We now progress from focusing primarily on issues of the Standard Model and QCD. Since throughout much of the rest of the book a focus will be placed on lepton scattering, particularly on electron scattering, we collect in this chapter some of the basic ideas behind this subject. The emphasis will be placed on the general aspects of the leptonic and hadronic tensors which, when contracted together, yield the basic quantity that determines the semileptonic cross section. Furthermore, the detailed discussions will be limited to inclusive scattering, namely, to reactions where the scattered lepton is assumed to be detected, but where any outgoing particles other than this lepton are not detected; the latter reaction where the lepton and at least one other particle are detected is called semi-inclusive and will be treated in later chapters (Chapter 9 for particle physics and Chapter 16 for nuclear physics). In addition to the general formalism for parity-conserving and parity-violating electron scattering, an introduction to the development of electromagnetic (EM) multipole operators is presented, as this will be important for later chapters where discrete states in nuclei that have good angular momentum and parity quantum numbers are considered.
After the formal developments in the present chapter we progress in Chapter 8 to elastic electron scattering from the proton and the insights that this gives us into the structure of the nucleon and its relevance for low-Q 2, strong-coupling QCD. Chapter 9 goes on to treat inelastic ep scattering with its underlying partonic modeling. Then, after an insertion (Chapter 10) where high-energy hadronic reactions are discussed as the way one studies quark–quark, quark–gluon and gluon–gluon interactions, we continue with the succeeding chapters where the developments here are employed – in few-body nuclei in Chapters 11 and 12, and in many-body nuclei in Chapters 13–16.
The lepton scattering process from a nucleon target provides a detailed “snapshot” of the target structure at a particular level of resolution. The highest resolution is provided by energetic, charged leptons, which interact with individual quarks and antiquarks inside a proton or neutron. These interactions, being sensitive to the motion of the struck quarks, can map the probability for finding the various constituents as a function of the fraction they carry of the nucleon's overall momentum.
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