the finiteness of the results of higher order electromagnetic processes
requires gauge invariance, which in turn requires zero mass particles. How, then,
can the massive bosons be incorporated? Glashow discussed this problem in 1961, (2)
realized that it was a “principal stumbling block,” and suggested neutral currents.
Both Salam and Weinberg believed that the spontaneous symmetry breaking introduced
in chapter 12 could provide masses to the “intermediate” bosons in a gauge
theory which begins with massless particles, and that the resultant theory would
be finite. (3) The mathematical proof of the fact that a finite theory, to all orders
in the appropriate coupling constant, could be constructed in this manner did not
come until later. (4) The proof makes use of the important point that the symmetry
breaking does not spoil the gauge invariance of the theory. The electroweak theory
was formulated and predicted the masses of the W + and Z 0 before these particles
were found experimentally.
13.2 The Gauge Bosons and Weak Isospin
If a theory is to combine electromagnetism and the weak interactions, it must include
the photon as well as the massive intermediate bosons. A gauge theory, as described
in Section 12.4, requires that the charged bosons be supplemented by a neutral one
in order to make an isospin multiplet and to have current conservation. The massive
gauge bosons do not have strong interactions, thus the relationship between them is
called “weak isospin”. Since there are three charge states, corresponding to charged
and neutral currents, the intermediate boson must have weak isospin 1. These
particles are not necessarily those observed in nature. Nevertheless, we call the three
gauge bosons W + ,W − ,andW 0 ; they have zero mass to begin with, as required by
a gauge theory. In addition, there is a neutral “electromagnetic” field with a weak
isospin singlet particle we shall call the B 0 . Then, in the theory of Weinberg and
Salam, the neutral particles associated with the weak and electromagnetic fields,
andobservedinnature,theZ 0 and the photon, are mixtures of the B 0 and the W 0 ,
γ =cosθW B 0 − sin θW W 0 , Z 0 =cosθW W 0 +sinθW B 0 . (13.1)
The mixing angle θW is called the Weinberg angle and can be determined from
experiment, as we shall see. The photon and Z 0 are mixtures of a weak isospin
singlet, B 0 , and a component, W 0 , of the isospin triplet W bosons. They are not
simple particles, even though the photon has zero mass. We have seen in chapter 10
that the photon is a mixture of isospin zero and one for strong isospin; now we see
that the photon is also a mixture of weak isospin zero and one. The Higgs mechanism
is responsible for giving the W and Z bosons their masses. The masses of the Z 0
2 S. L. Glashow, Nucl. Phys. 22, 579 (1961).
3 S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, Nobel Symposium, No. 8 (N.
Svartholm, ed.), Almqvist and Wiksell, Stockholm, 1968, p. 367.
4 G. ‘t Hooft, Nucl. Phys. B33, 173 (1971), B35, 167 (1971); G. ‘t Hooft and M. Veltman,
Nucl. Phys. B44, 189 (1972), B50, 318 (1972).