Renormalization of Higher-Dimensional Operators from On-shell Amplitudes

Understand

On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations.

• We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators from a product of tree-level amplitudes.
• We show how this works for dimension-6 operators of the Standard Model, providing explicit examples of the simplicity, elegance and efficiency of the method.
• Many anomalous dimensions can be calculated from the same Standard Model tree-level amplitude, displaying the attractive recycling aspect of the on-shell method.