Anomalous dimensions via on-shell methods: Operator mixing and leading mass effects

We elaborate on the application of on shell and unitarity-based methods for evaluating renormalization group coefficients, and generalize this framework to account for the mixing of operators with different dimensions and leading mass effects. We derive a master formula for anomalous dimensions stemming from the general structure of operator mixings, up to two-loop order, and show how the Higgs low-energy theorem can be exploited to include leading mass effects. A few applications on the renormalization properties of popular effective field theories showcase the strength of the proposed approach, which drastically reduces the complexity of standard loop calculations. Our results provide a powerful tool to interpret experimental measurements of low-energy observables, such as flavor violating processes or electric and magnetic dipole moments, as induced by new physics emerging above the electroweak scale. Published by the American Physical Society 2024