The Kobayashi–Maskawa matrix, which delineates what combinations of quark fields are operative in the charge changing weak interaction, was introduced in Chapter 9. Its elements Vij have occurred repeatedly in the preceding chapters and are crucial in providing quantitative results from the theory. We here address the issue of measuring these matrix elements and of summarizing the present knowledge of them.

In the SM the weak currents are all expressed as KM matrix elements multiplying currents built up from the quark fields which, for brevity, we denote by u, d, …, ū, d̄, … In some cases the latter currents can be identified as the conserved Noether currents corresponding to symmetries of the strong interactions, for example, isotopic spin invariance. In that case, as explained in Appendix 3, the matrix elements (at least the forward ones) of the conserved currents are known exactly. Thus the weak transition amplitude appears as a Vij multiplied by a known matrix element, thereby allowing the measurement of that particular Vij. To the extent that the symmetry is not perfect and that one is seeking very precise knowledge of the Vij, one must attempt to correct for the symmetry breaking. This is a highly technical procedure for which the reader should consult Leutwyler and Roos (1984) and Donoghue, Holstein and Klimt (1987), and the major review article by Paschos and Türke (1988). We shall only deal with the case of perfect symmetry and will illustrate the approach in β-decay type reactions.

Jets have by now become a major component of high energy particle physics. It is widely (if not universally) accepted that jets are implied by perturbative QCD and that they are the simplest and perhaps best evidence supporting it. This means that jets are to be found in all large pT phenomena irrespective of whether they are initiated by hadronic or by leptonic processes. In spite of this, for pedagogical and historical reasons we shall present the discussion of jets in hadronic and in e+e− reactions separately.

A drastic selection has had to be made to reduce the material on jets to an acceptable size. For additional material see Cavasinni (1990), Altarelli (1989) and Jacob (1990) and references therein. [See also the various contributions in the CERN 89-08 (vol 1–3) edited by Altarelli, Kleiss and Verzegnassi, 1989].

Note that a complete set of formulae for the cross-sections of all the 2 → 2 partonic reactions discussed herein can be found in Appendix 7.

Introduction

We here discuss the evidence that hadronic reactions involving large transfers of transverse momentum (pT) are controlled by the direct collision of constituents within the colliding hadrons, with subsequent fragmentation of these constituents into showers of hadrons. Naturally, it is supposed that these constituents are the quarks and gluons discussed in previous chapters.

It is well known that high energy hadronic interactions are dominated by the production of a large number of particles, mostly confined to the nearly forward direction, i.e. dominated by events in which the produced secondaries have small PT leading to the conclusion that strong interactions at high energy are generally rather ‘soft’.

Introduction

As we have constantly stressed, the great achievement of the SM model is the unification of the weak and electromagnetic interactions into a single gauge theory SU(2)L × U(1). The strong interaction gauge theory, the SU(3)C of QCD, is totally separate, and the totality of weak, electromagnetic and strong interactions has been treated as the juxtaposition SU(2)L × U(1) × SU(3)C. There are many attempts to unify all these forces into larger schemes such as a grand unification theory (GUT), i.e. to look for a single semi-simple Lie group to describe all the interactions, and which would contain SU(2)L × U(1) × SU(3)C as a subgroup.

There were early attempts to establish a ‘baryon–lepton’ (B–L) symmetry (Gamba, Marshak and Okubo, 1959). In more recent years, the outpouring of theoretical papers on grand unification theories, supersymmetric theories, supergravity theories and the boom of superstring theories is, perhaps, only exceeded by the frustration caused by the lack of any experimental indication that any one of these attempts is relevant to nature. The present limit of > 1032 years on the proton lifetime has ruled out the so-called minimal SU(5) (see Section 28.4) but this seems to be the only concrete assertion to emerge. It is very difficult at this time to imagine, for instance, that measurements of the proton lifetime will be able to discriminate among the various models. The rate of background due to cosmic rays will make it hard to detect proton decay if τp > 1033 years.

Our eventual aim is a simple and intelligible discussion of QCD and its applications to deep inelastic scattering, the Drell–Yan process and the cross-section for e+e− → hadrons etc. To achieve this, in this chapter we present a heuristic treatment of the ideas of regularization, renormalization and the powerful renormalization group technique. Then we introduce the concept of scaling and asymptotic freedom, initially for the case of scalar particles. The renormalization group results derived for scalar particles will be extended to the realistic case in Chapter 21, and applications, follow in Chapter 22. All technical elements are relegated to the Appendix to this chapter (Section 20.10) where we explain the technique of dimensional regularization.

Introduction

Most discussions of renormalization theory, in textbooks on field theory, are impenetrable and bogged down in technical complexities. Previously this did not matter very much. The important thing was to know that the theory was renormalizable, and the calculation of a few important effects could be left to a handful of experts. But the realization of the importance of the renormalization group in perturbative QCD and its constant use in all calculations of hard hadronic processes has meant that it is essential to understand at least the main ideas about schemes of regularization and renormalization.

For a book of its genre, our previous book, An introduction to gauge theories and the “new physics” (1982) was a great success. It was not, alas, sold in airport lounges, but it did run to two additional printings (1983, 1985), and to extensively revised editions in Russian (1990), and in Polish (1991). More importantly, it seemed to achieve the principal goal which we had set ourselves, namely, to present a pedagogical account of modern particle physics with a balance of theory and experiment, which would be intelligible and stimulating for both theoretical and experimental graduate students. We did not try to write a profound book on field theory, nor a treatise on sophisticated experimental techniques. But we did wish to stress the deep, intimate and fruitful interaction between theoretical ideas and experimental results. Indeed, for us, it is just this aspect of physics which makes it seem so much more exciting than say pure mathematics. Our greatest pleasure came from the favourable reaction of students who were working through the book and from those reviewers who caught what we hoped was its essential flavour—‘the writing creates the feeling of an active progression of ideas arising from the repeated interaction of theoretical prejudice with experimental observation’, ‘unlike most textbooks, it is highly readable, and makes everything appear simple and obvious’. Well, the last comment is surely an exaggeration but that was our aim.

Introduction

Although the earliest evidence for jets came from hadronic physics, it is in e+e− collisions that jets can be studied most cleanly. Thus, the first hint of planar (i.e. three-jet) configurations implying the existence of gluon jets came from PETRA in 1979. The field is, by now, dominated by LEP data at which energies several jets can be produced.

In this chapter we briefly discuss the historical developments and then turn to the most recent results. Some mention is made of models designed to bridge the gap between the QCD perturbative hard reactions and the non-perturbative process of hadronization. All these models use Monte Carlo simulations based on probabilistic descriptions; thus they cannot describe the subtle quantum mechanical effects that might occur. One should be able to attack this problem analytically but it may be a long time before a viable approach is found.

General outline of e+e− jets

Evidence for two-jet formation in the multihadronic final states in e+e− reactions above 5 GeV/c first emerged from the SLAC-LBL magnetic detector (Hanson et al., 1975; many excellent reviews of this group's data have appeared, see, for example, Hanson, 1976) at SPEAR and was based on the following pieces of data: (i) analysis of the mean sphericity variable (see below) to reconstruct the jet axis and comparison between a pure (isotropic) phase space model and a jet model;