Standard Model Effective Field Theory Research Articles

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.

Study on the sensitivity of the Higgs boson couplings in photon–photon collision at CLIC and muon collider

In a model-independent way, we explore the potential of photon-induced interactions with the process γ*γ* → ZZ to investigate CP-conserving and CP-violating dimension-six operators of Higgs-gauge boson couplings using the standard model effective field theory. The existence of anomalous H γ γ and HZZ couplings is discussed at 3 TeV compact linear collider (CLIC) and 10 TeV muon collider (MuC) with integrated luminosities of 5 and 10 ab−1, respectively. All signal and relevant background events are generated in MadGraph and passed through PYTHIA for parton showering and hadronization. The detector effects are evaluated using CLIC and MuC detector cards tuned in Delphes. We report the 95% confidence level limits on the Wilson coefficients c¯γ , c¯HB , c¯HW , c̃γ , c̃HB , and c̃HW and compare them with the experimental and phenomenological limits.

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.

Test of CP-invariance of the Higgs boson in vector-boson fusion production and in its decay into four leptons

A search for CP violation in the decay kinematics and vector-boson fusion production of the Higgs boson is performed in the H → ZZ* → 4ℓ (ℓ = e, μ) decay channel. The results are based on proton-proton collision data produced at the LHC at a centre-of-mass energy of 13 TeV and recorded by the ATLAS detector from 2015 to 2018, corresponding to an integrated luminosity of 139 fb−1. Matrix element-based optimal observables are used to constrain CP-odd couplings beyond the Standard Model in the framework of Standard Model effective field theory expressed in the Warsaw and Higgs bases. Differential fiducial cross-section measurements of the optimal observables are also performed, and a new fiducial cross-section measurement for vector-boson-fusion production is provided. All measurements are in agreement with the Standard Model prediction of a CP-even Higgs boson.

Walls, bubbles and doom — the cosmology of HEFT

As experiment charts new territory at the electroweak scale, the enterprise to characterise all possible theories becomes all the more necessary. In the absence of new particles, this ambitious enterprise is attainable and has led to the Higgs Effective Field Theory (HEFT) as the most general characterising framework, containing the Standard Model Effective Field Theory (SMEFT) as a subspace. The characterisation of this theory space led to the dichotomy SMEFT vs. HEFT SMEFT as the two possible realisations of symmetry breaking. The criterion to distinguish these two possibilities is non-local in field space, and phenomena which explore field space beyond the neighbourhood of the vacuum manifold are in a singular position to tell them apart. Cosmology allows for such phenomena, and this work focuses on HEFT SMEFT, the less explored of the two options, to find that first order phase transitions with detectable gravitational wave remnants, domain wall formation and vacuum decay in the far, far distant future can take place and single out HEFT SMEFT. Results in cosmology are put against LHC constraints, and the potential of future ground- and space-based experiments to cover parameter space is discussed.

Renormalisation group running effects in pp→tt¯h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$pp\\rightarrow t{\\bar{t}}h$$\\end{document} in the Standard Model Effective Field Theory

We study the effects of renormalisation group running of the Wilson coefficients in Standard Model Effective Field Theory, using the process pp→tt¯h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$pp \\rightarrow t {\\bar{t}}h$$\\end{document} as a showcase. We consider both strong and top Yukawa running effects, since the latter can be relevant in presence of large Wilson coefficients. We study the difference between the use of a dynamical and fixed renormalisation scale by exploring different scenarios for the higher-dimensional operators at the high energy scale of new physics, assumed to be at the TeV scale.

Using the effective weak mixing angle as an input parameter in SMEFT

We implement electroweak renormalisation schemes involving the effective weak mixing angle to NLO in Standard Model Effective Field Theory (SMEFT). After developing the necessary theoretical machinery, we analyse a select set of electroweak precision observables in such input schemes. An attractive feature is that large corrections from top-quark loops appearing in other schemes are absorbed into the definition of the effective weak mixing angle. On the other hand, the renormalisation condition which achieves this involves a large number of flavour-specific SMEFT couplings between the Z boson and charged leptons, motivating simple flavour assumptions such as minimal flavour violation for practical applications. The results of this paper provide a valuable new component for estimating systematic uncertainties in SMEFT fits by performing analyses in multiple input schemes.

Lepton flavor violation by two units

Charged lepton flavor violation arises in the Standard Model Effective Field Theory at mass dimension six. The operators that induce neutrinoless muon and tauon decays are among the best constrained and are sensitive to new-physics scales up to 107GeV. An entirely different class of lepton-flavor-violating operators violates lepton flavors by two units rather than one and does not lead to such clean signatures. Even the well-known case of muonium–anti-muonium conversion that falls into this category is only sensitive to two out of the three ΔLμ=−ΔLe=2 dimension-six operators. We derive constraints on many of these operators from lepton flavor universality and show how to make further progress with future searches at Belle II and future experiments such as Z factories or muon colliders.

Sensitivity prospects for lepton-trijet signals in the ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}SMEFT at the LHeC

The observation of neutrino oscillations and masses motivates the extension of the standard model with right-handed neutrinos, leading to heavy neutrino states possibly in the electroweak scale, which could be impacted by new high-scale weakly coupled physics. A systematic tool for studying these interactions is the neutrino-extended standard model effective field theory ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}SMEFT. In this work we study the prospects of the future LHeC electron-proton collider to discover or constrain the ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}SMEFT interactions, performing the first dedicated and realistic analysis of the well known lepton-trijet signals, for both the lepton flavor violating pe-→μ-+3j\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p ~ e^{-} \\rightarrow \\mu ^{-} + 3 \ extrm{j}$$\\end{document} (LFV) and the lepton number violating pe-→μ++3j\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p ~ e^{-} \\rightarrow \\mu ^{+} + 3 \ extrm{j}$$\\end{document} (LNV) channels, for HNLs masses in the electroweak scale range: 100GeV≤mN≤500GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100 ~{\ extrm{GeV}} \\le m_N \\le 500 ~{\ extrm{GeV}}$$\\end{document}. The obtained sensitivity prospects show that the LHeC with 100fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100 ~{\ extrm{fb}}^{-1}$$\\end{document} luminosity could be able to probe the scenario of a heavy N and constrain the effective couplings to a region of the parameter space as tight as the bounds that are currently considered for the O(10)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(10)$$\\end{document} GeV scale masses, with effective couplings of O(10-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(10^{-1})$$\\end{document} for NP scale Λ=1TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda =1 \\,{\ extrm{TeV}}$$\\end{document}.

The standard model effective field theory at work

The standard model effective field theory at work

Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart

In this article we study the phenomenological implications of multiple Higgs boson production from longitudinal vector boson scattering in the context of effective field theories. We find compact representations for effective tree-level amplitudes with up to four final state Higgs bosons. Total cross sections are then computed for scenarios relevant at the LHC in which we find the general Higgs Effective Theory (HEFT) prediction avoids the heavy suppression observed in Standard Model Effective Field Theory (SMEFT).

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.

Revisiting renormalization group equations of the SMEFT dimension-seven operators

In this work, we revisit the renormalization group equations (RGEs) of dimension-seven (dim-7) operators in the Standard Model effective field theory (SMEFT) resulting from mixing among dim-7 operators themselves by means of the background field method. Adopting a recently proposed physical basis for dim-7 operators, we achieve the explicit RGEs of all non-redundant dim-7 operators in the SMEFT for the first time. Together with those originating from the dim-5 and dim-6 operators, these results constitute the complete RGEs of dim-7 operators, and hence can be exploited to study full RG-running effects on some lepton- or baryon-number-violating processes involving dim-7 operators in the SMEFT, such as neutrino masses, neutrinoless double beta decay, meson and nucleon decays. We perform an analysis of the structure and perturbative power counting of the obtained one-loop anomalous dimension matrix, which is consistent with a non-renormalization theorem and the naive dimension analysis. Additionally, a partial check on some results is carried out by means of different tools and quantum field gauges.

A complete set of the dimension-8 Green’s basis operators in the Standard Model effective field theory

We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We propose an off-shell amplitude formalism such that this new kind of amplitude has a one-to-one correspondence to general operators carrying all kinds of redundancies. The advantage of such formalism is that all kinds of redundancies can be formulated explicitly in terms of the off-shell spinors and thus be removed systematically from the exhaustive list of the general off-shell amplitudes. Following such procedures, redundant operators can be reduced to the ones with the only redundancy from the equation of motion kept, the Green’s basis. We find there are (993+1649) independent (on-shell + off-shell) operators for one generation of fermions and (44807+66197) ones for three generations at dimension 8. This systematic method can be applied to obtain the Green’s basis at any mass dimension for general EFTs.

Two loop renormalization of scalar theories using a geometric approach

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order p6.

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.

More accurate σGG→h,Γh→GGAAΨ¯Ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sigma \\left(\\mathcal{GG}\ o h\\right),\\Gamma \\left(h\ o \\mathcal{GG},\\mathcal{AA},\\overline{\\Psi}\\Psi \\right) $$\\end{document} and Higgs width results via the geoSMEFT

We develop Standard Model Effective Field Theory (SMEFT) predictions of σ(GG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{GG} $$\\end{document} → h), Γ(h → GG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{GG} $$\\end{document}), Γ(h → AA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{AA} $$\\end{document}) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h → Ψ¯Ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\\Psi}\\Psi $$\\end{document}) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σ to a full set of corrections at Ov¯T2/Λ216π22\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\overline{v}}_T^2/{\\varLambda}^2{\\left(16{\\pi}^2\\right)}^2\\right) $$\\end{document} and Ov¯T4/Λ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\overline{v}}_T^4/{\\Lambda}^4\\right) $$\\end{document}, where v¯T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{v}}_T $$\\end{document} is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h → Ψ¯Ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\\Psi}\\Psi $$\\end{document}), we include results at Ov¯T2/Λ216π2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\overline{v}}_T^2/{\\Lambda}^2\\left(16{\\pi}^2\\right)\\right) $$\\end{document} in the limit where subleading mΨ → 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects.

Higgs associated production with a vector decaying to two fermions in the geoSMEFT

We present the inclusive calculations of a Higgs boson produced in association with massive vector bosons in the Standard Model Effective Field Theory (SMEFT) to order 1/\Lambda^41/Λ4 for the 13 TeV LHC. The calculations include the decay of the vector boson into massless constituents and are done using the geometric formulation of the SMEFT supplemented by the relevant dimension eight operators not included in the geoSMEFT. We include some discussion of distributions to motivate how detailed collider and experimental searches for SMEFT signals could be improved.

Long-lived neutral fermions at the DUNE near detector

At the Deep Underground Neutrino Experiment (DUNE), a proton beam hits a fixed target leading to large production rates of mesons. These mesons can decay and potentially provide a source of long-lived neutral fermions. Examples of such long-lived fermions are heavy neutral leptons which can mix with the standard-model active neutrinos, and the bino-like lightest neutralino in R-parity-violating supersymmetry. We show that the Standard Model Effective Field Theory extended with right-handed singlet neutrinos can simultaneously describe heavy neutral leptons and bino-like neutralinos in a unified manner. We use the effective-field-theory framework to determine the sensitivity reach of the DUNE near detector in probing various scenarios of long-lived neutral fermions.

Global analysis of the ALP effective theory

We perform a global fit of the effective Lagrangian for axion-like particles (ALPs) to data. By combining LHC observables from top physics, dijet and di-boson production with electroweak precision observables, we resolve the full parameter space of ALPs with flavor-universal couplings. Using the renormalization group to evolve the effective ALP couplings to low energies allows us to investigate the impact of flavor observables on the global analysis. We show that resonance searches in B → K meson decays significantly enhance the sensitivity to ALPs with sub-GeV masses. The lifetime of the ALP plays a crucial role in resolving the multi-dimensional parameter space with searches for prompt, displaced and invisible ALP decays. Our analysis points out the differences in probing an effective theory with new light particles, compared to scenarios with only non-resonant effects of heavy particles at low energies, as in the Standard Model Effective Field Theory.