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

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…
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