Standard Model Effective Field Theory Operators Research Articles

EFT diagrammatica: UV roots of the CP-conserving SMEFT

The Standard Model Effective Field Theory (SMEFT) is an established theoretical framework that parametrises the impact a UV theory has on low-energy observables. Such parametrization is achieved by studying the interactions of SM fields encapsulated within higher mass dimensional (≥ 5) operators. Through judicious employment of the tools of EFTs, SMEFT has become a source of new predictions as well as a platform for conducting a coherent comparison of new physics (beyond Standard Model) scenarios. 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. We have elucidated the links of a chain connecting specific CP conserving dimension-6 SMEFT operators with unique sets of heavy field representations. The contact interactions representing each effective operator have been unfolded into tree- and (or) one-loop-level diagrams to reveal unique embeddings of heavy fields within them. For each case, the renormalizable vertices of a UV model serve as the building blocks for all possible unfolded diagrams. Based on this, we have laid the groundwork to construct observable-driven new physics models. This in turn also prevents us from making redundant analyses of similar models. While we have taken a predominantly minimalistic approach, we have also highlighted the necessity for non-minimal interactions for certain operators.

ALP \u2014 SMEFT interference

The Standard Model Effective Field Theory (SMEFT) offers a powerful theoretical framework for parameterizing the low-energy effects of heavy new particles with masses far above the scale of electroweak symmetry breaking. Additional light degrees of freedom extend the effective theory. We show that light new particles that are weakly coupled to the SM via non-renormalizable interactions induce non-zero Wilson coefficients in the SMEFT Lagrangian via renormalization-group evolution. For the well-motivated example of axions and axion-like particles (ALPs) interacting with the SM via classically shift-invariant dimension-5 interactions, we calculate how these interactions contribute to the one-loop renormalization of the dimension-6 SMEFT operators, and how this running sources additional contributions to the Wilson coefficients on top of those expected from heavy new states. As an application, we study the ALP contributions to the magnetic dipole moment of the top quark and comment on implications of electroweak precision constraints on ALP couplings.

Anomalous dimensions from Yukawa couplings in SMNEFT: four-fermion operators

The Standard Model Neutrino Effective Field Theory (SMNEFT) is the Standard Model Effective Field Theory (SMEFT) augmented with right-handed neutrinos. Building on our previous work, arXiv:2010.12109, we calculate the Yukawa coupling contributions to the one-loop anomalous dimension matrix for the 11 dimension-six four-fermion SMNEFT operators. We also present the new contributions to the anomalous dimension matrix for the 14 four-fermion SMEFT operators that mix with the SMNEFT operators through the Yukawa couplings of the right-handed neutrinos.

Top, Higgs, diboson and electroweak fit to the Standard Model effective field theory

The search for effective field theory deformations of the Standard Model (SM) is a major goal of particle physics that can benefit from a global approach in the framework of the Standard Model Effective Field Theory (SMEFT). For the first time, we include LHC data on top production and differential distributions together with Higgs production and decay rates and Simplified Template Cross-Section (STXS) measurements in a global fit, as well as precision electroweak and diboson measurements from LEP and the LHC, in a global analysis with SMEFT operators of dimension 6 included linearly. We present the constraints on the coefficients of these operators, both individually and when marginalised, in flavour-universal and top-specific scenarios, studying the interplay of these datasets and the correlations they induce in the SMEFT. We then explore the constraints that our linear SMEFT analysis imposes on specific ultra-violet completions of the Standard Model, including those with single additional fields and low-mass stop squarks. We also present a model-independent search for deformations of the SM that contribute to between two and five SMEFT operator coefficients. In no case do we find any significant evidence for physics beyond the SM. Our underlying Fitmaker public code provides a framework for future generalisations of our analysis, including a quadratic treatment of dimension-6 operators.

Non-standard interactions in SMEFT confronted with terrestrial neutrino experiments

The Standard Model Effective Field Theory (SMEFT) provides a systematic and model-independent framework to study neutrino non-standard interactions (NSIs). We study the constraining power of the on-going neutrino oscillation experiments T2K, NOνA, Daya Bay, Double Chooz and RENO in the SMEFT framework. A full consideration of matching is provided between different effective field theories and the renormalization group running at different scales, filling the gap between the low-energy neutrino oscillation experiments and SMEFT at the UV scale. We first illustrate our method with a top- down approach in a simplified scalar leptoquark model, showing more stringent constraints from the neutrino oscillation experiments compared to collider studies. We then provide a bottom-up study on individual dimension-6 SMEFT operators and find NSIs in neutrino experiments already sensitive to new physics at ∼20 TeV when the Wilson coefficients are fixed at unity. We also investigate the correlation among multiple operators at the UV scale and find it could change the constraints on SMEFT operators by several orders of magnitude compared with when only one operator is considered. Furthermore, we find that accelerator and reactor neutrino experiments are sensitive to different SMEFT operators, which highlights the complementarity of the two experiment types.

Constraining SMEFT operators with associated hγ production in weak boson fusion

We consider the associated production of a Higgs boson and a photon in weak boson fusion in the Standard Model (SM) and the Standard Model Effective Field Theory (SMEFT), with the Higgs boson decaying to a pair of bottom quarks. Analysing events in a cut-based analysis and with multivariate techniques we determine the sensitivity of this process to the bottom-Yukawa coupling in the SM and to possible CP-violation mediated by dimension-6 operators in the SMEFT.

SMEFT atlas of \u2206F = 2 transitions

We present a model-independent anatomy of the ∆F = 2 transitions K0− {overline{K}}^0 , Bs,d− {overline{B}}_{s,d} and D0− {overline{D}}^0 in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude [M12]BSM. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale μew and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale Λ. The coefficients {P}_a^{ij} entering these formulae contain all the information below the scales μew and Λ, respectively. Renormalization group effects from the top-quark Yukawa coupling play the most important role. The collection of the individual contributions of the SMEFT operators to [M12]BSM can be considered as the SMEFT atlas of ∆F = 2 transitions and constitutes a travel guide to such transitions far beyond the scales explored by the LHC. We emphasize that this atlas depends on whether the down-basis or the up-basis for SMEFT operators is considered. We illustrate this technology with tree-level exchanges of heavy gauge bosons (Z′, G′) and corresponding heavy scalars.

Higgs decay to fermion pairs at NLO in SMEFT

The calculation of next-to-leading order (NLO) perturbative corrections at fixed operator dimension in Standard Model Effective Field Theory (SMEFT) has been a topic of much recent interest. In this paper we obtain the NLO corrections from dimension-6 operators to the Higgs boson decays hto foverline{f} , where the fermions f ∈ {μ, τ, c}. This extends previous results for hto boverline{b} to all phenomenologically relevant Higgs boson decays into fermions, and provides the basis for future precision analyses of these decays within effective field theory. We point out the benefits of studying ratios of decay rates into different fermions in SMEFT, the most surprising of which is enhanced sensitivity to anomalous hγγ and hgg couplings induced by flavor-universal SMEFT operators, especially in scenarios where flavor-dependent Wilson coefficients are constrained by Minimal Flavor Violation.

LHC dijet angular distributions as a probe for the dimension-six triple gluon vertex

In the absence of a concrete discovery of new physics at the LHC, global analyses of the standard model effective field theory (SMEFT) are important to find and describe the impact of new physics beyond the energy reach of the LHC. Among the SMEFT operators that can be constrained via various measurements, the dimension six triple gluon operator involves neither the Higgs boson nor the top quark, yet its variation can have measurable effects on top and Higgs production. Without independent constraints on its impact, the sensitivity of measurements in the top and Higgs sectors to new physics is reduced. Previous analyses have used various techniques to constrain the influence of the triple gluon operator. We show that the dijet angular distribution is a powerful observable for probing the triple gluon operator because of the different helicity structure of the dimension-six interaction, namely the lack of a t-channel exchange term, as compared with expectations from QCD. Using this novel approach, we set the most stringent limit on the size of the triple gluon effective coupling by reinterpreting the results of a search for new phenomena in dijet events using 35.9 fb−1 of pp collision data collected at s=13 TeV performed by the CMS Collaboration.

Putting standard model EFT fits to work

The Standard Model Effective Field Theory (SMEFT) provides a consistent framework for comparing precision measurements at the LHC to the Standard Model. The observation of statistically significant non-zero SMEFT coefficients would correspond to physics beyond the Standard Model (BSM) of some sort. A more difficult question to answer is what, if any, detailed information about the nature of the underlying high scale model can be obtained from these measurements. In this work, we consider the patterns of SMEFT operators present in five example models and discuss the assumptions inherent in using global fits to make BSM conclusions. We find that including renormalization group effects has a significant impact on the interpretation of the results. As a by-product of our study, we present an up-dated global fit to SMEFT coefficients in the Warsaw basis including some next-to-leading order QCD corrections in the SMEFT theory.

Extending low energy effective field theory with a complete set of dimension-7 operators

We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon (∆B) and lepton (∆L) numbers violated. Including Hermitian-conjugated operators, there are in total 3168, 750, 588, 712 operators with (∆B, ∆L) = (0, 0), (0, ±2), (±1, ∓1), (±1, ±1) respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare various neutrino-photon scattering cross sections with their counterparts in the standard model and highlight the new features. Finally, we illustrate how these effective interactions could arise from ultraviolet completion.

Removing flat directions in standard model EFT fits: How polarized electron-ion collider data can complement the LHC

We study the potential of future Electron-Ion Collider (EIC) data to probe four-fermion operators in the Standard Model Effective Field Theory (SMEFT). The ability to perform measurements with both polarized electron and proton beams at the EIC provides a powerful tool that can disentangle the effects from different SMEFT operators. We compare the potential constraints from an EIC with those obtained from Drell-Yan data at the Large Hadron Collider. We show that EIC data plays an important complementary role since it probes combinations of Wilson coefficients not accessible through available Drell-Yan measurements.

Flavourful SMEFT likelihood for Higgs and electroweak data

We perform an updated fit to LHC Higgs data and LEP electroweak precision tests in the framework of the Standard Model Effective Field Theory (SMEFT). We assume a generic structure of the SMEFT operators without imposing any flavour symmetries. The implementation is released as part of the public global SMEFT likelihood. This allows one to fit parameters of a broad class of new physics models to combined Higgs, electroweak, quark flavour, and lepton flavour observables.

Constraining the SMEFT with Bayesian reweighting

We illustrate how Bayesian reweighting can be used to incorporate the constraints provided by new measurements into a global Monte Carlo analysis of the Standard Model Effective Field Theory (SMEFT). This method, extensively applied to study the impact of new data on the parton distribution functions of the proton, is here validated by means of our recent SMEFiT analysis of the top quark sector. We show how, under well-defined conditions and for the SMEFT operators directly sensitive to the new data, the reweighting procedure is equivalent to a corresponding new fit. We quantify the amount of information added to the SMEFT parameter space by means of the Shannon entropy and of the Kolmogorov-Smirnov statistic. We investigate the dependence of our results upon the choice of alternative expressions of the weights.

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

We present 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. 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 latter include generation of ghost vertices). Further options allow to treat neutrino fields as massless Weyl or massive Majorana fermions. The derived Lagrangian in the mass basis can be exported in various formats supported by FeynRules, such as UFO and FeynArts. Initialisation of numerical values of d=6 Wilson coefficients used by SmeftFR is interfaced to WCxf format. The package also includes dedicated Latex generator allowing to print the result in clear human-readable form. SmeftFR can be downloaded from the address www.fuw.edu.pl/smeft. Program summaryProgram Title:SmeftFR v2.0Program Files doi:http://dx.doi.org/10.17632/yyv9fpmwzv.1Licensing provisions: GPLv3Programming language: Mathematica 11.3 or later (earlier versions were reported to have problems running this code).Nature of problem: Standard Model Effective Field Theory (SMEFT) has become in recent years a commonly used model to parameterise the potential effects of New Physics. Calculation of physical observables within such a complicated theory requires large degree of automatisation, starting from the generation of Feynman rules in various formats, which could be further imported to Monte Carlo generators or symbolic packages calculating transition amplitudes. SmeftFR package generates such Feynman rules for SMEFT in physical (mass) field basis for the user defined subset of dimension 5 and 6 operators, in unitary or linear Rξ-gauges.Solution method: Implementation (as the Mathematica package) of the results of Ref. [1]. SmeftFR generates dynamically “model files” for the FeynRules package [2], based on user-defined set of options — most important are SMEFT operators subset, gauge fixing choice and numerical input for Wilson coefficients in the WCxf format [3]. Subsequently FeynRules engine is used to calculate SMEFT Feynman rules, which can be later manipulated or exported in several formats, such as UFO, FeynArts, Latex, WCxf and others, by SmeftFR auxiliary routines.Additional comments: Running the code requires prior installation of the FeynRules package [2], https://feynrules.irmp.ucl.ac.be.[1] A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek and K. Suxho, “Feynman rules for the Standard Model Effective Field Theory in Rξ-gauges,” JHEP 1706, 143 (2017).[2] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr and B. Fuks, “FeynRules 2.0 - A complete toolbox for tree-level phenomenology,” Comput. Phys. Commun. 185, 2250 (2014).[3] J. Aebischer, et al., WCxf: an exchange format for Wilson coefficients beyond the Standard Model, Comput. Phys. Commun. 232 (2018) 71–83.

Off-shell single-top-quark production in the Standard Model Effective Field Theory

We present a fully differential and spin-dependent t-channel single-top-quark calculation at next-to-leading order (NLO) in QCD including off-shell effects by using the complex mass scheme in the Standard Model (SM) and in the Standard Model Effective Field Theory (SMEFT). We include all relevant SMEFT operators at 1/Λ2 that contribute at NLO in QCD for a fully consistent comparison to the SM at NLO. In addition, we include chirality flipping operators that do not interfere with the SM amplitude and contribute only at 1/Λ4 with a massless b-quark. Such higher order effects are usually captured by considering anomalous right-handed Wtb and left-handed Wtb tensor couplings. Despite their formal suppression in the SMEFT, they describe an important class of models for new physics. Our calculation and analysis framework is publicly available in MCFM.

Reactor neutrino oscillations as constraints on effective field theory

We study constraints on the Standard Model Effective Field Theory (SMEFT) from neutrino oscillations in short-baseline reactor experiments. We calculate the survival probability of reactor antineutrinos at the leading order in the SMEFT expansion, that is including linear effects of dimension-6 operators. It is shown that, at this order, reactor experiments alone cannot probe charged-current contact interactions between leptons and quarks that are of the (pseudo)vector (V±A) or pseudo-scalar type. We also note that flavor-diagonal (pseudo)vector coefficients do not have observable effects in oscillation experiments. In this we reach novel or different conclusions than prior analyses of non-standard neutrino interactions. On the other hand, reactor experiments offer a unique opportunity to probe tensor and scalar SMEFT operators that are off-diagonal in the lepton-flavor space. We derive constraints on the corresponding SMEFT parameters using the most recent data from the Daya Bay and RENO experiments.

Indirect signs of the Peccei-Quinn mechanism

In the Standard Model, the renormalization of the QCD vacuum angle $\theta$ is extremely tiny, and small $\theta$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $\Delta\theta$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $\theta$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $\theta=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $\theta$ is small in the infrared. We study the quadratic divergences in $\theta$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.

Anomalies in bottom from new physics in top

We analyze the possibility to accommodate current b→sℓ+ℓ− anomalies with TeV-scale mediators that couple to right-handed top quarks and muons, contributing to b→sℓ+ℓ− at the one-loop level. We use the Standard Model Effective Field Theory (SMEFT) framework but also look at specific scenarios by taking into account all possible irreducible representations of the Lorentz and Standard Model gauge group for the mediators. From a global fit of b→sℓ+ℓ− data and LEP-I observables we find that the Wilson coefficients of two SMEFT operators: Oℓu=(ℓ¯LμγαℓLμ)(t¯RγαtR) and Oeu=(μ¯RγαμR)(t¯RγαtR) need to satisfy Ceu∼Cℓu. New physics enters then in b→sℓ+ℓ− mainly through the operator O9=(s¯γμPLb)(ℓ¯γμℓ) of the Weak Effective Theory. After discussing all possible mediators, we concentrate on two scenarios: A vector boson in the irreducible representation Zμ′∼(1,1,0) of the Standard Model gauge group with vectorial coupling to muons, and a combination of two leptoquarks: the scalar R2∼(3,2,7/6) and the vector U˜1μ∼(3,1,5/3). We derive LHC constraints by recasting di-muon resonance, pp→tt¯tt¯ and SUSY searches. Additionally, we analyze the prospects for discovering these mediators during the high-luminosity phase of the LHC.

Gauge-invariant implications of the LHCb measurements on lepton-flavor nonuniversality

We study the implications of the recent measurements of $R_K$ and $R_{K^*}$ by the LHCb collaboration. We do that by adopting a model-independent approach based on the Standard Model Effective Field Theory (SMEFT), in which the dominant new physics effects are encoded in the coefficients of dimension-six operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for $R_K$ and $R_{K^\ast}$, we determine the implications of the recent LHCb results for these observables on the coefficients of the SMEFT operators at low and high energies. We also take into account all $b\to s \ell\ell$ data, which combined lead to effective New Physics (NP) scenarios with SM pulls in excess of 5~$\sigma$. Thus the operators discussed in this paper would be the first dimension-six terms in the SM Lagrangian to be detected experimentally. Indirect constraints on these operators are also discussed. The results of this paper transcend the singularity of the present situation, and set a standard for future analyses in $b\to s$ transitions when the NP is assumed to lie above the electroweak scale.