Introducing 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 realistic 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 MS β-functions in broad classes of models. The package and example notebooks are available from the GitHub repository

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.Comment: 24 pages, 5 figures. Matches published versio

On ambiguities and divergences in perturbative renormalization group functions

There is an ambiguity in choosing field-strength renormalization factors in the 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

Revealing BSM composite dynamics via topological interactions at future colliders

In composite Higgs models, new composite pseudoscalars can interact with the Higgs and with electroweak gauge bosons via anomalous interactions, which stem from the topological structure of the underlying theory. A future 100 TeV pp collider (FCC-pp) will be able to test these anomalous interactions and thus shed light on the strong dynamics which generates the Higgs and other composite resonances. We will discuss the topological interactions of a minimal composite Higgs model with fermionic ultraviolet completion, based on the coset SU(4)/Sp(4). We will indicate the strategy to test these interactions at the FCC-pp and the expected reach.Comment: 5 pages, 3 figures, to appear in the Proceedings of the EPS Conference on High Energy Physics (EPS-HEP), Venice, July 201

A Model of Muon Anomalies

The Standard Model (SM) is augmented with a $\mathrm{U}(1)_{B-3L_\mu}$ 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 $\mathrm{U}(1)_{B-3L_\mu}$ mediate the intriguing effects observed in muon $(g-2)$, $R_{K^{(*)}}$ and $b \to s \mu^+ \mu^-$, 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.Comment: 11 pages, 4 figures. Version2: Updated after the g-2 release. Discussion on alternative models extended. References adde

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 (https://github.com/aethomsen/SMEFTflavor) to facilitate similar analyses for flavor symmetries not covered in this work

Addressing the muon anomalies with muon-flavored leptoquarks

Significant deviations from Standard Model (SM) predictions have been observed in b→sμ+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]

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.Comment: 17 pages, 1 figure, 2 table