  We use the on-shell S-matrix and form factors to compute anomalous dimensions
of higher dimension operators in the Standard Model Effective Field Theory. We
find that in many instances, these computations are made simple by using the
on-shell method. We first compute contributions to anomalous dimensions of
operators at dimension-six that arise at one-loop. Then we calculate two-loop
anomalous dimensions for which the corresponding one-loop contribution is
absent, using this powerful method.
