QCD and formal methods

Abstract

This chapter begins with a brief introduction to quantum chromodynamics (QCD), highlighting the similarities and differences with quantum electrodynamics (QED). QCD gives a non-linear force that confines quarks inside hadrons at large distances but is weak at short distances, thus providing justification for the simple QPM. Essential ‘tree-level’ diagrams are evaluated using the corresponding QED processes and QCD colour factors. The problems of infrared and ultraviolet divergences in both QED and QCD are outlined, with emphasis on the physical ideas underlying their resolution. This leads on to the idea of a running coupling. The rest of the chapter is concerned with an outline of the operator product expansion, which is the more formal method used to derive many results used in the QCD-enhanced parton model. Finally, the crucial idea of factorization — the calculation of a DIS cross-section by convolution of a point-like cross-section with parton momentum densities — is introduced.