The description of scattering processes using quantum mechanics, as discussed in Chapter 2, has two obvious deficiencies. Firstly, it is not formulated in a relativistically invariant manner. The particle spin, which was incorporated by having a multicomponent wave function, must also be treated in a Lorentz invariant way. Secondly, it deals with scattering processes where the incident particle is scattered by a force represented by a fixed potential (or effective potential). However, in high energy scattering processes particles can be created or annihilated. Fermions must be created or destroyed as particle–antiparticle pairs, whereas any number of bosons may be involved. Thus the formalism needed to discuss the interaction of particles must include these points. Indeed, great care must be taken as to the actual definition of a particle and its properties. For example, a ‘free’ electron can dissociate (see Fig. 3.1) into an electron and a photon, or more complex states involving loops of e+ e- (or any other charged particles). A ‘dressed’ particle, with which we deal experimentally, has different properties to the ‘bare’ particle, the wave equations of which are discussed in this chapter.

The fundamental particles in the standard electroweak model are the spin ½ leptons and quarks, the spin 1 gauge bosons W±, γ and Z0 (which propagate the forces), and the spin 0 Higgs bosons (which are necessary to give the W±, Z0 and the fermions their masses).

The development of our present understanding of the weak and electromagnetic interactions, and of their unification, has proven to be a fascinating dialogue between profound theoretical insights and remarkable experimental discoveries. The electromagnetic and weak interactions appear to be describable by local gauge theories. Phenomena involving charged leptons and photons can be described, to impressive precision, by the relativistic field theory of Quantum Electrodynamics. The incorporation of weak phenomena led, eventually, to the Glashow–Salam–Weinberg model, the so-called standard model. This theory describes the electroweak properties of leptons and quarks, and successfully predicted the existence of the massive W± and Z0 vector bosons. At present, the standard model is compatible with all well established experimental data, amassed by some tens of thousands of man-years of effort. This is an impressive state of affairs.

This book has its origins in a course of lectures given to first-year postgraduate students (mainly experimentalists) in high energy physics in Oxford. An elementary knowledge of high energy particle physics, together with the basic ideas of quantum mechanics and relativity, is assumed. However, these topics, in as far as they are required for later use, are reviewed in Chapters 1 and 2. An introduction to group theories and symmetries, concepts of great importance in particle physics, is also given in Chapter 2. In Chapter 3, the single particle wave equations for spin 0, spin ½ and spin 1 particles are developed, and an introduction to some of the concepts of field theory is given.

In this chapter the production and properties of the massive gauge bosons W± and Z0 are discussed. The properties of the other gauge boson, the massless photon, were described in Chapters 4, 5 and 7. The properties of time-like virtual W± particles were discussed in Chapters 6 and 8, in the context of the decays of leptons and hadrons. Both the photon and the W± can be used as probes of the elementary constituents of hadrons. Here, for space-like four momenta such that Q2 ≳ 5 GeV2, the gauge bosons behave essentially as point-like probes. For much lower values of Q2, the W±, Z0 and the photon (in particular, the real photon) have hadronic components, arising from their fluctuations to qq pairs. Because of the difficulty in measuring the variables xBJ and Q2 in deep inelastic scattering in the case of neutral current interactions, these reactions have mainly been used to study the couplings of the Z0 to quarks (Section 8.8), rather than to study QCD effects. Interference phenomena between γ and Z0 exchange have been observed for space-like momenta in charged lepton deep inelastic scattering (Section 8.9.1), and for time-like momenta in e+ e- annihilation (Section 6.3 and 8.9.2).

Experimentally, the most important missing ingredient of the standard model is the Higgs scalar, which is needed to give masses to the particles. The complete list of quarks and leptons must also be established.

Nuclear beta decay has played a very important historical role in the development of our present understanding of weak interactions. For more than 20 years these reactions were the primary source of information on the weak force. In the first part of this chapter, the theoretical ideas developed to account for the experimental measurements on beta decays (and later on the weak decays of hadrons) are reviewed, leading to the V – A theory of weak interactions. This theory, however, gives badly divergent cross-sections at high energy and, moreover, does not account for the weak neutral current interactions which are observed in nature. The standard model of Glashow, Salam and Weinberg, which is based on the principle of local gauge symmetry, predicted such currents and, indeed, successfully explains the bulk of all experimental measurements on weak and electromagnetic phenomena. After discussion on the basic framework of this model, the problem of the introduction of particle masses is reviewed. Non-zero masses would appear to violate the required gauge invariance of the theory. However, if the underlying group symmetry is spontaneously broken, then the particle masses can be generated at the price of introducing one or more fundamental scalars (Higgs particles) into the theory. The predictions of the standard model, for a wide class of reactions, together with a comparison of the experimental results, are discussed in subsequent chapters.

STRONG, ELECTROMAGNETIC AND WEAK INTERACTIONS

One of the main objectives of physics is to find out what, if any, are the basic constituents of matter and to understand the nature of the forces by which they interact. Fundamental particles appear, at present, to be of two distinct types. The first group consists of quarks and leptons. These are spin ½ particles obeying Fermi–Dirac statistics (fermions). The second group consists of the so-called gauge bosons. These are integral spin particles obeying Bose–Einstein statistics (bosons). The gauge bosons appear to be responsible for mediating the interaction forces between quarks and leptons. Existing results show clear evidence for four types of interactions in nature. These are the strong, electromagnetic, weak and gravitational interactions. Our knowledge of these interactions stems, to a great extent, from our understanding of the underlying symmetries which appear to exist in nature and in the way in which they appear to be broken.

The world is made up of ninety-two naturally occurring chemical elements. The properties of a given isotope of an element do not, as far as we know, depend on its origin. These elements are composed of electrons and nuclei, which are in turn composed of protons and neutrons. The electrons are fermions and obey the Pauli exclusion principle. This leads to an elaborate shell structure and important differences in the chemical properties of the elements. Prior to the development of particle accelerators, studies in particle physics were limited to indirect means.