arXiv subjects

Anders Eller Thomsen

Publications and source records attributed to Anders Eller Thomsen.

At least 37 records · Page 2Linked to original sources

arXiv2022

LHC EFT WG Note: Precision matching of microscopic physics to the Standard Model Effective Field Theory (SMEFT)

This note gives an overview of the tools for the precision matching of ultraviolet theories to the Standard Model effective field theory (SMEFT) at the tree level and one loop. Several semi- and fully automated codes are presented, as well as some supplementary codes for the basis conversion and the subsequent running and matching at low energies. A suggestion to collect information for cross-validations of current and future codes is made.

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arXiv2022

Leptoquarks with Exactly Stable Protons

We explore a novel mechanism to restrict TeV-scale leptoquark interactions and render the proton exactly stable to all orders in the effective field theory expansion. A scalar condensate breaks a lepton-flavoured $\mathrm{U}(1)_X$ gauge symmetry in the ultraviolet and generates neutrino masses, leaving a discrete $\mathbb{Z}_9$ or $\mathbb{Z}_{18}$ gauge symmetry in the infrared, forbidding $ΔB = 1$ processes. This provides an elegant framework to address the flavour anomalies and can be adapted to many other new-physics models. The $ \mathrm{U}(1)_X $ can emerge from a gauge-flavour unified $ \mathrm{SU}(12) \times \mathrm{SU}(2) \times \mathrm{SU}(2) $ theory at even higher energies.

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arXiv2022

On $(g-2)_μ$ From Gauged $\mathrm{U}(1)_X$

We investigate an economical explanation for the $(g-2)_μ$ anomaly with a neutral vector boson from a spontaneously broken $\mathrm{U}(1)_X$ gauge symmetry. The Standard Model fermion content is minimally extended by 3 right-handed neutrinos. Using a battery of complementary constraints, we perform a thorough investigation of the renormalizable, quark flavor-universal, vector-like $\mathrm{U}(1)_X$ models, allowing for arbitrary kinetic mixing. Out of 419 models with integer charges not greater than ten, only 7 models are viable solutions, describing a narrow region in model space. These are either $L_μ-L_τ$ or models with a ratio of electron to baryon number close to $-2$. The key complementary constraints are from the searches for nonstandard neutrino interactions. Furthermore, we comment on the severe challenges to chiral $\mathrm{U}(1)_X$ solutions and show the severe constraints on a particularly promising such candidate.

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arXiv2021

Muonic Force Behind Flavor Anomalies

We develop an economical theoretical framework for combined explanations of the flavor physics anomalies involving muons: $(g-2)_μ$, $R_{K^{(*)}}$, and $b \to s μ^+ μ^-$ angular distributions and branching ratios, that was first initiated by some of us in Ref. [1]. The Standard Model (SM) is supplemented with a lepton-flavored $\mathrm{U}(1)_X$ gauge group. The $\mathrm{U}(1)_X$ gauge boson with the mass of $\mathcal{O}(0.1)$ GeV resolves the $(g-2)_μ$ tension. A TeV-scale leptoquark, charged under the $\mathrm{U}(1)_X$, carries a muon number and mediates $B$-decays without prompting charged lepton flavor violation or inducing proton decay. We explore the theory space of the chiral, anomaly-free $\mathrm{U}(1)_X$ gauge extensions featuring the above scenario, and identify many suitable charge assignments for the SM$+3ν_R$ fermion content with the integer charges in the range $X_{F_i} \in [-10,10]$. We then carry out a comprehensive phenomenological study of the muonic force in representative benchmark models. Interestingly, we found models which can resolve the tension without conflicting the complementary constraints, and all of the viable parameter space will be tested in future muonic resonance searches. Finally, the catalog of the anomaly-free lepton-non-universal charge assignments motivated us to explore different directions in model building. We present a model in which the muon mass and the $(g-2)_μ$ are generated radiatively from a common short-distance dynamics after the $\mathrm{U}(1)_X$ breaking. We also show how to charge a vector leptoquark under $\mathrm{U}(1)_{μ- τ}$ in a complete gauge model.

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arXiv2021

Addressing the Muon Anomalies With Muon-Flavored Leptoquarks

Significant deviations from Standard Model (SM) predictions have been observed in $ b \to s μ^+ μ^-$ decays and in the muon $g-2$. Scalar leptoquark extensions of the SM are known to be able to address these anomalies, but generically give rise to lepton flavor violation (LFV) or even proton decay. We propose new muon flavored gauge symmetries as a guiding principle for leptoquark models that preserve the global symmetries of the SM and explain the non-observation of LFV. A minimal model is shown to easily accommodate the anomalies without encountering other experimental constraints. This talk is mainly based on Ref. [1].

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arXiv2021

General Gauge-Yukawa-Quartic $β$-Functions at 4-3-2--Loop Order

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa $ β$-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the $ β$-functions, we compare the general form to the specific $ β$-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination.

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arXiv2021

SuperTracer: A Calculator of Functional Supertraces for One-Loop EFT Matching

We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field redefinitions might still be necessary. The code and example notebooks are publicly available at https://gitlab.com/supertracer/supertracer.

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arXiv2021

On Ambiguities and Divergences in Perturbative Renormalization Group Functions

There is an ambiguity in choosing field-strength renormalization factors in the $ \overline{\text{MS}} $ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved $ β$-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa $ β$-functions and provide the first calculation of the flavor-improved 3-loop SM $ β$-functions in the gaugeless limit.

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arXiv2021

A Model of Muon Anomalies

The Standard Model (SM) is augmented with a $\mathrm{U}(1)_{B-3L_μ} $ gauge symmetry spontaneously broken above the TeV scale when an SM-singlet scalar condenses. Scalar leptoquarks $S_{1(3)} = (\overline{\mathbf{3}},\, \mathbf{1} (\mathbf{3}),\, ^1\!/_3)$ charged under $\mathrm{U}(1)_{B-3L_μ} $ mediate the intriguing effects observed in muon $(g-2)$, $R_{K^{(*)}}$ and $b \to s μ^+ μ^-$, while generically evading all other phenomenological constraints. The fermionic sector is minimally extended with three right-handed neutrinos, and a successful type-I seesaw mechanism is realized. Charged lepton flavor violation is effectively suppressed, and proton decay - a common prediction of leptoquarks - is postponed to the dimension-6 effective Lagrangian. Unavoidable radiative corrections in the Higgs mass and muon Yukawa favor leptoquark masses interesting for collider searches. The parameters of the model are radiatively stable and can be evolved by the renormalization group to the Planck scale without inconsistencies. Alternative lepton-flavored gauge extensions of the SM, under which leptoquarks become muoquarks, are proposed for comparison.

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arXiv2021

RGBeta: A Mathematica Package for the Evaluation of Renormalization Group $ β$-Functions

In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $ β$-functions are known to the 3-2-2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply these results to specific models without the use of dedicated computer tools. We describe a procedure for extracting $ β$-functions using the general results and introduce RGBeta, a dedicated Mathematica package for extracting the $ \overline{\text{MS}} $ $ β$-functions in broad classes of models. The package and example notebooks are available from the GitHub repository at https://github.com/aethomsen/RGBeta .

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arXiv2020

Stability of the Higgs Sector in a Flavor-Inspired Multi-Scale Model

We analyze the stability of the Higgs sector of a three-site model with flavor-non-universal gauge interactions, whose spectrum of non-Standard-Model states spans three orders of magnitude. This model is inspired by deconstructing a five-dimensional theory where the generation index is in one-to-one relation to the position in the fifth dimension. It provides a good description of masses and mixing of the SM fermions in terms of scale hierarchies. We demonstrate that, within this construction, the mass term of the SM-like Higgs does not receive large corrections proportional to the highest mass scales. The model suffers only of the unavoidable "little hierarchy problem" between the electroweak scale and the lightest NP states, which are expected to be at the TeV scale.

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arXiv2019

Gauge coupling beta functions to four-loop order in the Standard Model

We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $γ_5$ in $D=4-2ε$ space-time dimensions is required; however, in our calculation we determine the $γ_5$-dependent terms by exploiting relations with beta function coefficients at lower loop orders.

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arXiv2019

Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field Theory

The $ β$-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the $β$-functions by parametrizing the terms in Osborn's equation as polynomials in the couplings, then eliminating unknown $\tilde{A}$ and $T_{IJ}$ coefficients. In this paper we extend this program to completely general gauge theories with arbitrarily many Abelian and non-Abelian factors. We detail the computational strategy used to extract consistency conditions on $ β$-functions, and discuss our automation of the procedure. Finally, we implement the procedure up to 4-, 3-, and 2-loops for the gauge, Yukawa and quartic couplings respectively, corresponding to the present forefront of general $ β$-function computations. We find an extensive collection of highly non-trivial constraints, and argue that they constitute an useful supplement to traditional perturbative computations; as a corollary, we present the complete 3-loop gauge $β$-function of a general QFT in the $\bar{\text{MS}}$ scheme, including kinetic mixing.

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arXiv2018

$a$-theorem at large $N_f$

We determine the Jack and Osborn a-function and related metric for gauge-fermion theories to leading order in the large number of fermions and to all orders in the gauge coupling, demonstrating that the strong a-theorem is violated for the minimal choice of the a-function.

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arXiv2018

Gauge-Yukawa theories: Beta functions at large $N_f$

We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semi-simple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the leading $1/N_f$ Yukawa and quartic beta functions. Our work elucidates, consolidates and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.

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arXiv2017

Flavor Physics and Flavor Anomalies in Minimal Fundamental Partial Compositeness

Partial compositeness is a key ingredient of models where the electroweak symmetry is broken by a composite Higgs state. Recently, a UV completion of partial compositeness was proposed, featuring a new strongly coupled gauge interaction as well as new fundamental fermions and scalars. We work out the full flavor structure of the minimal realization of this idea and investigate in detail the consequences for flavor physics. While CP violation in kaon mixing represents a significant constraint on the model, we find many viable parameter points passing all precision tests. We also demonstrate that the recently observed hints for a violation of lepton flavor universality in $B\to K^{(*)}\ell\ell$ decays can be accommodated by the model, while the anomalies in $B\to D^{(*)}τν$ cannot be explained while satisfying LEP constraints on $Z$ couplings.

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arXiv2017

Minimal Fundamental Partial Compositeness

Building upon the fundamental partial compositeness framework we provide consistent and complete composite extensions of the standard model. These are used to determine the effective operators emerging at the electroweak scale in terms of the standard model fields upon consistently integrating out the heavy composite dynamics. We exhibit the first effective field theories matching these complete composite theories of flavour and analyse their physical consequences for the third generation quarks. Relations with other approaches, ranging from effective analyses for partial compositeness to extra dimensions as well as purely fermionic extensions, are briefly discussed. Our methodology is applicable to any composite theory of dynamical electroweak symmetry breaking featuring a complete theory of flavour.

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arXiv2017

Uncovering new strong dynamics via topological interactions at the 100 TeV collider

In models of composite Higgs dynamics new composite pseudoscalars can interact with the Higgs and electroweak gauge bosons via anomalous interactions, stemming from the topological sector of the underlying theory. We show that a future 100 TeV proton-proton collider (FCC-pp) will be able to test this important sector and thus shed light on the strong dynamics which generates the Higgs and other composite states. To elucidate our results we focus on the topological interactions of a minimal composite Higgs model with a fermionic ultraviolet completion, based on the coset $\text{SU}(4)/\text{Sp}(4)$. We suggest the strategy to test these interactions at the FCC-pp and analyse the expected reach.

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