Understanding the QCD Cascade

QCD probed at high energies has effectively massless degrees of freedom. Thus it readily decays into softer modes. Thus a fundamental problem for those who want to understand the energetic hard interactions of a modern collider is understanding the properties of this cascade. Exclusive observables that constrain all of phase space with a single parameter allow for a clean theoretical treatment of the cascade, as shown by the comparison between theory and data for the thrust distribution for electron-positron colliders. Such observables, since they constrain all of phase space, are often called global. The properties of these global observable are closely tied to the quantum fluctuations of QCD, the virtual corrections. As soon as one asks more differential questions (non-global) about the phase space, carving it up into regions, the distribution of energies becomes much more difficult to predict from first principles. One needs to know the consistent history of the quantum mechanical decay from the UV to the IR. I will discuss how one can understand this consistent history as a quasi-particle like description of the QCD partons, resumming them into jets, which paves the way for a systematic theoretical control of phase space. Time permitting, I will also discuss the coherence properties of the QCD cascade, connections to small-x physics, and attempt to clarify the meaning of the renormalization group for these non-global observables.