ABSTRACT
Our analysis of QCD in Chapter 17 was founded on the principle of asymptotic freedom, which told us that strong interaction processes with large momentum transfer might reliably be treated in weak-coupling perturbation theory. So far, however, we have made little use in QCD of the more powerful tools of the renormalization group. In this chapter, we will work out some implications of the Callan-Symanzik equation in QCD. We will see that asymptotically free theories have their own characteristic scaling behavior, with corrections in the form of anomalous powers of logarithms of the momentum scale. Though these corrections are generally weaker than those in the scalar field theories studied in Chapter 13, they nevertheless have important qualitative effects on the strong interactions.
