The developments of the previous chapters provide the ingredients that one can use to construct models of spontaneously broken non-Abelian gauge theories. In Chapters 21–23 we shall discuss quantum chromodynamics (QCD) which is proposed as a model for strong interactions. Here we shall concentrate on models which attempt to unify the weak and electromagnetic interactions into a unique renormalisable theory.

We first give the general rules to be followed for model building. Then we apply them to the most successful of these models—in fact, the only one that has so far passed all experimental tests—the electroweak standard model (SM) and show how its structure arises.

In the literature, the term standard model sometimes refers to the combination of the electroweak sector with the colour SU(3) theory of strong interaction mentioned above (QCD). In this and in the following chapters, we shall use the term standard model for the purely electroweak part of the theory. The SM is due to various authors (Glashow, 1961; Weinberg, 1967; Salam, 1968) and its predictions are in good agreement with the data.

With the recent coming into operation of the electron–positron collider (LEP) at CERN, where over 106Z0s are collected in a year of operation, it becomes possible to test the predictions of the SM to a fantastic accuracy. So far, all the evidence is that the SM works incredibly well.

Model building (towards the standard model)

The general principles to be followed in constructing models are:

1. (a) Choose a gauge group G and as many vector fields as there are generators of G.