Foundations of Perturbative QCD

Abstract

The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

An effective field theory for forward scattering and factorization violation

“…We will see that this pattern persists for hard scattering graphs (active-active graphs), but is not the case once we consider graphs with spectator quarks or gluons, where some Glauber exchange can be absorbed into collinear Wilson lines, while others cannot be absorbed at all. The fact that for partons in hard scattering the active-active Glauber contributions can be absorbed into soft Wilson lines is consistent with the contour deformation picture of CSS, where the combined soft+Glauber loop integral is deformed away from the Glauber region for active-active diagrams, and then further expanded to leave only contributions from what we call the naive soft region [21,31]. Similar logic to that of CSS was used to avoid having Glaubers in the amplitude level factorization theorem for final state particle production in [119].…”

“…The diagrams in figure 22a arise because there is a two-quark two-gluon Feynman rule in the L (0) n and L (0) n collinear Lagrangians. This n-collinear loop graph is proportional to a vanishing loop integral 31) and the same is true for then-collinear loop graph. On the other hand, the tadpole diagrams in figure 22b do not have vanishing collinear integrals.…”

“…First we note that in the CSS formalism [21,31] that Glauber contributions are discussed in detail, but are treated as a momentum region and hence are not fully separated from soft and collinear gluon dynamics. This has advantages for certain steps of a factorization proof, but makes it more difficult to associate unique contributions with Glauber exchange, and also to see how factorization arises for processes that retain nontrivial soft functions.…”

“…With this regulator the Glauber cross-box integral becomes 30) since the poles are on the same side. For the Glauber box integral we get 31) where the k z integral is evaluated in eq. (B.4).…”

Generalized Parton Distributions

“…-In this subsection we sketch the main steps in establishing a factorized description of a process. We will gloss over many technical details and refer the reader to [6,7,8] for a more careful treatment. The discussion will proceed in parallel for two example processes:…”