One of the most dramatic events in the history of elementary particle physics was the unification of the electromagnetic and the weak interactions into a single, beautiful gauge theory, which was created by Weinberg, Salam and Glashow and which is nowadays referred to as the ‘Standard Model’ (SM). For a detailed pedagogical account of the need for and development of such a theory, the reader is referred to Leader and Predazzi (1996). We simply recall that this tightly knit theory contains the astounding and incredible prediction of the existence of a set of three vector bosons, W±, Z0, with huge masses, mw ≈ 80 GeV/c2, mz ≈ 90 GeV/c2, and that these unlikely objects were eventually discovered. (The W was identified at CERN in January 1983 and the Z0, also at CERN, a few months later.) A test for the spin of the W is described in subsection 8.2.1(ix).

In the Standard Model the electroweak interactions are mediated by the exchange of photons, Zs and Ws, whose coupling to the basic fermions (leptons and quarks) is a mixture of vector and axial-vector. To begin with all particles are massless, and their masses are generated by spontaneous symmetry breaking. The usual mechanism of symmetry breaking requires a neutral scalar particle, the Higgs meson H, whose mass is not determined by the theory. H has not yet been detected experimentally and is the most serious missing link in the theory. But in every other respect the theory has been remarkably successful.

Quantum chromodynamics (QCD) is the beautiful theoretical structure believed to control the strong interactions of elementary particles. On the one hand, being a theory of strong interactions it is surprising that one can attack certain problems by perturbative methods, and where this has been done the agreement between theory and experiment is generally impressive. On the other hand a number of non-perturbative problems, which used to seem intractable, are now being attacked by lattice methods, but it is too early to say how significant the results are vis-à-vis experiment.

Because the theory deals with partons (quarks and gluons), whereas experiments are performed with hadrons, there is always some uncalculable piece in any theoretical treatment of a reaction. Consequently there is, to date, no single crucial experiment, which, analogous to the Lamb shift in QED, could be said to prove or disprove the validity of QCD. It is thus important to test the theory in as many ways as possible.

Historically, spin-dependent experiments have played a seminal rôle in verifying or falsifying theories. QCD has a very simple and clear-cut spin structure, so that the study of spin-dependent reactions should provide an excellent way to probe and test the theory further. In fact, as we shall see in Section 14.3 there is apparently serious disagreement between theory and experiment in several reactions, but it is now believed that this is a result of the naivety of the calculations.

Ultimately our fundamental goal in particle physics is to understand the dynamics, i.e. to have a theory from which we can actually calculate transition amplitudes. Tests of the theory will involve, at the crudest level, measurements of differential cross-sections or decay rates but, at a more sophisticated and more probing level, measurements of all kinds of spindependent phenomena. On the one hand, given a dynamical theory it is probably simplest to calculate the helicity transition amplitudes and from them the formulae for the spin-dependent observables that can be tested against experimental data. On the other hand, in the absence of a theory it would seem best to try to obtain information on the behaviour of the transition amplitudes from a sufficiently large number of different independent measurements. In this way one would hope to be led to deduce the nature of the underlying dynamics.

In both these situations it is important to bear in mind that certain properties are intrinsic to transition amplitudes, i.e. they do not depend upon detailed dynamical theory but rather follow from very general conservation laws, principally from the conservation of angular momentum.

The study of reactions thus divides into two phases:

1. (1) the general properties of transition amplitudes and the connection between their behaviour and the underlying dynamics; and

2. (2) the relationship between transition amplitudes and observables.

In this chapter we concentrate upon the former. The latter will be discussed in Chapter 5.