arXiv subjects

Anders Eller Thomsen

Publications and source records attributed to Anders Eller Thomsen.

At least 19 recordsLinked to original sources

arXiv2026

UFO Sightings with Matchete: Connecting BSM Lagrangians with Event Generators

We present a tool for the automated generation of Universal Feynman Output (UFO) files, used as input by many event generators, for generic Beyond the Standard Model (BSM) theories and their low-energy Effective Field Theory (EFT) descriptions. Building on the Matchete package, which provides a convenient interface for defining BSM models and deriving their EFTs via matching, our extension obtains the Lagrangian in the broken phase of the electroweak symmetry, performs automatic gauge fixing, computes all Feynman rules, imposes flavor symmetries, and exports the model in the UFO format. This significantly streamlines BSM and EFT analyses, as we illustrate with an EFT validity study for a multi-channel leptoquark search. As an application, we provide a complete UFO implementation of the Standard Model EFT up to dimension eight using the $M_W$ electroweak input scheme.

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arXiv2026

On the Renormalization Group in EFTs: On-Shell Bases, Ambiguities, and Divergences

Recent results for two-loop renormalization group (RG) functions in effective field theories exhibit unphysical divergences when calculated in an on-shell operator basis. We demonstrate that this can be understood to be a result of omitting non-minimal source terms in the renormalized vacuum functional, which are essential to maintaining renormalizability of and describing the RG flow of Green's functions in an on-shell framework. With the inclusion of the missing source terms, any remaining divergences are ambiguous, generating only unphysical RG flow directed along flavor rotations, and the RG functions are RG-finite. We carefully examine the role of flavor rotations in generating ambiguities in both on- and off-shell RG functions and explore the geometry of a physical coupling space.

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arXiv2026

When Two Loops Matter: Electroweak Precision in the SMEFT

We identify a novel next-to-leading order renormalization effect in the dimension-six SMEFT with direct phenomenological impact. The Higgs-Yukawa operator that modifies the top-Higgs coupling $κ_t$ induces a shift in the $ W $ mass at two-loop order through a large anomalous dimension, rendering electroweak precision observables a powerful indirect probe of $κ_t$. We show that this effect is essential for the consistent interpretation of data from future Tera-$Z$ and Giga-$W$ factories such as FCC-ee. The effect is realized in a simple renormalizable two-Higgs doublet model.

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arXiv2026

Next-to-Leading Order Running in the SMEFT

The next-to-leading order (NLO) Standard Model Effective Field Theory (SMEFT) renormalization group equations are needed to account for phenomenologically relevant operator mixing and ensure renormalization scale independence in NLO calculations of observables. For the first time, we present the renormalization group equations of the baryon-number-conserving sector of the dimension-six SMEFT up to two-loop order. Our calculations have been performed using functional methods with an anticommuting $ γ_5 $-scheme. A variety of strategies are employed to mitigate the reading-point ambiguities inherent to this scheme choice. We also describe how a local version of the $ \boldsymbol{R}^\ast $-method is adapted to handle the evanescent operators arising in dimensional regularization. The results are provided in various supplementary files to make them accessible for both human inspection and numerical implementation.

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arXiv2026

Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting $γ_5$

We present a systematic functional approach to calculating symmetry-restoring counterterms in Effective Field Theories (EFTs) regulated using the Breitenlohner--Maison--'t Hooft--Veltman (BMHV) scheme. Building on a recently developed method that employs auxiliary spurion fields, our approach automates the extraction of these counterterms directly from the one-loop effective action, offering a streamlined and efficient procedure. We demonstrate its efficacy by applying it to the Standard Model Effective Field Theory (SMEFT) at dimension six, providing the first complete determination of its symmetry-restoring counterterms in the BMHV scheme. Our work establishes a robust foundation for consistent one-loop matching and two-loop running computations in EFTs with chiral gauge symmetries.

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arXiv2025

Insights on the Cosmic Origin of Matter from Proton Stability

We investigate the phenomenology of a model in which the proton is rendered absolutely stable by an IR mechanism that remains robust against unknown quantum gravity effects. A linear combination of baryon number and lepton flavors is gauged and spontaneously broken to a residual $\mathbb{Z}_9$ discrete gauge symmetry enforcing a strict selection rule: $ΔB = 0\,(\mathrm{mod}\,3)$. Despite its minimal field content, the model successfully accounts for established empirical evidence of physics beyond the SM. High-scale symmetry breaking simultaneously provides a seesaw mechanism explaining the smallness of neutrino masses, minimal thermal leptogenesis, and a viable phenomenology of the majoron as dark matter. Any cosmic string-wall network remaining after inflation is unstable for numerous charge assignments. Lepton flavor non-universality, central to the construction, leads to predictive neutrino textures testable via oscillation experiments, neutrinoless double beta decay, and cosmology. The model motivates searches in $X$- and $γ$-ray lines, neutrino telescopes, and predicts CMB imprints.

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arXiv2025

A Guide to Functional Methods Beyond One-Loop Order

Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the expansion of the path integral in a manifestly gauge-covariant manner. We also generalize the method to theories with mixed spin statistics and prove the validity of the hard-region matching formula to all loop orders. The methods are exemplified with a two-loop matching calculation of the Euler-Heisenberg Lagrangian resulting from decoupling the electron in QED.

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arXiv2025

Two-Loop Running in the Bosonic SMEFT Using Functional Methods

The next goalpost in precision calculations for physics beyond the Standard Model is determining the two-loop renormalization group (RG) equations in the Standard Model Effective Field Theory (SMEFT). We progress towards this goal by determining the RG equations for a simplified version of the SMEFT without any fermion fields. Our calculation relies on functional methods that are newly developed for multi-loop computations and adapted for the determination of RG equations here.

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arXiv2025

A Partially Fixed Background Field Gauge

We examine the incorporation of gauge symmetries in the modern effective field theory (EFT) matching paradigm with a particular focus on spontaneously broken symmetries. The presence of gauge symmetries entails the introduction of gauge-fixing terms in matching calculations, which may prevent (partial) cancellation between loops from the underlying theory and those of the EFT, thereby preventing the establishment of a hard-region matching formula. While this is not an issue when using the background field (BF) gauge for unbroken gauge theories, we find ourselves unable to demonstrate the cancellation with the ordinary BF gauge in spontaneously broken gauge theories when the massive vectors are heavy and decouple from the theory. As a convenient alternative, we construct a partially fixed BF gauge that, in addition to being simpler than the ordinary BF gauge, allows us to prove a hard-region matching formula.

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arXiv2024

General Quartic $β$-Function at Three Loops

We determine the three-loop $\overline{\text{MS}}$ quartic $ β$-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ β$-function is compared to known $ β$-functions for specific theories to fix all coefficients. Three-loop $ β$-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.

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arXiv2024

Flavor Hierarchies From SU(2) Flavor and Quark-Lepton Unification

In our recent attempt to explain flavor hierarchies [1], a gauged SU(2) flavor symmetry acting on left-handed fermions provides a ground to introduce three independent rank-one contributions to the Yukawa matrices: a renormalizable one for the third family, a mass-suppressed one for the second family, and an additional loop-suppressed factor for the first family. Here, we demonstrate how minimal quark-lepton unification à la Pati-Salam, relating down-quarks to charged leptons, can significantly improve this mechanism. We construct and thoroughly analyze a renormalizable model, performing a comprehensive one-loop matching calculation that reveals how all flavor hierarchies emerge from a single ratio of two scales. The first signatures may appear in the upcoming charged lepton flavor violation experiments.

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arXiv2024

Functional Matching and Renormalization Group Equations at Two-Loop Order

We present a systematic method for determining the two-loop effective Lagrangian resulting from integrating out a set of heavy particles in an ultraviolet scalar theory. We prove that the matching coefficients are entirely determined from the (double-)hard region of the loop integrals and present a master formula for matching, applicable to both diagrammatic and functional approaches. We further employ functional methods to determine compact expressions for the effective Lagrangian that do not rely on any previous knowledge of its structure or symmetries. The same methods are also applicable to the computation of renormalization group equations. We demonstrate the application of the functional approach by computing the two-loop matching coefficients and renormalization group equations in a scalar toy model.

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arXiv2024

Computing Tools for Effective Field Theories

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th-16th September 2022. The current document collects and summarizes the content of this workshop.

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arXiv2024

U(2) is Right for Leptons and Left for Quarks

We posit that the distinct patterns observed in fermion masses and mixings are due to a minimally broken $\mathrm{U}(2)_{q+e}$ flavor symmetry acting on left-handed quarks and right-handed charged leptons, giving rise to an accidental $\mathrm{U}(2)^5$ symmetry at the renormalizable level without imposing selection rules on the Weinberg operator. We show that the symmetry can be consistently gauged by explicit examples and comment on realizations in $\mathrm{SU}(5)$ unification. Via a model-independent SMEFT analysis, we find that selection rules due to $\mathrm{U}(2)_{q+e}$ enhance the importance of charged lepton flavor violation as a probe, where significant experimental progress is expected in the near future.

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arXiv2023

Rising Through the Ranks: Flavor Hierarchies from a Gauged SU(2) Symmetry

We propose an economical model to address the mass hierarchies of quarks and charged leptons. The light generations of the left-handed fermions form doublets under an $ \mathrm{SU}(2) $ flavor symmetry, which is gauged. The generational hierarchies emerge from three independent rank-one contributions to the Yukawa matrices: one is a renormalizable contribution, the second is suppressed by a mass ratio, and the last by an additional loop factor. The model is renormalizable and features only a handful of new fields and is remarkably simple compared to typical completions of gauged flavor symmetries or Froggatt-Nielsen. The model has a rich phenomenology, and we highlight promising signatures, especially in the context of $K$ and $B$ meson physics. This includes an interpretation of the latest $B^+ \to K^+ ν\bar ν$ measurement from Belle II.

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arXiv2023

A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at https://gitlab.com/matchete/matchete.

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arXiv2023

Adding Flavor to the SMEFT

We study the flavor structure of the lepton and baryon number--conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor to facilitate similar analyses for flavor symmetries not covered in this work.

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arXiv2023

Evanescent Operators in One-Loop Matching Computations

Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces -- the evanescent operators -- can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

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