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QCD

Multiple gluon/parton radiation

In this chapter one of the essential features of perturbative QCD will be presented and illustrated with a few, phenomenologically relevant examples. As a starting point the process ee→ hadrons will be discussed at first order in the strong coupling constant. This translates into the inclusion of a real or virtual gluon to the quark pair production at "parton-level". It will be shown that in so doing a new type of divergence occurs in both the real and the virtual part of the correction, but that these contributions cancel each other. This emergence of infrared divergences is related to the occurrence of massless spin-1 gauge bosons and it is a common feature to both QCD and QED. However, analysing them in some detail it will turn out that the real emission piece exhibits some logarithmically enhanced pieces; therefore the perturbation theory is rather the coupling constant times some large logarithm(s), αlog, than the coupling constant alone. Since the QCD coupling is roughly a factor of ten larger in than in QED this of course has a much more important effect. One of its visible results is the fact that QCD events often have a jetty structure, i.e. acclomerations of hadronic energy in well defined regions of phase space. This is one of the leading log effects. In fact, as it will turn out, some of the leading large logarithms can be resummed to all orders, thus taking proper care of all orders in αlog. This is important in particular when either jets in the final state or hadrons in the initial state are considered, a prime example for the latter being the case of deep inelastic ep-scattering. There, the logarithmic scaling violations where noticed first, namely in the behaviour of structure functions and parton distribution functions; they were treated in evolution equations such as the DGLAP equation. Another example fro the occurence of the same effect is the Drell-Yan process, where a lepton pair is produced in a hadron-hadron collision. This process will also be discussed. Therefore, the outline of this section is as follows: