Deep inelastic scattering at high energies

Lippstreu, Luke

Deep inelastic scattering at high energies

Master Thesis

2018

Abstract

The primary purpose of this thesis is to provide a pedagogical introduction into the general formalism for applying the theory of Quantum Chromodynamics (QCD) to collider phenomenology. To this end, we frame the discussion in terms of one of the simplest, yet still one of the most important collider observables, the process of deep inelastic scattering. We begin by recounting three landmark experiments which lead to crucial breakthroughs in our understanding of the nucleus’s’ structure. We first describe the Geiger-Marsden experiment which provided the first evidence for the existence of the nucleus. We then describe the elastic electron-proton scattering experiments which first determined the scale of the nucleus. This is then followed by a discussion of the deep inelastic scattering experiments which gave the first evidence of Bjorken scaling. We then explain the theoretical line of reasoning which lead to the conclusion that Bjorken scaling implies that the field theory describing the nucleus must be of the Yang-Mills type. In the next chapter we outline the theory of factorization, which is the central framework for any collider experiment prediction. We first develop the tools necessary for the proof of factorization in DIS. This involves the general investigation of infrared singularities in a quantum field theory by use of the theory of pinch singular surfaces (PSS). We describe how PSS offer a useful tool for understanding many aspects of field theories such as the cancellation of infrared divergences in certain observables, as well as the existence of jets in collider experiments. We then outline the proof of factorization in DIS. We then describe the definitions and properties of the parton distribution functions and the hard scattering co-efficients used in factorization theorems. In the final chapter we study the cusp anomalous dimension which governs the large Bjorken-x behavior of parton distribution functions. We first motivate the use of a cusped Wilson line in the kinematic regime of large-x scattering. We then perform the one-loop calculation of a double cusped Wilson line. We then study the renormalization properties of lightlike Wilson lines. In so doing we are lead to an important QCD quantity the lightlike cusped anomalous dimension. Finally we indicate how this quantity governs the large-x behavior of the DGLAP splitting functions

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