Mixed Heavy-Light Matching in the Universal One-Loop Effective Action

TL;DR

This paper extends the Universal One-Loop Effective Action framework to include mixed heavy-light particle loops, providing a simple, universal method for calculating their contributions to effective field theories, demonstrated with an electroweak triplet example.

Contribution

It introduces a straightforward prescription for incorporating mixed heavy-light loops into the universal one-loop effective action, preserving its structure and identifying previously neglected terms.

Findings

The method accurately accounts for mixed heavy-light loop contributions.

Application to electroweak triplet scalar demonstrates practical utility.

New structures in the effective action are identified and characterized.

Abstract

Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass-dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.