17. Heavy-Quark and Soft-Collinear Effective Theory 1 17. HEAVY-QUARK AND SOFT-COLLINEAR EFFECTIVE THEORY

Quantum field theories represent the most precise computational tool for describing physics at the highest energies. One of their characteristic features is that they almost inevitably involve multiple length scales. When trying to determine the value of an observable, quantum field theory demands that all possible virtual states and hence all particles be included in the calculation. Since these particles have widely different masses, the final prediction is sensitive to many scales. This fact represents a formidable challenge from a practical point of view. No realistic quantum field theories can be solved exactly, so that one has to resort to approximation schemes; these, however, are typically most straightforward when only a single scale is involved at a time. Effective field theories (EFTs) provide a general theoretical framework to deal with the multi-scale problems of realistic quantum field theories. This framework aims to reduce such problems to a combination of separate and simpler single-scale problems; simultaneously, however, it provides an organization scheme whereby the other scales are not omitted but allowed to play their role in a separate step of the computation. The philosophy and basic principles of this approach are very generic, and correspondingl