The Universal One-Loop Effective Action

TL;DR

This paper derives a universal one-loop effective action applicable to various operators and models, simplifying the process of matching ultraviolet theories to low-energy effective field theories by eliminating complex loop integrals.

Contribution

It provides a general, universal formula for one-loop effective actions up to dimension six, applicable to both fermions and bosons, streamlining EFT matching procedures.

Findings

Validated against existing literature results.

Applied to supersymmetric squark models to extract Wilson coefficients.

Simplifies one-loop matching by reducing calculations to matrix evaluations.

Abstract

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has been checked against partial results available in the literature. The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is now reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate. We illustrate the relationship of our results to the Standard Model (SM) EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields.