The Regge theory we have described in the previous chapters applies equally well when either or both of the initial hadrons is replaced with a current, for example the electromagnetic current. In particular, we may replace one of the hadrons with a real photon. This is obviously true if we may use the vector-meson dominance model, in which the photon is assumed to behave just like an on-shell ρ or another vector particle. But the vector-dominance assumption is not necessary: the applicability of Regge theory does not depend on it. Most reactions discussed in this chapter are ones involving pomeron exchange. However in section 5.6 we discuss pion photoproduction with two objectives: one is to compare and contrast π0 photoproduction with π–p charge exchange; and the other is to look at the role of pion exchange in charged pion photoproduction.

Photon-proton and photon-photon total cross sections

The photon-proton total cross section should be fitted by forms similar to the hadron-hadron total cross sections in figures 3.1 and 3.2. This is verified in figure 5.1. Extending the fit to low energies confirms the two-component duality hypothesis, as is seen in figure 5.2. We discuss in section 7.5 whether the fit should include an additional component, the hard pomeron.

The γγ total cross section can be predicted from the known pp, p̅p, pn, p̅n and γp total cross sections. We need to determine the C = +1 exchange contributions.

In 1935 the Japanese physicist Hideki Yukawa predicted that there must be a particle, now known as the pion, which would transmit the strong interaction. The pion was duly discovered more than ten years later. However, we now know that although pion exchange is an important component of the static force, when the force acts between a pair of particles with high energy a very large number of particles collaborate in transmitting it. Regge theory provides a simple quantitative description of the combined effect of all these particle exchanges.

It was soon realised that the exchanges of the known particles, even though several hundred are listed in the data tables, are not sufficient to describe a striking feature of the strong force: that it retains its strength as the energy increases and even becomes yet stronger. To explain this, it must be that something else is exchanged. This new object was named after the Russian physicist Isaac Pomeranchuk. It was originally called the pomeranchukon, but this was later abbreviated to pomeron. Events in which a pomeron is exchanged are often called diffractive events. The reason for this is that pomeron exchange dominates in high-energy elastic scattering and, as we describe in chapter 3, when plotted against scattering angle the differential cross section has a striking dip, reminiscent of the intensity distribution in optical diffraction. However, we explain that actually the mechanism for dip generation in high-energy scattering is more complicated than in optical diffraction.

The experimental and theoretical study of diffractive phenomena has been very fruitful over the last two decades. With the ongoing experiments at HERA, the Tevatron and RHIC, and the start-up of the LHC, this field of research will remain of high topical interest. It is clear that the description of diffractive phenomena through QCD is rather complicated. Thus, what can we hope to learn by studying diffractive phenomena? For testing the basic principles of QCD in experiment and for determining the fundamental parameters of QCD we should choose simple reactions where perturbation theory is without doubt applicable. In the nonperturbative domain we should choose quantities which can be calculated reliably on the lattice. Diffractive phenomena are unlikely to be of direct benefit here, until theorists make significant progress with their calculational methods. Diffraction can be considered as an area for “applied QCD”, where theorists have been developing various approximation schemes in order to understand the observed phenomena. For this a continual interplay of experiment and theory has been essential, and in the future will still be so. It has been the experimental possibility of studying diffractive phenomena under conditions very different from elastic hadron-hadron scattering which has brought diffractive phenomena to the fore and stimulated so much theoretical development. In this final chapter we review briefly the outstanding issues.

Regge theory, introduced more than forty years ago, remains remarkably successful in providing a phenomenological description of soft high-energy hadronic and photon-induced processes.

In this chapter we discuss an approach whereby soft diffractive phenomena are treated from a microscopic point of view starting from the scattering of the hadrons constituents, that is quarks and gluons, and we relate scattering phenomena to properties of the QCD vacuum. We have argued in chapter 6 that in QCD total cross sections are essentially nonperturbative quantities. Thus it is quite natural to think about a possible connection between the nontrivial vacuum structure of QCD, which is a typical nonperturbative phenomenon, and soft high-energy reactions.

The Landshoff-Nachtmann model

The Landshoff-Nachtmann model[7] seeks to understand some features of diffractive phenomena in hadron-hadron scattering in terms of the exchange of two nonperturbative gluons between quarks. It was shown that this model is capable of reproducing the additive-quark rule for total cross sections[89,415417], which we introduced in chapter 3. If one calculates two-gluon exchange in QCD perturbation theory, one does not obtain such a result[418,298]. By making detailed assumptions about the nature of the wave functions of mesons and baryons, it is possible to obtain the additive-quark rule for total cross sections from perturbative two-gluon exchange [419,420]. However, this perturbative exchange of two gluons gives the elastic hadron-hadron scattering amplitudes a singularity at t = 0 and does not reproduce the t dependence found in experiment. The observed t dependence is rather related to the elastic form factor and is obtained naturally when one makes the pomeron couple to single quarks like an even-signature isoscalar photon.

Modern high-energy physics may be said to have begun with the deep-inelastic electron-scattering experiments at the Stanford Linear Accelerator in the late 1960s. In these experiments, an electron is made to collide with a proton; the electron radiates a virtual photon γ*, which strikes the proton and breaks it up, as is shown in figure 7.1. Similar experiments have since been performed, at progressively higher energies. Some of these instead have been with muon beams, and there have also been related experiments with neutrino beams. The highest energy achieved so far has been at the electron-proton collider HERA in Hamburg.

In this chapter we describe the phenomenology and the theory of deep-inelastic lepton scattering. The theory relates it to various other semi-hard processes and brings together perturbative QCD and Regge ideas.

Deep-inelastic lepton scattering

Figure 7.1 describes deep-inelastic electron or muon scattering. We see that, effectively, it explores the scattering of the virtual photon on the proton, so as to form a system X of hadrons. Factoring off a γ* flux from figure 7.1, we may identify the remaining factor as the γ*p cross section. Figure 7.1 is well-defined but, as one may adopt different definitions of a γ* flux, the precise definition of σγ*p is a matter of convention, except for the case of real photons; see (7.6). Whatever definition is used, the optical theorem relates the total γ*p cross section, summed over X, to the imaginary part of the forward virtual-Compton amplitude; see figure 7.2.