The strong interaction between hadrons and nuclei leads to the phenomenon of shadowing. However, in the special situation of high-momentum-transfer coherent processes, these interactions can be turned off, causing the shadowing to disappear and the nucleus to become quantum-mechanically transparent. This phenomenon is known as colour transparency. In more technical language, colour transparency is the vanishing of initial- and final-state interactions, predicted by QCD to occur in high-momentum-transfer quasi-elastic nuclear reactions. These are coherent reactions in which one adds different contributions to obtain the scattering amplitude. Under such conditions the effects of gluons emitted by small colour-singlet systems vanish. Thus colour transparency is also known as colour coherence. The name ‘colour transparency’ is rather unusual. One might think that it concerns transparent objects that have colour, but it is really about how a medium can be transparent to objects without colour. This chapter provides a pedagogic review that defines the phenomenon and the conditions necessary for it to occur, assesses the role of colour transparency in strong interaction physics and reviews experimental and theoretical progress.

Point-like configurations

Strong interactions are strong: when hadrons hit nuclei they generally break up the nucleus or themselves. Indeed, a well-known classical formula states that the intensity of a beam of hadrons falls exponentially with the penetration distance. It is remarkable that QCD admits the possibility that, under certain conditions, the strong interactions can effectively be turned off and hadronic systems can move freely through a nuclear medium.

Within the Standard Model of particle physics, it is the strong phase of QCD that is least understood, and the electromagnetic interaction that is best understood. It is therefore natural to use the electromagnetic interaction as a relatively gentle probe of the internal structure of hadrons and of other aspects of non-perturbative strong interactions.

This approach is hardly new: electron scatteringwas first used to measure the charge distribution within the proton some 50 years ago. However, its importance has been enormously enhanced by the recent development of many experimental facilities dedicated to electromagnetic interactions, and the realization that other laboratories can access electromagnetic interactions in novelways. These facilities are primarily at low and medium energies, which probe the small-Q2 kinematic regions, and upgrades are planned. In contrast, existing high energy electron accelerators, such as HERA, are soon to close, and even B-factories in e+e- annihilation are coming to the end of their lives. The focus of electromagnetic and hadron physics will be on QCD in the strong interaction regime (‘strong QCD’) as distinct from perturbative QCD physics.

The physics of strong QCD falls mainly into two areas: hadron spectroscopy at low energies and non-perturbative aspects of high-energy processes. In spectroscopy, the ability to tune the virtuality of the photon in electroproduction enables the spatial structure of baryons to be explored; and since photons only couple directly to charged particles, they are a vital tool in separating the roles of quark and gluonic degrees of freedom within hadrons, and hence in filtering glueballs and hybrid mesons.

This chapter deals with properties of hadrons in high-energy scattering processes with special emphasis on spin dependence. We consider electroweak interactions, specifically lepton–hadron scattering that allows a separation of the scattering amplitude for the reaction into a leptonic part and a hadronic part, where the leptonic part involving elementary particles is known. The structure of the hadronic part is constrained by its Lorentz structure and fundamental symmetries and can be parametrized in terms of a number of structure functions. The resulting expression for the scattering amplitude can be used to calculate the cross sections in terms of these structure functions and, in turn, a theoretical study of the structure functions can be made. Part of this can be done rigorously with the only input, or assumption if one prefers, the known interactions of the hadronic constituents, quarks and gluons, within the standard model. For this both the electroweak couplings of the quarks needed to describe the interactions with the leptonic part via the exchange of photon, Z0 or W± bosons, as well as the strong interactions of the quarks among themselves via the exchange of gluons are important. For a general reference see the books of Roberts [1] or Leader [2].

Leptoproduction

In this section we discuss the basic kinematics of a particular set of hard electroweak processes, namely the scattering of a high-energy lepton, for example an electron, muon or neutrino, from a hadronic target, (k)H(P) l(k)X.

Generalized parton distributions (GPDs) have been recognized as a versatile tool to investigate and describe the structure of hadrons at the quark–gluon level. They are closely related to conventional parton distributions and also to hadronic form factors, but contain information that cannot be accessed with either of these quantities. Important areas where GPDs can provide new insight are the spatial distribution of quarks and gluons within a hadron and the contribution of quark orbital angular momentum to the nucleon spin. In this chapter we present the basics of the theory of GPDs, the dynamics they encode and the efforts of phenomenology and experiment to measure them in exclusive scattering processes. We do not attempt to give a comprehensive account of the vast literature and refer to the reviews [1–5] for more detailed discussion and references.

Experimental access to GPDs is provided in suitable hard scattering processes with exclusive final states, especially in processes initiated by a highly virtual photon. Recall that the cross section for inclusive deep inelastic scattering (DIS) is related to the amplitude for forward Compton scattering, γ* p → γ* p, via the optical theorem. In the Bjorken limit of large Q2 = -q2 at fixed xB = Q2/(2pq), this amplitude factorizes into a short-distance process involving quarks and gluons and the usual parton distributions which encode the structure of the target hadron at quark–gluon level. At leading order in αs one then obtains the handbag diagram in figure 9.1(a)

It has long been recognized that the study of nucleon resonances (N*) is one of the important steps in the development of a fundamental understanding of strong interactions. While the existing data on the nucleon resonances are consistent with the well-studied SU(6) ⊗ O(3) constituent-quark-model classification, many open questions remain. On the fundamental level, there exists only very limited understanding of the relationship between QCD [1], the fundamental theory of strong interactions, and the constituent-quark model or alternative hadron models. Experimentally, we still do not have sufficiently complete data that can be used to uncover unambiguously the structure of the nucleon and its excited states. For instance, precise and consistent data on the simplest nucleon form factors and the nucleon–Δ(1232) resonance (N–Δ) transition form factors up to sufficiently high momentum transfer are becoming available. Thus the study of N* structure remains an important task in hadron physics, despite its long history.

With the development since the 1990s of various facilities with electron and photon beams, extensive data on electromagnetic production of mesons have now been accumulated for the study of N* physics. These facilities include JLab, LEGS at Brookhaven National Laboratory and MIT-Bates in the USA; MAMI at Mainz and ELSA at Bonn in Germany; GRAAL at Grenoble in France and LEPS at Spring-8 in Japan. The details of these facilities are summarized in [2] and will not be included here. The main purpose of this chapter is to review the theoretical models used in analysing these data, and to highlight the results obtained.

Afundamental goal of nuclear and particle physics is to understand the structure and behaviour of strongly interacting matter in terms of its fundamental constituents. An excellent model of atomic nuclei is that they consist of protons and neutrons interacting by the exchange of pions. This is the view of the nucleus studied at low resolution. Hence, protons, neutrons and pions can be considered as the building blocks of the nuclei, a description valid for almost all practical purposes. Nonetheless, these building blocks are themselves composite particles, and studying their electromagnetic structure has been one of the main research thrusts of electron scattering.

The first studies of the electromagnetic structure of nucleons using energetic electron beams as probes began in the 1950s with the work by Hofstadter et al [1]. The experimental goal in these early measurements and in those that followed was to understand how the electromagnetic probe interacts with the charge and current distributions within nucleons. The embodiment of these interactions are the electromagnetic form factors. These quantities could be calculated if a complete theory of hadron structure existed. In the absence of such a theory, they provide an excellent meeting ground between experimental measurements and model calculations.

These nucleon form-factor measurements become increasingly difficult at high Q2 because the cross section is found to fall as ∼ Q-12 at high Q2 and the counting rates drop correspondingly. However, experimental techniques have progressed greatly since the early experiments and, together with the exploitation of spin degrees of freedom, have produced an impressive data set out to large Q2.

Chromostatics

The discovery of quarks in inelastic electron scattering experiments, following their hypothesized existence to explain the spectroscopy of hadrons, led rapidly to the quantum chromodynamic (QCD) theory and the Standard Model, which has underpinned particle physics for three decades. Today, all known hadrons contain quarks and/or antiquarks.

The QCD Lagrangian implies that gluons also exist, and the data for inelastic scattering at high energy and large momentum transfer confirm this. What is not yet established is the role that gluons play at low energies in the strong interaction regime characteristic of hadron spectroscopy. QCD implies that there exist ‘glueballs’, containing no quarks or antiquarks, and also quark–gluon hybrids. The electromagnetic production of hybrids is one of the aims of JLab. Glueballs, on the other hand, are not expected to have direct affinity for electromagnetic interactions; hence hadroproduction of a meson that has suppressed electromagnetic coupling is one of the ways that such states might be identified.

Quarks are fermions with spin ½ and baryon number ⅓. A baryon, with half-integer spin, thus consists of an odd number of quarks (q) and/or antiquarks (q), with a net excess of three quarks. Mesons are bosons with baryon number zero, and so must contain the same number of quarks and antiquarks.

In the Standard Model the up and down quarks – the constituents of normal matter – couple very weakly to the electroweak Higgs field. The resulting ‘current’ masses for these quarks are of the order of 10 MeV. This is much smaller than the typical energies of hadronic states (several hundred MeV or more). In the context of low-energy QCD, this means that these quarks are nearly massless and so, to a good approximation, their chiralities are preserved as they interact with vector fields (gluons, photons, Ws and Zs). This conservation of chirality has important consequences for hadronic physics at low energies.

If chirality is conserved, then right- and left-handed quarks are independent and we have two copies of the isospin symmetry which relates up and down quarks. The QCD Lagrangian therefore is symmetric under the chiral symmetry group, SU(2)R x SU(2)L. However, the hadron spectrum shows no sign of this larger version of isospin symmetry; in particular, particles do not come in doublets with opposite parities. Moreover, constituent quarks, as the building blocks of hadrons, appear to have masses that are much larger than their current masses.

This conundrum can be resolved if the chiral symmetry of the theory is hidden (or spontaneously broken) in the QCD vacuum. A non-vanishing condensate of quark- antiquark pairs is present in the vacuum, and this is not invariant under SU(2)R SU(2)L transformations. The energy spectrum of quarks propagating in this vacuum has a gap (like that for electrons in a superconductor), implying that masses have been dynamically generated.

Charged-current interactions are the most frequent and occur in decays, as well as in particle reactions. They have been analyzed in many books, especially those written before 1970. Charged-current interactions, especially decays, were instrumental in establishing properties of the currents. We can classify them according to the degree of our theoretical understanding. The simplest reactions are purely leptonic. They are relatively simple to calculate, because the couplings of leptons to currents are precisely known and, now that the theory is renormalizable, we can include loop corrections. Some leptonic reactions were presented in Chapter 8. We shall not study them further.

The next class of reactions consists of the semileptonic ones, which can also be treated successfully with various theoretical methods. They involve a single coupling of the currents to hadrons, which can be understood at low energy and/or at low momentum transfer in terms of form factors. They are also understood at high energies in terms of the short-distance behavior of the currents. We shall study several processes in this chapter: deep inelastic scattering and quasi-elastic scattering.

Non-leptonic interactions are the most difficult to analyze. They do not include any leptons and involve both strong and weak interactions. The interplay between the two interactions is still a developing field of research.

Deep inelastic scattering

High-energy neutrino interactions have been used to probe the inner structure of protons and neutrons: these studies were crucial for establishing the quark substructure of matter and giving quantitative support to the field theory of quark interactions (quantum chromodynamics). In Chapter 10 we described the general structure of the cross sections and some consequences of the scaling phenomenon.