Express the sum in (11.57) in terms of the valence and sea...

Express the sum in (11.57) in terms of the valence and sea quark structure functions introduced in Chapter 9. Do the same for lepton pair production in $\overline{\mathrm{p}} \mathrm{p}$ and $\pi{ }^{ \pm} \mathrm{p}$ interactions.

Key Concepts

Structure Functions

Structure functions provide a quantitative description of how momentum and spin are distributed among the partons (quarks and gluons) inside hadrons. They are fundamental in deep inelastic scattering and related high-energy processes, encapsulating the probability densities for finding a parton carrying a fraction of the parent hadron’s momentum. In this context, they are re-expressed in terms of contributions from different types of quarks.

Quark-Parton Model

The quark-parton model is a framework used to describe hadrons as composites of quarks and gluons. In high-energy experiments, the scattering processes are understood by considering interactions between the incoming lepton and the constituent partons. This model underlies the interpretation of structure functions and the separation of contributions from valence and sea quarks in various processes.

Valence Quark Distributions

Valence quark distributions describe the momentum distributions of the quarks that determine the quantum numbers of the hadron. They represent the dominant, intrinsic components of the hadron’s structure and are essential for understanding the leading contributions to the structure functions in scattering processes.

Sea Quark Distributions

Sea quark distributions account for quark-antiquark pairs that are spontaneously created from the gluon field within the hadron. These distributions are important for capturing the full partonic content of the hadron, contributing to corrections in processes and measurements where non-valence quark contributions are significant.

Lepton Pair Production (Drell-Yan Process)

Lepton pair production in hadronic collisions, commonly described by the Drell-Yan process, involves the annihilation of a quark and an antiquark into a virtual photon or Z boson that subsequently decays into a lepton pair. Expressing the summation in terms of valence and sea quark structure functions enables one to analyze the contributions from different parton sources in both proton–antiproton and meson–proton interactions.

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