In December 1947 I was invited to a small conference in the Dublin Institute of Advanced Studies. The Dublin Institute had been founded by the Irish government before World War II. The Irish saw the plight of Jewish and liberal scientists in Central Europe at that time. Eamon de Valera, the Taoiseach, a mathematician, saw he could help some of the scientists, and his own country, at the same time. So the Institute was started, with two schools, one for Theoretical Physics and one for Celtic Studies. Both have been very successful.

The Theoretical Physics school was established around two of the leaders of the early days of quantum mechanics, Erwin Schrödinger and Walter Heitler. After World War II de Valera decided to extend his very successful Institute by the addition of a School of Cosmic Physics, comprising three sections, meteorology, astronomy and cosmic radiation. He asked Lajos Janossy, another refugee who had spent World War II working in P. M. S. Blackett's laboratory in Manchester, to take charge of the cosmic ray section. Janossy had been one of my supervisors when I took my Master's degree at Manchester and he asked me would I be interested in the Assistant Professorship. So I went to Dublin to be inspected (and to inspect) as well as to attend the small conference.

One of the leading speakers at the conference was George Rochester, my other supervisor. He showed two Wilson cloud chamber pictures that he and Clifford Butler had taken with Blackett's magnetic cloud chamber.

When Gell-Mann and Zweig put forward their quark hypothesis, the maximum energy available at accelerators was 30 GeV (at Brookhaven National Laboratory, New York). This machine accelerated protons to this energy and then collided them against a stationary target. Machines of this type have now (May 1982) reached energies of 500 GeV (NAL) and 300 GeV (CERN). NAL is the National Accelerator Laboratory (often called Fermilab) at Batavia, Illinois and CERN is the Centre Européenne pour la Recherche Nucleaire at Geneva, Switzerland. But there is a class of accelerator, called colliding beam accelerators, in which, instead of colliding an accelerated beam of particles with a stationary target, we collide a beam with a beam. The first large machine of this type is the Intersecting Storage Rings (ISR) device at CERN. It collides two beams of 30 GeV protons. Because of relativity effects this is equivalent to colliding a beam of ˜ 2000 GeV protons with a stationary target. Recently, CERN has brought its SPS device into operation. This collides two beams, one of protons, the other of anti-protons, at energies of 250 GeV each. This is equivalent to an energy rather greater than 100000 GeV in a machine with a stationary target.

In 1963, 30 GeV seemed a large energy – quite enough to liberate a quark from a proton. One method of checking the quark hypothesis was to collide the protons and search the debris for fractionally-charged particles, with their characteristic ‘low ionisation’ signature. Another method was to examine the protons, looking for their internal structure, in the same way that Rutherford and his co-workers had looked at the structure of atoms.

This chapter deals with the search for free, unbound quarks. In the last chapter, and perhaps even more so in this, we have reached the cutting edge of research in particle physics. And as in many similar frontier style activities, things are not always nice, tidy and civilised. One of the main questions we address in this chapter is ‘have free quarks been found?’. There are three main answers: ‘yes’, ‘no’ and ‘maybe’. Of course, many people would prefer their answer to be qualified, such as ‘no, I don't think so’ or ‘maybe, but the evidence is not by any means totally convincing’. But of these three broad categories the answers of most particle physicists today would lie in the final two, ‘no’ or ‘maybe’ and the majority of these, I guess, would be in the ‘no’ class. I, on the other hand, would say ‘yes’. The first four chapters, I believe, are fairly unbiassed. I hope this one also turns out that way. But if there are any biasses you now know which way they are likely to lie.

The failure of the early attempts to find free quarks using accelerators at energies around 30 GeV had several consequences. The first of these was to stimulate searches in other areas, particularly in cosmic radiation, where energies much higher than 30 GeV occur. A related area to search is in condensed matter, where one might expect free quarks to accumulate if they came from the cosmic radiation, or were, perhaps, left over from an earlier stage of the Cosmos. Another consequence was to start people wondering if free quarks are ‘allowed’.

Introduction

Though many-body final states provide the bulk of the high energy scattering cross-section, individual final states are hard to analyse. They are hard to extract experimentally because it is essential to test (using energy, momentum, and quantum-number arguments) that the final-state particles observed in the detecting apparatus were the only particles produced, and to exclude all the many other different types of events which could have occurred. In particular the production of neutral particles is especially hard to detect. And, as we have found in the previous chapter, final states are also hard to analyse theoretically both because the number of independent variables increases rapidly with the number of particles, and because only a fraction of the events occur in regions of phase space which are easy to parametrize, such as the low sub-energy resonance region, or the high sub-energy Regge region.

Because of these problems it has been found more useful to concentrate attention on so-called ‘inclusive processes’, that is, processes in which a given particle or set of particles is found to occur in the final state, but no questions are asked about all the other particles which may also be present in this final state.

Introduction

One of the most important conclusions of chapters 2 and 4 was that whenever a Regge trajectory, α(t), passes through a right-signature integral value of J - v a t-plane pole will occur in the scattering amplitude because of the vanishing of the factor sin[π(α(t) + λ′)] in (4.6.2). And, as we found in section 1.5, such poles correspond to physical particles; to a particle which is stable against strong-interaction decays if the pole occurs below the t-channel threshold, or to a resonance which can decay into other lighter hadrons if it occurs above threshold. If a given trajectory passes through several such integers it will contain several particles of increasing spin, and so it is possible to classify the observed particles and resonances into families, each family lying on a given Regge trajectory. Some examples are given in figs. 5.5 and 5.6 below.

This chapter is mainly devoted to presenting the evidence for this Regge classification, but as there will be a different trajectory for each different set of internal quantum numbers such as B, I, S, etc. it will be useful for us first to examine briefly the way in which the particles have been classified according to their internal quantum numbers using SU(3) symmetry and the quark model. Readers requiring a more complete discussion than we have space for here will find the books by Carruthers (1966), Gourdin (1967), and Kokkedee (1969) very helpful.

Introduction

In section 4.8 we demonstrated that the occurrence of Gribov–Pomeranchuk fixed poles at wrong-signature nonsense points, generated by the third double spectral function, ρsu, requires that there be cuts in the t-channel angular-momentum plane. Otherwise it is impossible to satisfy t-channel unitarity. We have also found in section 6.8 that, despite the many successes of Regge pole phenomenology, there are some features of the data that poles alone cannot explain. These are mainly failures of factorization, and it seems natural to try an invoke Regge cuts, which correspond to the exchange of two or more Reggeons and so are not expected to factorize, to make good these defects.

Unfortunately we still have a much less complete understanding of the properties of Regge cuts than of the properties of poles. On the phenomenological side, this is mainly because it is difficult to be sure whether cuts or poles are responsible for what is observed, since the main tests, logs behaviour (see (8.5.12) below) and lack of factorization, are hard to apply. Though cuts do not have to factorize some models suggest that they do, at least approximately. We shall review some of these problems in section 8.7.

Also the various theoretical models which have been used to gain insight into the behaviour of Regge poles (discussed in chapter 3) are harder to apply to cuts. For example in potential scattering, which has only elastic unitarity and no third double spectral function, there are no Regge cuts if the potentials are well behaved.

Introduction

Having identified, in the previous chapter, some of the leading Regge trajectories from the resonance spectrum, we next want to look more closely at the other main aspect of Regge theory, the way in which Regge poles in the crossed t channel control the high energy behaviour of scattering amplitudes in the direct s channel.

For spinless-particle scattering this presents few problems; we would simply use the expression (2.8.10) in the region where t is small and negative, and s is large. However, for real experiments with spinning particles it is a bit more difficult because, as we shall find in the next section, the t-channel helicity amplitudes contain various kinematical factors, and are subject to various constraints, which must also be incorporated in the Regge residues. Also we shall need to look closely at the behaviour of the residue function when a trajectory passes through the nonsense points discussed in section 4.5. Only when we have clarified these kinematical requirements can we write down correct expressions for the Regge pole contribution to a scattering amplitude based on (4.6.15).

In exploring these kinematical problems we shall discover that some of the difficulties at t = 0 may imply the occurrence of additional trajectories called ‘daughters’ and ‘conspirators’, and we shall briefly review the application of group theoretical techniques to such problems. Also we examine the way in which the internal SU(2) and SU(3) symmetries constrain Regge pole exchange models.

Introduction

So far in this book we have been solely concerned with hadronic interactions, which are the principal field in which Regge theory has been used. We have ignored electromagnetic effects in assuming that isospin is an exact symmetry of the scattering processes, and have not needed to mention the weak-interaction properties of the particles such as β-decay, etc. But of course any discussion of the electromagnetic or weak interactions of hadrons necessarily involves consideration of their hadronic properties too, because it is the strong interaction which is mainly responsible for the composite structure of the hadrons. Regge theory has played a small but not insignificant role in the development of theories of these weaker interactions, and clearly if there is to be any chance of unifying all the interactions they must be reconciled with Regge theory. In this chapter we shall look rather briefly at the problems which may arise in so doing.

Basically there are two such problems. First, weak interactions (and from now on we shall usually use the word ‘weak’ to refer to both electromagnetism and the weak interaction) are generally formulated in terms of a Lagrangian field theory for the interaction of a basic set of elementary particles. These are the leptons, l (i.e. electron e, muon μ, and neutrinos ve, vμ), photon γ, vector boson W, etc., and elementary hadrons (which at least initially do not lie on Regge trajectories but occur as Kronecker δαJ terms in the J plane).