  On-shell amplitude methods have proven to be extremely efficient for
calculating anomalous dimensions. We further elaborate on these methods to show
that, by the use of an angular momentum decomposition, the one-loop anomalous
dimensions can be reduced to essentially a sum of products of partial waves. We
apply this to the SM EFT, and show how certain classes of anomalous dimensions
have their origin in the same partial-wave coefficients. We also use our result
to obtain a generic formula for the one-loop anomalous dimensions of nonlinear
sigma models at any order in the energy expansion, and apply our method to
gravity, where it proves to be very advantageous even in the presence of IR
divergencies.
