  We show how to use on-shell unitarity methods to calculate renormalization
group coefficients such as beta functions and anomalous dimensions. The central
objects are the form factors of composite operators. Their discontinuities can
be calculated via phase-space integrals and are related to corresponding
anomalous dimensions. In particular, we find that the dilatation operator,
which measures the anomalous dimensions, is given by minus the phase of the
S-matrix divided by pi. We illustrate our method using several examples from
Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and
beyond.
