Search

The Two-Higgs Doublet Model (2HDM) is a well understood alternative to the Standard Model of particle physics. If the new particles included in the 2HDM are at an energy scale much greater than the weak scale, the theory can be matched to the Standard Model Effective Field Theory (SMEFT). We compute for the first time the complete one-loop matching at dimension-6. We compare its numerical impact with that of tree-level matching at dimension-8 by performing a global fit to single Higgs and precision electroweak measurements, and we emphasize the importance of comparing one-loop SMEFT results with corresponding one-loop results in the full 2HDM model. In the SMEFT, we consider the relative importance of both one-loop matching and the inclusion of renormalization group evolution. Our results demonstrate the necessity of studying the impact of various expansions to quantify the uncertainties of the SMEFT matching., Comment: 28 pages, 4 figures. Updated to published version. Auxiliary files at https://github.com/BDFH-2024/BDFH

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., Comment: 116 pages, 10 figures. Based on the contributions to SMEFT-Tools 2022 (https://indico.icc.ub.edu/event/128/). v2: version published in EPJC

We discuss axion-like particles (ALPs) within the framework of Higgs Effective Field Theory, targeting instances of close alignment of ALP physics with a custodial singlet character of the Higgs boson. We tension constraints arising from new contributions to Higgs boson decays against limits from high-momentum transfer processes that become under increasing control at the LHC. Going beyond leading-order approximations, we highlight the importance of multi-top and multi-Higgs production for the pursuit of searches for physics beyond the Standard Model extensions., Comment: 8 pages, 5 figures

We compute the renormalization group equations (RGEs) of the Standard Model effective field theory (EFT) extended with a real scalar singlet, up to dimension-five and one-loop accuracy. We compare our renormalization results with those found in the shift-symmetry preserving limit, which characterizes axion-like particles (ALPs). The matching and running equations below the electroweak scale are also obtained, including the mixing effects in the scalar sector. Such mixing leads to interesting phenomenological consequences that are absent in the EFT at the renormalizable level, namely new correlations among the triplet and quartic Higgs couplings are predicted. All RGEs obtained in this work are implemented in a new Mathematica package - ALPRunner, together with functions to solve the running numerically for an arbitrary set of UV parameters. As an application, we obtain the improved electric dipole moment constraints on particular regions of the singlet parameter space, and quantify the level of shift-breaking in these regions., Comment: 35 pages, 5 figures, 5 tables

We present the renormalisation group running of the bosonic operators of the Standard Model effective field theory by the Lepton Number Violating operators (LNVs) at 1-loop order up to $\mathcal{O}(v^4/\Lambda^4)$, with $v \sim 246$ GeV as the electroweak scale and $\Lambda$ as the SMEFT cut-off. Using these relations with the positivity bounds on Wilson coefficients of $\phi^4 D^4$ class, we derive sign-constraints on the Wilson coefficients of LNV operators for models where $\phi^4 D^4$ operators do not appear at tree-level. We inspect these constraints for the LNV Wilson coefficients generated from matching the Type-I and III seesaw models to SMEFT up to dimension seven at tree-level. We also exhibit the unique bounds induced by the T-parameter on LNVs., Comment: 31 pages, 3 figures, 5 tables, version accepted in JHEP. Discussion on ADM zeroes elaborated

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., Comment: 23 pages, 2 figures

The wealth of experimental data collected at laboratory experiments suggests that there is some scale separation between the Standard Model (SM) and phenomena beyond the SM (BSM). New phenomena can manifest itself as small corrections to SM predictions, or as signals in processes where the SM predictions vanish or are exceedingly small. This makes precise calculations of the SM expectations essential, in order to maximize the sensitivity of current and forthcoming experiments to BSM physics. This topical group report highlights some past and forthcoming theory developments critical for maximizing the sensitivity of the experimental program to understanding Nature at the shortest distances., Comment: 36 pages, 2 figures. Report of the TF06 topical group for Snowmass 2021. V2: minor updates

We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order $v^4/\Lambda^4$, with $v\sim 246$ GeV being the electroweak scale and $\Lambda$ the unknown new physics threshold. We focus on contributions driven by one dimension-eight term and SM couplings, thus extending (and completing) the effort initiated in arXiv:2106.05291, in which quantum corrections from pairs of dimension-six interactions were considered. We highlight some interesting consequences, including the renormalisation of loop-induced interactions by tree-level generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings., Comment: 21 pages, 5 tables, 2 figures, minor typos edited in Table 2, Github file updated. Further corrections will be only updated in Github

In this contribution to the Snowmass 2021 process we review theoretical developments in the Standard Model Effective Field Theory (SMEFT) with a focus on effects at the dimension-8 level and beyond. We review the theoretical advances that led to the complete construction of the operator bases for the dimension-8 and dimension-9 SMEFT Lagrangians. We discuss the possibility of obtaining all-orders results in the $1/\Lambda$ expansion for certain SMEFT observables as well as the current status of renormalization group running and implications for positivity, and briefly present the on-shell approach to constructing SMEFT amplitudes. Finally we present several new phenomenological effects that first arise at dimension-8 and discuss the impact of these terms on experimental analyses., Comment: 37 pages, 6 figures; contribution to Snowmass 2021; new section and additional authors

In this paper, we work with 16 different single scalar particle extensions of the Standard Model. We present the sets of dimension-6 effective operators and the associated Wilson coefficients as functions of model parameters after integrating out the heavy scalars up to 1-loop, including the heavy-light mixing, for each such scenario. Using the correspondence between the effective operators and the observables at electroweak scale, and employing Bayesian statistics, we compute the allowed ranges of new physics parameters that are further translated and depicted in 2-dimensional Wilson coefficient space in the light of the latest CMS and ATLAS data up to $137 \text{ fb}^{-1}$ and $139\text{ fb}^{-1}$, respectively. We also adjudge the status of those new physics extensions that offer similar sets of relevant effective operators. In addition, we provide a model-independent fit of $23$ Standard Model effective field theory Wilson coefficients using electroweak precision observables, single and di-Higgs data as well as kinematic distributions of di-boson production., Comment: 50 pages (including appendices), 7 figures, and 22 tables; updated to version published in PRD

We consider a wide range of UV scenarios with the aim of informing searches for CP violation at the TeV scale using effective field theory techniques. We demonstrate that broad theoretical assumptions about the nature of UV dynamics responsible for CP violation map out a small subset of relevant operators at the TeV scale. Concretely, this will allow us to reduce the number of free parameters that need to be considered in experimental investigations, thus enhancing analyses' sensitivities. In parallel, reflecting the UV dynamics' Wilson coefficient hierarchy will enable a streamlined theoretical interpretation of such analyses in the future. We demonstrate a minimal approach to analysing CP violation in this context using a Monte Carlo study of a combination of weak boson fusion Higgs and electroweak diboson production, which provide complementary information on the relevant EFT operators., Comment: 22 pages, 6 figures, 1 table; v2 accepted by NPB, 7 figures, 3 tables

Effective Field Theories are an established framework to bridge the gap between UV and low energy theories. In the context of the Standard Model, the bottom-up approach extends its operator set and thus equips us to astutely probe its observables while encapsulating indirect evidence of unknown high scale theories. While the top-down approach, on the other hand, employs functional techniques to integrate out the heavy fields from a BSM Lagrangian leading to a set of SMEFT operators. An intricate interplay of the two approaches enhances the efficacy of the SMEFT in making meaningful predictions while providing a platform for conducting a coherent comparison of new physics scenarios. However, while the bottom-up approach fails to indicate the origin of the effective operators, the top-down approach is highly dependent on the specific model assumptions of the UV theory. We, for the first time, are proposing a diagrammatic approach to establish selection criteria for the allowed heavy field representations corresponding to each SMEFT operator. This, in turn, paves the way to construct observable driven new physics models. While we take a predominantly minimalistic approach, we also highlight the necessity for non-minimal interactions for certain operators., Comment: 37 pages, 11 figures

Effective theories are well established theoretical frameworks to describe the effect of energetically widely separated UV models on observables at lower energy scales. Due to the complexity of the effective theory when taking all the Standard Model symmetries and degrees of freedoms into account, tensioning the entire system in a completely agnostic way against experimental measurements results in constraints on the Wilson Coefficients of the effective operators that either bears little information or challenge intrinsic assumptions imposed on the effective field theory framework. In general, a specific high-scale extension of the Standard Model only induces a subset of all possible operators. Thus, by investigating which operators are induced by different classes of the Standard Model extensions and comparing to which precision observables they contribute, we show that it is possible to obtain an improved understanding of which UV model is realised in nature. We consider 15 UV models which are single scalar field extensions of the Standard Model and compute their dimension-6 operators after integrating out the heavy scalars up to 1-loop level. Only very few of these scenarios remain indistinguishable, while most of the models can be phenomenologically separated from one another. Most of these scenarios possess their own characteristic operator signature. Following the approach outlined here, a comparative analysis of a wide range of models will allow to assess at what level the effective field theory series can be truncated and which experimental measurements to prioritise., Comment: 19 pages, 9 figures

Recognizing the potential of effective field theories to posit multiple BSM scenarios in similar footing, with a possibility to compare them, we inspect the effects of 11 single scalar-multiplet extensions of the SM on the combined set of electroweak precision observables and Higgs signal strength data, by systematically integrating out the heavy multiplets and computing the resulting SMEFT operators and Wilson coefficients (WCs) up to one-loop level. Noting that multiple BSM models give rise to a degenerate set of WCs, we then perform Bayesian statistical inference both directly on the BSM parameters and on the associated set of independent WCs. Using the posteriors of the BSM parameters, we infer the respective (correlated) WC-distributions and compare both the model-independent and dependent analyses by overlaying the 2-D marginal WC-posteriors from both processes, thus laying the ground for a data-driven attempt to compare diverse BSM theories of different origins, and hopefully, a possible way to approach the intractable inverse problem. We also demonstrate, with an example model, the crucial role of theoretical constraints to rule out large chunks of BSM parameter spaces. The entirety of numerical results is available in GitHub., Comment: 36 pages, 11 captioned figures, Numerical results are in https://github.com/effExTeam/SMEFT-EWPO-Higgs

CP violation beyond the Standard Model (SM) is a crucial missing piece for explaining the observed matter-antimatter symmetry in the Universe. Recently, the ATLAS experiment at the Large Hadron Collider has performed an analysis of electroweak $Zjj$ production, thereby excluding the SM locally at 95\% confidence level in the measurement of CP-sensitive observables. We take the excess' interpretation in terms of anomalous gauge-Higgs interactions at face value and discuss further steps that are required to scrutinize its origin. In particular, we discuss the relevance of multi-boson production using adapted angular observables to show how they can be used to directly tension the reported $Zjj$ excess in a more comprehensive analysis. To connect the excess to a concrete UV scenario for which the underlying assumptions of the $Zjj$ analysis are valid, we identify vector-like leptons as a candidate theory consistent with the observed CP-odd Wilson coefficient hierarchy observed by ATLAS. We perform a complete one-loop matching calculation to motivate further model-specific and correlated new physics searches. In parallel, we provide estimates of the sensitivity reach of the LHC's high luminosity phase for this particular scenario of CP-violation in light of electroweak precision and Run-2 Higgs data. These provide strong constraints on the model's CP-even low-energy phenomenology, but also inform the size of the CP-odd SM deformation indirectly via our model hypothesis., Comment: 22 pages, 4 figures, 4 tables; version published in PRD

Effective Field Theory technique is one of the most elegant ways to capture the impact of high scale theory, if any, at some low energy by incorporating higher mass dimensional ($\geq 5$) effective operators ($\mathcal{O}_i$). The low energy EFT is described in terms of only light degrees of freedom which can appear on-shell. An essential task while developing the EFT framework is to compute these $\mathcal{O}_i$'s. Hilbert Series is a novel and mathematically robust method to construct the complete set of gauge invariant independent, effective operators. The HS requires the knowledge of the transformation properties of the light DOF and the covariant derivatives under the internal gauge symmetries and conformal groups. The Hilbert Series method, by its virtue, automatically takes care of the redundancies in the operator set due to the Equations of Motion of fields and Integration by Parts with impeccable accuracy. In this paper, we have adopted this methodology to construct the complete set of independent operators up to dimension-6 in the ``Warsaw"-like basis for two different Beyond Standard Model scenarios -- 2HDM and MLRSM. For both these cases, we have calculated the corrections to the scalar, gauge boson and fermion mass spectra due to the dimension-6 operators. The additional contributions to all the Feynman vertices are computed and their impact on different observables, namely Weak mixing angle, Fermi constant, $\rho$ and oblique parameters. We have further discussed how the magnetic moments of charged leptons and production and decay of the massive BSM particles, e.g., charged scalar and different rare processes are affected in the presence of effective operators. We have also constructed the effective scalar four-point interactions and commented on the possible reinvestigation of the theoretical constraints, e.g., unitarity and vacuum stability within these frameworks., Comment: 120 pages, 14 figures, 50 tables

CoDEx is a Mathematica package that calculates the Wilson Coefficients (WCs) corresponding to effective operators up to mass dimension-6. Once the part of the Lagrangian involving single as well as multiple degenerate heavy fields, belonging to some Beyond Standard Model (BSM) theory, is given, the package can then integrate out propagators from the tree as well as 1-loop diagrams of that BSM theory. It then computes the associated WCs up to 1-loop level, for two different bases: "Warsaw" and "SILH". CoDEx requires only very basic information about the heavy field(s), e.g., Colour, Isospin, Hyper-charge, Mass, and Spin. The package first calculates the WCs at the high scale (mass of the heavy field(s)). We then have an option to perform the renormalisation group evolutions (RGEs) of these operators in "Warsaw" basis, a complete one (unlike "SILH"), using the anomalous dimension matrix. Thus, one can get all effective operators at the electro-weak scale, generated from any such BSM theory, containing heavy fields of spin: 0, 1/2, and 1. We have provided many example models (both here and in the package-documentation) that more or less encompass different choices of heavy fields and interactions. Relying on the status of the present day precision data, we restrict ourselves up to dimension-6 effective operators. This will be generalised for any dimensional operators in a later version. Site: https://effexteam.github.io/CoDEx, Comment: 25 pages, 1 figure, corrections and citations added