New Covariant Feynman Rules for Effective Field Theories

TL;DR

This paper introduces a new, general formalism for calculating effective field theory matching contributions in a gauge covariant manner, utilizing Feynman rules and heat kernel techniques, with practical computational tools included.

Contribution

It presents a novel, simplified approach to compute effective actions at any loop order using covariant Feynman rules and heat kernel coefficients, enhancing previous methods.

Findings

Formalism is fully gauge covariant and general.

Provides a Mathematica code for computing heat kernel coefficients.

Applicable at any loop order for effective field theory matching.

Abstract

We provide a new and completely general formalism to compute the effective field theory matching contributions from integrating out massive fields in a manifestly gauge covariant way, at any desired loop order. The formalism is based on old ideas such as the background field method and the heat kernel, however we add some crucial new ingredients that greatly improve the simplicity and general applicability of the approach. We formulate our method in terms of Feynman rules, the resulting effective action is expressed in terms of local heat kernel coefficients. We also provide as supplementary material a mathematica code that facilitates the computation of these coefficients.