One-loop non-renormalization results in EFTs

In Effective Field Theories (EFTs) with higher-dimensional operators many anomalous dimensions vanish at the one-loop level. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to understand why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making the superfield formalism a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1)U(1) model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Lagrangian. This provides an understanding of why most “current–current” operators do not renormalize “loop” operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.