Theoretical Framework
Jet physics, in particular at a hadron collider such as the LHC, cannot be understood without being thoroughly familiar with the theory of the strong interaction: quantum chromodynamics or short QCD. The material presented in this chapter is intended to p
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Theoretical Framework
Jet physics, in particular at a hadron collider such as the LHC, cannot be understood without being thoroughly familiar with the theory of the strong interaction: quantum chromodynamics or short QCD. The material presented in this chapter is intended to provide the required proficiency to comprehend experimental and phenomenological publications on the subject of jet physics, some of which will be discussed in detail in the later chapters of this book. Basic knowledge of other aspects of the Standard Model (SM) of particle physics is implied or expected to be looked up in one of the many relevant textbooks. Hints for further reading will be given at the relevant occasions. Before presenting a brief outline of the following sections, some notations need to be specified. Natural units, i.e. = c = 1 will be employed throughout so that energy, momentum, and mass all have units of eV = e · 1 V ≈ 1.6 × 10−19 J. In this context, it is particularly useful to recall that c = 1 ≈ 200 MeV · fm can be exploited to translate energy units into units of length and time. Cross sections are given in the customary unit of “barn”,1 1 b = 10−24 cm2 , with metric prefixes of “pico” or “femto” as appropriate for measurements in particle physics. The coordinate system that will be used is shown in Fig. 2.1, which defines the x, y, and z axes as well as some angular quantities. Symbols written as p represent three-vectors, while p normally denotes a four-vector. The notation for matrices is M. This chapter starts with a historical overview of the development of QCD, followed by a brief reminder of the basics of QCD theory. The next section deals with the central aspects of perturbative QCD. Subsequently, Monte Carlo event generators are introduced, followed by a thorough discussion of jet algorithms. The chapter is completed by a section on theoretical uncertainties and associated techniques for their evaluation. 1 The
use of the unit “barn” goes back to December 1942, when it was introduced during wartime by M.G. Holloway and C.P. Baker. Because of its connection to nuclear physics this information was classified until 1948 [1]. © Springer International Publishing Switzerland 2017 K. Rabbertz, Jet Physics at the LHC, Springer Tracts in Modern Physics 268, DOI 10.1007/978-3-319-42115-5_2
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2 Theoretical Framework towards the surface y
θ
φ
LHC beam pipe
westward z x towards the LHC centre
Fig. 2.1 Illustration of the coordinate system used by the LHC experiments at the example of the CMS detector: The experiments define a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z axis pointing along the direction of the counterclockwise beam. The x axis points from the IP to the centre of the LHC ring, and the y axis points upwards, perpendicular to the plane of the LHC ring. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the po
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