This book has covered many of the primary topics in perturbative QCD, with a focus on certain inclusive processes for which particularly systematic treatments are available. It should provide the reader with a sound conceptual framework for further study and research. However, hadronic interactions form a vast subject, and there is an enormous literature where perturbatively based methods have been applied.

This chapter gives a summary of a selection of important areas of further application of perturbative QCD.

One common theme, a prerequisite for actual perturbative calculations, is that the reactions have in some sense a controlling hard subprocess, occurring on a short distance scale, i.e., a distance scale significantly less than 1 fm, or, more-or-less equivalently, a momentum transfer significantly larger than the typical hadronic scale of a few hundred MeV.

Another recurring idea, perhaps the closest to a unifying motif, is the idea that one should try to separate (factor) phenomena on different scales of distance and momentum. This refers not just to scales of different virtuality, but also to a separation of phenomena at widely different rapidities. A characteristic here is that almost scattering processes examined in high-energy physics are ultra-relativistic. Thus time dilation and Lorentz contraction of fast-moving hadrons by themselves provide a wide range of distance scales. For example at the Tevatron collider we have proton and antiproton beams of energy almost 1 TeV. This allows the measurement of hard processes with momentum scales of several hundred GeV.