Standard Model Effective Field Theory Operators Research Articles

Flavor violating di-Higgs couplings

Di-Higgs couplings to fermions of the form h2f‾f are absent in the Standard Model, however, they are present in several physics Beyond Standard Model (BSM) extensions, including those with vector-like fermions. In Effective Field Theories (EFTs), such as the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT), these couplings appear at dimension 6 and can in general, be flavour-violating (FV). In the present work, we employ a bottom-up approach to investigate the FV in the lepton and quarks sectors through the di-Higgs effective couplings. We assume that all FV arises from this type of couplings and assume that the Yukawa couplings Yij are given by their SM values, i.e. Yij=2miδij/v. In the lepton sector, we set upper limits on the Wilson coefficients Cll′ from l→3l′ decays, l→lγ decays, muonium oscillations, the (g−2)μ anomaly, LEP searches, muon conversion in nuclei, FV Higgs decays, and Z decays. We also make projections on some of these coefficients from Belle II, the Mu2e experiment and the LHC's High Luminosity (HL) run. In the quark sector, we set upper limits on the Wilson coefficients Cqq′ from meson oscillations and from B-physics searches. A key takeaway from this study is that current and future experiments should set out to measure the effective di-Higgs couplings Cff′, whether these couplings are FV or flavour-conserving. We also present a matching between our formalism and the SMEFT operators and show the bounds in both bases.

One-loop analysis of β decays in SMEFT

We perform a loop-level analysis of charged-current (CC) processes involving light leptons and quarks within the Standard Model Effective Field Theory (SMEFT). This work is motivated by the high precision reached in experiment and Standard Model calculations for CC decays of mesons, neutron, and nuclei, and by a lingering tension in the Cabibbo universality test. We identify the SMEFT operators that induce the largest loop-level contributions to CC processes. These include four-quark and four-fermion semileptonic operators involving two third-generation quarks. We discuss the available constraints on the relevant effective couplings and along the way we derive new loop-level bounds from K → πνν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\pi \ u \\overline{\ u} $$\\end{document} on four-quark operators involving two top quarks. We find that low-energy CC processes are quite competitive with other probes, set constraints that do not depend on flavor-symmetry assumptions, and probe operators involving third-generation quarks up to effective scales of Λ ≃ 8 TeV. Finally, we briefly discuss single-field ultraviolet completions that could induce the relevant operators.

Probing flavor constrained SMEFT operators through tc production at the muon collider

We investigate flavor violating four-Fermi Standard Model Effective Field Theory (SMEFT) operators of dimension-six that can be probed via tct¯c+tc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left(\\overline{t}c+t\\overline{c}\\right) $$\\end{document} production at the multi-TeV muon collider. We study different FCNC and FCCC processes related to B, Bs, K and D decays and mixings, sensitive to these operators and constrain the corresponding couplings. The tensor operator turns out to be most tightly bound. We perform event simulation of the final state signal from tc production together with the SM background to show that operators after flavor constraint can reach the discovery limit at 10 TeV muon collider. We further adopt the optimal observable technique (OOT) to determine the optimal statistical sensitivity of the Wilson coefficients and compare them with the flavor constraints. We use the limits to predict the observational sensitivities of the rare processes like KL → π0ℓℓ, D0 → μμ, t → cℓℓ.

Complete UV resonances of the dimension-8 SMEFT operators

The effective field theory approach parameterizes the low energy behaviors of all possible ultraviolet (UV) theories in a systematic way. One of the most important tasks is thus to find the connection between the effective operators and their UV origins. The redundancy relations among operators make the connection very subtle, hence we proposed the J-basis prescription to illuminate the correspondence between operators and their UV resonances in the bottom-up way. In this work, we work out the dimension-8 J-basis operators in the standard model effective field theory (SMEFT), and find all the 146 (82) tree-level UV resonances along with their couplings up to mass dimension 5 (4). Furthermore, we point out a few subtleties on operator generation via field redefinition and on the UV Lagrangian for generic spin resonances. We also provide a data base storing our results and a Mathematica notebook for extracting those results for the reader’s conveinence.

Probing lepton number violation: a comprehensive survey of dimension-7 SMEFT

Observation of lepton number violation would represent a groundbreaking discovery with profound consequences for fundamental physics and as such, it has motivated an extensive experimental program searching for neutrinoless double beta decay. However, the violation of lepton number can be also tested by a variety of other observables. We focus on the possibilities of probing this fundamental symmetry within the framework of the Standard Model Effective Field Theory (SMEFT) beyond the minimal dimension-5. Specifically, we study the bounds on ∆L = 2 dimension-7 effective operators beyond the electron flavor imposed by all relevant low-energy observables and confront them with derived high-energy collider limits. We also discuss how the synergy of the analyzed multi-frontier observables can play a crucial role in distinguishing among different dimension-7 SMEFT operators.

Combining chromomagnetic and four-fermion operators with leading SMEFT operators for gg → hh at NLO QCD

We present the calculation of the contribtuions from the chromomagnetic and four-top-quark-operators within Standard Model Effective Field Theory (SMEFT) to Higgs boson pair production in gluon fusion, combined with QCD corrections that are at NLO with full mt-dependence for the leading operators. We study the effects of these operators on the total cross section and the invariant mass distribution of the Higgs-boson pair, at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}$$\\end{document} = 13.6 TeV. These subleading operators are implemented in the generator ggHH_SMEFT, in the same Powheg-Box-V2 framework as the leading operators, such that their effects can be easily studied in a unified setup.

Anomalies in global SMEFT analyses. A case study of first-row CKM unitarity

Recent developments in the Standard Model analysis of semileptonic charged-current processes involving light quarks have revealed ~ 3σ tensions in Cabibbo universality tests involving meson, neutron, and nuclear beta decays. In this paper, we explore beyond the Standard Model explanations of this so-called Cabibbo Angle Anomaly in the framework of the Standard Model Effective Field Theory (SMEFT), including not only low-energy charged current processes (‘L’), but also electroweak precision observables (‘EW’) and Drell-Yan collider processes (‘C’) that probe the same underlying physics across a broad range of energy scales. The resulting ‘CLEW’ framework not only allows one to test explanations of the Cabibbo Angle Anomaly, but is set up to provide near model-independent analyses with minimal assumptions on the flavor structure of the SMEFT operators. Besides the global analysis, we consider a large number of simpler scenarios, each with a subset of SMEFT operators, and investigate how much they improve upon the Standard Model fit. We find that the most favored scenarios, as judged by the Akaike Information Criterion, are those that involve right-handed charged currents. Additional interactions, namely oblique operators, terms modifying the Fermi constant, and operators involving right-handed neutral currents, play a role if the CDF determination of the W mass is included in the analysis.

SMEFT at NNLO+PS: Vh production

In the context of the Standard Model effective field theory (SMEFT) the next-to-next-to-leading (NNLO) QCD corrections to the Higgsstrahlungs (Vh) processes in hadronic collisions are calculated and matched to a parton shower (PS). NNLO+PS precision is achieved for the complete sets of SMEFT operators that describe the interactions between the Higgs and two vector bosons and the couplings of the Higgs, a W or a Z boson, and light fermions. A POWHEG-BOX implementation of the computed NNLO SMEFT corrections is provided that allows for a realistic exclusive description of Vh production at the level of hadronic events. This feature makes it an essential tool for future Higgs characterisation studies by the ATLAS and CMS collaborations. Utilising our new Monte Carlo code the numerical impact of NNLO+PS corrections on the kinematic distributions in pp → Zh → ℓ+ℓ−h production is explored, employing well-motivated SMEFT benchmark scenarios.

Optimal estimation of dimension-8 neutral triple gauge couplings at the e+e− colliders

We investigate the measurement of non-standard ZZV (V = γ, Z) couplings through Z-boson pair production at the e+e− colliders. We adopt the Standard Model Effective Field Theory (SMEFT) approach to study these anomalous neutral triple gauge couplings. There are one CP-conserving and three CP-violating dim-8 SMEFT operators that contribute to ZZV couplings. Using the optimal observable technique, the sensitivity of these new physics couplings has been estimated and compared with the latest experimental limits on dim-8 couplings at the LHC at CERN. The effect of beam polarization and correlations among CP-violating ZZV couplings are discussed. The comparison of statistical limits of new physics couplings between optimal observable technique and contemporary cut-based analysis has also been studied in detail.

Renormalization group equations for the SMEFT operators up to dimension seven

In this paper, we propose a Green’s basis and also a new physical basis for dimension-seven (dim-7) operators, which are suitable for the matching of ultraviolet models onto the Standard Model effective field theory (SMEFT) and the deviation of renormalization group equations (RGEs) for dim-7 operators in the SMEFT. The reduction relations to convert operators in the Green’s basis to those in the physical basis are achieved as well, where some redundant dim-6 operators in the Green’s basis are involved if the dim-5 operator exists. Working in these two bases for dim-7 operators and with the help of the reduction relations, we work out the one-loop RGEs resulting from the mixing among different dimensional operators for the dim-5 and dim-7 operators up to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(Λ−3) in the SMEFT. These new results complete the previous results for RGEs of the dim-5 and dim-7 operators and hence can be used for a consistent one-loop analysis of the SMEFT at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(Λ−3).

New Physics in CP violating and flavour changing quark dipole transitions

We explore CP-violating (CPV) effects of heavy New Physics in flavour-changing quark dipole transitions, within the framework of Standard Model Effective Field Theory (SMEFT). First, we establish the relevant dimension six operators and consider the Renormalisation Group (RG) evolution of the appropriate Wilson coefficients. We investigate RG-induced correlations between different flavour-violating processes and electric dipole moments (EDMs) within the Minimal Flavour Violating and U(2)3 quark flavour models. At low energies, we set bounds on the Wilson coefficients of the dipole operators using CPV induced contributions to observables in non-leptonic and radiative B, D and K decays as well as the neutron and electron EDMs. This enables us to connect observable CPV effects at low energies and general NP appearing at high scales. We present bounds on the Wilson coefficients of the relevant SMEFT operators at the high scale Λ = 5 TeV, and discuss most sensitive CPV observables for future experimental searches.

Exploring SMEFT operators in the tHq production at the LHC

We study the top-quark production along with a Higgs boson and a jet (tHq) at the LHC experiment within the framework of the Standard Model Effective Field Theory (SMEFT). A strategy is developed to constrain the Wilson Coefficients (WC) corresponding to the associated SMEFT operators using the latest LHC measurements. The best-fit values of these WCs are presented. Finally, we demonstrate the feasibility of finding the effects of these operators on various kinematical observables of the tHq process at the LHC. We find that for a set of best-fitted values of the considered WCs, the excess of signal over the backgrounds can be achieved with a reasonable significance at the center of mass energy s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV and for integrated luminosity options L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{L} $$\\end{document} =300 fb−1 and 3000 fb−1.

SmeftFR v3 – Feynman rules generator for the Standard Model Effective Field Theory

We present version 3 of SmeftFR, a Mathematica package designed to generate the Feynman rules for the Standard Model Effective Field Theory (SMEFT) including the complete set of gauge invariant operators up to dimension-6 and the complete set of bosonic operators of dimension-8. Feynman rules are generated with the use of FeynRules package, directly in the physical (mass eigenstates) basis for all fields. The complete set of interaction vertices can be derived, including all or any chosen subset of SMEFT operators. As an option, the user can also choose preferred gauge fixing, generating Feynman rules in unitary or Rξ-gauges. The novel feature in version-3 of SmeftFR is its ability to calculate SMEFT interactions consistently up to dimension-8 in EFT expansion (including quadratic dimension-6 terms) and express the vertices directly in terms of user-defined set of input-parameters. The derived Lagrangian in the mass basis can be exported in various formats supported by FeynRules, such as UFO, FeynArts, etc. Initialisation of numerical values of Wilson coefficients of higher dimension operators is interfaced to WCxf format. The package also includes a dedicated Latex generator allowing to print the result in clear human-readable form. The SmeftFR v3 is publicly available at http://www.fuw.edu.pl/smeft. Program summaryProgram Title:SmeftFR v3.0CPC Library link to program files:https://doi.org/10.17632/h4787mfvfz.1Licensing provisions: GPLv3Programming language: Mathematica 12.1 or later (earlier versions were reported to have problems running this code)External routines/libraries: Wolfram Mathematica programSubprograms used:FeynRules v2.3.49 or later packageNature of problem: Automatised generation of Feynman rules in physical (mass) basis for the Standard Model Effective Field Theory with user defined operator subset, gauge fixing and input-parameters scheme selection.Solution method: Expansion of SmeftFR v2 Mathematica package [1]: implementation of the results of Ref. [2] in the FeynRules package [3], including dynamic “model files” generation.

Double insertions of SMEFT operators in gluon fusion Higgs boson production

Deviations from the Standard Model (SM) can be parametrized in terms of the SM effective field theory (SMEFT), which is typically truncated at dimension-6. Including higher dimension operators---as well as considering simultaneous insertions of multiple dimension-6 operators---may be necessary in some processes, in order to correctly capture the properties of the underlying UV theory. As a step toward clarifying this in the Higgs boson production in gluon fusion process, we study double insertions of dimension-6 operators in the 1-loop virtual amplitude. We present needed Feynman rules up to $\mathcal{O}(1/{\mathrm{\ensuremath{\Lambda}}}^{4})$ and we numerically study the impact of various approximations to the $\mathcal{O}(1/{\mathrm{\ensuremath{\Lambda}}}^{4})$ expansion.

The bottom-up EFT: complete UV resonances of the SMEFT operators

The standard model effective field theory (SMEFT) provides systematic parameterization of all possible new physics above the electroweak scale. According to the amplitude-operator correspondence, an effective operator can be decomposed into a linear combination of several j-basis operators, which correspond to local amplitudes carrying certain spin and gauge quantum numbers in a particular scattering channel. Based on the Poincare and gauge symmetries of scattering amplitude, we construct the j-basis using the Casimir method for both the Lorentz and gauge sectors. The quantum numbers of the j-basis operators fix the quantum numbers of any intermediate state in the corresponding amplitudes, such as a UV resonance. This can be re-interpreted as the j-basis/UV correspondence, thus obtaining the j-bases in all partitions of fields for an operator amounts to finding all of its UV origins at tree level, constituting the central part of the bottom-up EFT framework. Applying the j-basis analysis to SMEFT, we obtain a complete list of possible tree-level UV origins of the effective operators at the dimension 5, 6, 7, and all the bosonic operators at dimension 8.

Distinguishing electroweak EFTs with WLWL→n×h

The electroweak symmetry-breaking sector is one of the most promising and uncharted parts of the Standard Model (SM); but it seems likely that new electroweak physics may be out of reach of the present accelerator effort and the hope is to observe small deviations from the SM. Given that, effective field theory (EFT) becomes the logic method to use, and Standard Model effective field theory (SMEFT) has become the standard. However, the most general theory with the known particle content is Higgs effective field theory (HEFT), and whether SMEFT suffices should be investigated in future experimental efforts. Building on investigations by other groups that established geometric criteria to distinguish SMEFT from HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding and present an analogous discussion aimed at a broader audience. We discuss various aspects of (multi)Higgs boson production from longitudinal electroweak gauge bosons ${W}_{L}{W}_{L}\ensuremath{\rightarrow}n\ifmmode\times\else\texttimes\fi{}h$ in the TeV region as the necessary information to characterize the flare function, $\mathcal{F}(h)$, that determines whether SMEFT or HEFT is needed. We also present tree-level amplitudes including contact and exchange channels, as well as a short discussion on accessing $\mathcal{F}$ from the statistical limit of many bosons. We also discuss the status of the coefficients of the series expansion of $\mathcal{F}(h)$, its validity, whether its complex-$h$ extension can be used to predict or not a tell-tale zero, and how they relate to the dimension-six and -eight SMEFT operators in the electroweak sector. We derive a set of new correlations among beyond the standard model corrections to the HEFT coefficients that help decide, from experimental data, whether we have a viable SMEFT. This analysis can be useful for machines beyond the LHC that could address the challenging final state with several Higgs bosons.

SMEFT analysis of mW

We use the Fitmaker tool to incorporate the recent CDF measurement of mW in a global fit to electroweak, Higgs, and diboson data in the Standard Model Effective Field Theory (SMEFT) including dimension-6 operators at linear order. We find that including any one of the SMEFT operators mathcal{O} HWB, mathcal{O} HD, mathcal{O} ℓℓ or {mathcal{O}}_{Hell}^{(3)} with a non-zero coefficient could provide a better fit than the Standard Model, with the strongest pull for mathcal{O} HD and no tension with other electroweak precision data. We then analyse which tree-level single-field extensions of the Standard Model could generate such operator coefficients with the appropriate sign, and discuss the masses and couplings of these fields that best fit the CDF measurement and other data. In particular, the global fit favours either a singlet Z′ vector boson, a scalar electroweak triplet with zero hypercharge, or a vector electroweak triplet with unit hypercharge, followed by a singlet heavy neutral lepton, all with masses in the multi-TeV range for unit coupling.

NNLO event generation for ppto Zhto {mathrm{ell}}^{+}{mathrm{ell}}^{-}boverline{b} production in the SM effective field theory

We consider associated Zh production with Z → ℓ+ℓ− and hto boverline{b} decays in hadronic collisions. In the framework of the Standard Model effective field theory (SMEFT) we calculate the QCD corrections to this process and achieve next-to-next-to-leading order plus parton shower (NNLO+PS) accuracy using the MiNNLOPS method. This precision is obtained for a subset of six SMEFT operators, including the corrections from effective Yukawa- and chromomagnetic dipole-type interactions. Missing higher-order QCD effects associated with the considered dimension-six operators are estimated to have a relative numerical impact of less than a percent on the total rate once existing experimental limits on the relevant Wilson coefficients are taken into account. We provide a dedicated Monte Carlo (MC) code that evaluates the NNLO SMEFT corrections on-the-fly in the event generation. This MC generator is used to study the numerical impact of NNLO+PS corrections on the kinematic distributions in ppto Zhto {mathrm{ell}}^{+}{mathrm{ell}}^{-}boverline{b} production employing simple SMEFT benchmark scenarios. We identify the invariant mass {m}_{boverline{b}} of the two b-tagged jets as well as the three-invariant jet mass {m}_{boverline{b}j} as particularly interesting observables to study SMEFT effects. These distributions receive contributions that change both their normalisation and shape with the latter modifications depending on the exact jet definition. To our knowledge SMEFT effects of this type have so far not been discussed in the literature. The presented MC generator can also serve as a starting point to obtain NNLO+PS accuracy for a suitable enlarged set of effective operators in the future.

B → cτ overline{nu} e,μ contributions to R(D(*))

The R(D(*)) puzzle stands for a ~ 3σ violation of lepton flavor universality between the decay rates of B → D(*)τν and B → D(*)ℓν, where ℓ = e, μ. If it is accounted for by new physics, there is no reason in general that the relevant neutrinos are, respectively, ντ and νℓ. We study whether the τ related rate could be enhanced by significant contributions to B → D(*)τνℓ from a class of operators in the Standard Model Effective Field Theory (SMEFT). We find the upper bounds from forbidden or rare meson decays imply that the contributions from the lepton flavor violating processes account for no more than about 4% of the required shift. Yet, no fine-tuned flavor alignment is required for the new physics. Searching for the related high-pT process pp → τ±μ∓ can at present put a lower bound on the scale of the lepton flavor violating new physics that is a factor of 2.2 weaker than the bound from meson decays. An exception to our conclusion arises from a specific combination of scalar and tensor SMEFT operators.

Searching for new physics from SMEFT and leptoquarks at the P2 experiment

The P2 experiment aims at high-precision measurements of the parity-violating asymmetry in elastic electron-proton and electron-$^{12}$C scatterings with longitudinally polarized electrons. We discuss here the sensitivity of P2 to leptoquarks, which within the P2 energy range can be described in the language of Standard Model Effective Field Theory (SMEFT). We give the expected P2 limits on the SMEFT operators and on the leptoquark parameters, which will test energy scales up to 15 TeV. In many cases those limits exceed current constraints from LHC and atomic parity violation (APV) experiments. We also demonstrate that degeneracies of different SMEFT operators can partially be resolved by use of APV experiments and different targets (protons and $^{12}$C) at P2. Moreover, we show that P2 could confirm or resolve potential tensions between the theoretical and experimental determinations of the weak charge of $^{133}$Cs.