Integrating out heavy particles with functional methods: a simplified framework

TL;DR

This paper introduces a simplified functional method to derive one-loop low-energy effective Lagrangians by integrating out heavy particles, streamlining the matching process in quantum field theories.

Contribution

It presents a new systematic procedure that simplifies the calculation of effective Lagrangians by focusing on the hard region of the functional determinant, reducing computational complexity.

Findings

The method accurately reproduces known effective Lagrangians.

It simplifies the matching procedure compared to traditional approaches.

The approach is validated with toy models and extensions of the Standard Model.

Abstract

We present a systematic procedure to obtain the one-loop low-energy effective Lagrangian resulting from integrating out the heavy fields of a given ultraviolet theory. We show that the matching coefficients are determined entirely by the hard region of the functional determinant involving the heavy fields. This represents an important simplification with respect the conventional matching approach, where the full and effective theory contributions have to be computed separately and a cancellation of the infrared divergent parts has to take place. We illustrate the method with a descriptive toy model and with an extension of the Standard Model with a heavy real scalar triplet. A comparison with other schemes that have been put forward recently is also provided.