One Formula To Match Them All: The Bispinor Universal One-Loop Effective Action

TL;DR

This paper introduces the BSUOLEA, a general pre-computed expression for one-loop effective actions, enabling automated matching of UV models to EFTs, including complex models with constraints, significantly streamlining effective field theory calculations.

Contribution

The paper develops the BSUOLEA framework, a universal, pre-computed one-loop effective action expression, and implements it in a Mathematica package for automated model-to-EFT matching, including non-renormalisable models.

Findings

Derived the general BSUOLEA expression for one-loop matching.

Implemented the framework in a Mathematica package for automated calculations.

Applied the method to the Singlet Extended SM and a vector resonance model.

Abstract

Extensions of the Standard Model (SM) often contain new particles with masses far above the electroweak scale. Due to the presence of a mass hierarchy, effective field theory (EFT) is a suitable tool for the study of such extensions. In this thesis, we provide a solution to the matching problem at the one-loop level in the form of the Bispinor Universal One-Loop Effective Action (BSUOLEA), which is a pre-computed expression for the effective action, parameterised in terms of derivatives of the Lagrangian of the ultraviolet (UV) model. The BSUOLEA is derived using functional methods and is sufficiently general to match any renormalisable, Lorentz invariant UV model to an EFT, containing operators of mass dimension up to and including six at the one-loop level. This includes supersymmetric models regularised in dimensional reduction. Since the pre-computed expression contains many operators, it is implemented into a currently private Mathematica package, which automatically performs the matching based on the BSUOLEA. We illustrate the use of this package, which will be made publicly available in the near future, by applying it to the matching of the Singlet Extended SM to the SM EFT. We then expand the framework in order to apply it to a non-renormalisable extension of the SM containing a vector resonance, which is assumed to arise from the confinement of a gauge group at high energies. This model raises some interesting theoretical questions since such a vector resonance comprises a system with second-class constraints. We perform the constraint analysis of the model and derive the generating functional in order to apply functional methods to the matching. We finally match the model to the SM EFT and present the full one-loop result including operators up to mass dimension six.