Covariant diagrams for one-loop matching

TL;DR

This paper introduces covariant diagrams, a diagrammatic method for simplifying one-loop matching calculations in effective field theories, enabling more concise derivations of universal results and accommodating complex structures.

Contribution

It presents a novel covariant diagram approach for one-loop matching, streamlining calculations and extending the applicability of universal formulas to complex scenarios.

Findings

Covariant diagrams organize one-loop matching terms effectively.

Universal results can be derived more concisely using this method.

The approach accommodates mixed heavy-light loops and other complex structures.

Abstract

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.