# Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients

## TL;DR

This paper extends the Universal One-Loop Effective Action (UOLEA) framework to include heavy-light loop contributions using covariant diagrams, simplifying the matching process for effective field theories involving both heavy and light particles.

## Contribution

It introduces a covariant diagram technique to incorporate heavy-light terms into the UOLEA, broadening its applicability for EFT matching.

## Key findings

- Successfully extended UOLEA to include heavy-light coefficients
- Demonstrated the method with a heavy singlet scalar example
- Simplifies the derivation of Wilson coefficients in EFTs

## Abstract

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.