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The QCD improved parton model provides the foundation on which all the remaining chapters are based. This chapter begins by covering the key ideas: tree level QCD Compton and boson-gluon fusion processes give rise to characteristic gluonic ‘radiative corrections’ to the QPM; infrared singularities are absorbed by renormalizing the parton densities, which thus become Q² dependent and no longer satisfy exact Bjorken scaling. The next section covers the DGLAP evolution equations, which enable the Q² dependence to be calculated perturbatively using ‘splitting functions’. To give an insight into the effect of these equations, some simple numerical examples are given in the following section. The relationship between the more formal Operator Product Expansion method outlined in the previous chapter and the DGLAP approach is indicated. The last three sections comment on: higher twist; the extension of the DGLAP formalism to accommodate heavy quarks; and the extension of the DGLAP formalism to higher orders.

This chapter is concerned with physics at low values of Bjorken x, below 0.01, where the q-qbar sea and gluon are the dominant partons and increasing rapidly as x decreases. It starts with an overview of the approaches considered and their regions of validity in the ln(1/x)-ln(Q² ) plane. Then follows an account of the ‘standard’ approaches: DGLAP equations at low x and the Regge approach to total cross-sections. The hard and soft Pomerons are introduced and explained, followed by the BFKL equation. Angular ordering of gluon radiation and the CCFM approach to DIS comes next. These aforementioned approaches are linear and lead to an undamped increasing structure function as x decreases, which will violate unitarity eventually. This problem and how non-linear effects ameliorate it are covered next. The last section gives a comparison of the low-x approaches with structure-function data and outlines the need for precision measurements of other observables.

This chapter begins with the formal derivation of QCD as a gauge theory based on the symmetry group SU(3). It then describes the basic reactions of lepton-lepton, lepton-hadron, and hadron-hadron scattering in the language of QCD, and derives the born-level expressions for the basic QCD cross-sections. The chapter addresses the issue of ultraviolet divergences and renormalization. It discusses the renormalization group equations and the issue of infrared-safety in the context of the QCD improved parton model. The treatment of soft gluons then leads naturally to the various hadronization models, which form the basis of the Monte Carlo models discussed in the following chapter.

This chapter centres around the treatment of QCD emissions to all orders. After introductory remarks about the analytic properties of the radiation pattern, some of the most striking phenomenological consequences of non-trivial quantum effects, in particular, the angular ordering property of QCD, are highlighted. Next, analytic resummation techniques are considered, expanding on the treatment of transverse momentum resummation from Chapter 2, and introducing the idea of threshold resummation. BFKL resummation, which resums large logarithms emerging in the high-energy limit, is also introduced. In the second part of this chapter, the probabilistic simulation of QCD radiation through the parton shower is discussed. After a detailed introduction to different schemes and algorithms, the discussion of the combination of the parton shower with fixed-order matrix elements beyond the Born approximation is considered, with a discussion of matching with NLO calculations and the merging with multijet matrix elements.

Parton Distribution Functions (PDFs) are a necessary ingredient in the calculation of cross sections at collider experiments with hadron beams. This chapter explores the techniques of determining the PDFs and their uncertainties, based on global analyses of data sets arising from a variety of hard-scattering processes. PDFs are determined at leading order, next-to-leading order, and next-to-next-to-leading order, with the corresponding orders of hard coefficients and evolution. Differences in the PDFs of different orders, and in their uncertainties, are described. Combinations of PDFs from different global fitting groups are discussed, and several useful tools for comparisons of PDFs are described.

This chapter first discusses the breaking of scale invariance of QCD with massless quarks by quantum corrections and explains that this effect is responsible for the bulk of hadron masses. Then the parton picture is introduced, where one replaces a hadron which is probed in a hard process by free quarks and gluons. Perturbative QCD describes via the DGLAP equations the evolution of parton distribution functions f(x,Q2) as functions of Q2, requires however as as input f(x,Q20) from measurements at a fixed scale Q0 »QCD. The total annihilation cross section e+e →hadrons is calculated and it is shown that infrared singularities due to massless gluons and quarks cancel.