Perturbative Qcd for Beginners

Basic elements of the perturbative QCD approach to multiparticle production in hard processes are discussed. Instead of Introduction I had a hard time writing these lectures. You will have a hard time reading them. Don't take it as the author's fault: it is rather part of the author's design. I met in Dubna young experimenters, eager to learn. Some of them would ask not just \How probable is it to have this-and-that", but the most clever questions such as \Why on earth..." or \How come that..." or even \How could I estimate the fraction of such-and-such events". Those students are to blame for what follows. Hearing things and an easy reading can only give an illusion of understanding. To really learn the game one should try playing. The present course was designed as a dull introduction into the realm of quarks and gluons as QCD partons. We shall discuss why and to which extent an entirely classical probabilistic language of partons is applicable to the analysis of multiparticle production in quantum eld theory in the rst place. We shall spend quite some time with the basic ingredients of the QCD parton picture: the nature of logarithmically enhanced contributions to high-order hard interaction cross sections; the notion of parton evolution; and the problem of coherence e ects due to quantum interference, which reveals itself in a clever choice of the \evolution time". We shall study the main building blocks: parton splitting functions, all-order double logarithmic form factors, the running coupling. Scanning through the text, you will occasionally see some formula-free pages. Don't rush in there. I believe these lectures may help you to develop physical intuition and to learn to apply it for practically producing interesting, reliable back-of-an-envelope estimates. To get there, however, you had better prepare yourself to a slow reading and keep a pencil and a (A4) notepad at hand. You will nd quite a few Exercises and Problems on the way. The former are to train your hand in performing typical calculations; the latter will require activation of grey cells prior to a hand. Try them. Don't hurry up to the solutions supplied. Good luck. May the colour force be with you. Lecture 1. BASICS OF BREMSSTRAHLUNG We start our excursion with a survey of the process of soft photon radiation accompanying hard scattering of an electron, that is the QED bremsstrahlung. Speaking of a hard process (scattering, interaction, etc.) one means a process in which a charged particle experiences an impact with large momentum transfer, Q jq2j m. The main characters of the rst lecture will be Electrons and Photons (with Quarks and Gluons explicitly appearing only on special occasions when QCD subtleties come onto the stage). It is implied that all conclusions we shall arrive at considering basic properties of QED bremsstrahlung hold in the QCD context as well, that is when soft gluon radiation is concerned. Consider electron scattering o an external eld V accompanied by the emission of a photon with the 4-momentum k. The radiation amplitude is described by the two graphs of Fig. 1.