Matchmakereft: automated tree-level and one-loop matching

TL;DR

Matchmakereft is an automated tool that performs tree-level and one-loop matching of models onto effective theories, ensuring gauge invariance and offering multiple checks, with broad applications in theoretical physics.

Contribution

It introduces a fully automated, flexible, and efficient tool for off-shell matching at one-loop level, including a detailed example with an extended Standard Model.

Findings

Successfully performs one-loop matching for complex models.

Provides multiple consistency checks through gauge invariance.

Enables automated calculation of renormalization group equations.

Abstract

We introduce matchmakereft, a fully automated tool to compute the tree-level and one-loop matching of arbitrary models onto arbitrary effective theories. Matchmakereft performs an off-shell matching, using diagrammatic methods and the background field method when gauge theories are involved. The large redundancy inherent to the off-shell matching together with explicit gauge invariance offers a significant number of non-trivial checks of the results provided. These results are given in the physical basis but several intermediate results, including the matching in the Green basis before and after canonical normalization, are given for flexibility and the possibility of further cross-checks. As a non-trivial example we provide the complete matching in the Warsaw basis up to one loop of an extension of the Standard Model with a charge -1 vector-like lepton singlet. Matchmakereft has been built with generality, flexibility and efficiency in mind. These ingredients allow matchmakereft to have many applications beyond the matching between models and effective theories. Some of these applications include the one-loop renormalization of arbitrary theories (including the calculation of the one-loop renormalization group equations for arbitrary theories); the translation between different Green bases for a fixed effective theory or the check of (off-shell) linear independence of the operators in an effective theory. All these applications are performed in a fully automated way by matchmakereft.