The Standard Model Effective Field Theory (SMEFT) provides a bottom-up, systematic way to quantify and explore the effects of physics beyond the Standard Model. In this context, my talk will describe how modern on-shell methods can aid the calculation of anomalous dimensions in EFTs with higher-dimension operators. Instead of the more familiar, but less physical, analysis of UV divergences and counterterms, the on-shell techniques focus directly on logarithms in physical quantities, and extract anomalous dimensions from their coefficients using unitarity cuts. I will present several applications of the on-shell formalism, including a new multi-loop non-renormalization theorem which constrains patterns of operator mixing; the reproduction of a significant part of the one-loop anomalous dimension matrix of the SMEFT computed by Manohar et al; and an exploration of the structure of the SMEFT two-loop anomalous dimension matrix.
