SSNSN-323-63February 22, 2021
CMS measurements of EFT parameters with top quarks
Nicolas Tonon on behalf of the CMS Collaboration
Deutsches Elektronen-Synchrotron (DESY)Notkestraße 85, 22607 Hamburg, Germany
Measurements carried out or reinterpreted within the framework ofeffective field theory (EFT) will constitute a key component of the LHClegacy in the quest towards physics beyond the standard model. NumerousEFT measurements were already published by the CMS Collaboration. Inthe top quark sector, four distinct approaches to EFT have been identified,each successfully applied in several analyses. We review the pros and consof each approach, while illustrating them with recent analyses in whichthey were adopted. PRESENTED AT th International Workshop on Top Quark PhysicsDurham, UK (videoconference), 14–18 September, 2020 a r X i v : . [ h e p - e x ] F e b Introduction
The standard model (SM) of particle physics predicts with great accuracy a tremen-dous number of experimental results covering a wide energy range up to the TeV scaleaccessible at the CERN LHC [1]. Still, it does not provide explanations for severalkey observations such as the existence of dark matter and energy, or the masses ofneutrinos. More generally, there exists a number of indications that the SM onlycorresponds to a low-energy approximation to a more fundamental theory beyondthe standard model (BSM).Various BSM models postulate the existence of new particles or mechanisms toaddress these shortcomings. However the SM does not predict the energy scale atwhich new physics may appear, and extensive research efforts notably carried out bythe ATLAS [2] and CMS [3] experiments at the LHC covering a large phase spaceregion did not yet indicate the presence of new physics.The large top quark mass of about 173 GeV and its Yukawa coupling to the Higgsboson close to unity suggest that it may play a special role within the SM, and thatits closer study may shed light on the electroweak symmetry breaking mechanism.Many BSM theories predict sizeable deviations of the top quark’s couplings with re-spect to SM predictions. Moreover, most of the canonical top quark processes havenow reached the precision era at the LHC, and their uncertainties are systematics-dominated. This motivates carrying out an ambitious research program in the topquark sector in order to reveal new physics effects indirectly through precision mea-surements.
One of the main theoretical frameworks to interpret potential deviations in a model-independent way is that of effective field theory (EFT). One key assumption of thisapproach is that the new physics is characterized by some unknown energy scale Λway beyond the energy reach of the LHC. Under this assumption, the SM Lagrangianis expanded with additional operators of higher mass dimensions ( d >
4) representingnew interactions between SM fields, whose coupling strengths are described by Wilsoncoefficients (WCs). Constraints placed on WCs may then be mapped onto any UV-complete model. An EFT thus offers a well-motivated and general framework tomaximize the discovery potential of massive BSM states at the LHC and beyond.For a given basis of operators, i.e. any complete and minimal set of operators ata given order, there is a large number of operators to consider: for instance there arealready 59 independent operators impacting the top quark at dimension 6, and thisnumber grows exponentially with mass dimension. Since constraining this huge pa-rameter space would require a wealth of data and the combination of a large number1f analyses targeting different final states (which is the ultimate goal), it is natural tomake motivated assumptions regarding the nature of new physics to restrict the con-sidered phase space. Most LHC EFT analyses up to now have considered dimension-6operators only, which are in general expected to describe most new physics effectssince higher-order operators are suppressed by powers of Λ; and operators of dimen-sion 5 or 7 lead to lepton flavor violation and are only relevant in specific analyses.Most useful guidelines and prescriptions on relevant assumptions are provided in anote arising from the LHCTopWG [4], which summarizes the fruitful outcomes of acollaboration between theorists and experimentalists.
Within the CMS Top group, four different strategies have been identified and em-ployed so far to constrain EFT operators. They can broadly be classified on a spec-trum ranging from post-measurement reinterpretations towards direct EFT measure-ments carried out at the detector level. In the following, we detail each approachwith its pros and cons, and provide recent examples of CMS top quark analyses inwhich they were adopted.
A first approach consists in reinterpreting a cross section measurement a posteriori.Its value can be parameterized with the EFT operators of interest, which makes itpossible to constrain their WCs in a straightforward manner. The main advantagesof this approach are its good scalability and its ease of combination with other mea-surements obtained with any experiment. It also does not require the generation ofany dedicated Monte-Carlo simulated sample including the impact of EFT operators.On the other hand, such reinterpretations typically rely on assumptions regardingnew physics, which usually does not only impact the cross section itself, but alsothe kinematic distributions of the objects used in an analysis for event selection andsignal extraction.This approach was adopted to reinterpret the cross section measurement of thefour-top process by CMS [5]. This analysis is particularly challenging since the signalhas an expected SM cross section σ ( SM ) = 9 . tt background. The four-top process is highly sensitive to four-heavy-quark operators. The signal cross section was parameterized at the generatorlevel with several EFT operators as: σ tttt = σ SMtttt + 1Λ (cid:88) k C k σ (1) k + 1Λ (cid:88) j ≤ k C j C k σ (2) j,k , (1)2here the linear terms C k σ (1) k represent the interference terms of the SM and dimension-6 EFT contributions, while the quadratic terms include two components: the squaredcontributions from diagrams containing one EFT operator, and the interference termsfor two diagrams both including the insertion of one operator. This parameterizationwas used to translate the measured cross section into 95% CL upper limits on eachindividual WC, while marginalizing over the other operators. A second approach consists in reinterpreting a differential measurement unfolded atthe generator level. Such reinterpretations may be combined with other results ifbin-to-bin correlation matrices are provided, and require the generation of differen-tial Monte-Carlo sample including EFT effects at the generator level. Differentialmeasurements of quantities sensitive to EFT make it possible to also exploit shapeinformation and typically lead to tighter constraints compared to inclusive ones, butignore the effects that new physics may have on the detector acceptance and selectionefficiencies.This procedure was followed in the CMS measurement of the differential tt crosssection as a function of kinematic observables of the top quarks, of its decay productsand of the tt system [6]. This analysis targeted the dileptonic opposite-sign finalstate. The measurements were unfolded both to the parton and particle levels, infull and fiducial phase spaces respectively. The angular separation between the twoleptons ∆ φ ( (cid:96)(cid:96) ) was simulated at generator level using the RIVET framework andparameterized with the O tG operator at next-to-leading order (NLO) in QCD. Thisoperator modifies SM vertices and introduces new coupling structures, thus impactingboth the yield and kinematics of the tt process. It is directly related to the top quarkchromomagnetic dipole moment (CMDM), which is predicted to have a small valuewithin the SM and is modified in several BSM models (2HDM, SUSY, technicolor,etc.). Limits were set on O tG at the particle level at NLO. The higher accuracy inQCD was found to enhance the effects of this operator, and to significantly reducetheoretical scale uncertainties compared to LO predictions.Using the same data and targeting the same final state, a CMS measurement [7]of the differential tt cross section performed as a function of polarization and spincorrelation observables was used to constrain O tG via a simultaneous χ fit to sev-eral kinematic observables sensitive to spin correlations. Exploiting these powerfulvariables allowed to improve the sensitivity to O tG by about 30% compared to theprevious analysis. 3 .3 Hybrid measurement performed at detector level A third approach dubbed “hybrid measurement” relies on the EFT parameterizationof yields or differential distributions at the generator level; this parameterization isthen translated to the detector level under SM assumptions to extract the results.This approach was adopted in a search for new physics targeting the tt and tW pro-cesses in the dileptonic final state [8]. Limits on six different operators were extractedfrom a simultaneous fit to counting experiments and neural network discriminants inseveral categories. This constituted a first important step towards more global fitswherein EFT effects are considered in more than one process.A CMS measurement of the ttZ cross section in 3 (cid:96) and 4 (cid:96) final states set limits onseveral EFT operators using a more involved procedure [9]: first, LO generator levelsamples were produced on a fine grid over the theory phase space (i.e. both at SMand non-SM points); ratios were computed at different points with respect to the SMprediction to scale the distributions of interest, before applying any event selection;finally, these weights were translated to the detector level and applied to the nominalNLO signal sample to emulate the EFT contributions. The validity of the entireprocedure was verified in closure tests. Two-dimensional differential distributionswere used to extract limits both within the EFT and anomalous coupling frameworks. Finally the direct measurement approach minimizes the number of SM assumptions tomake, and makes it possible to consider EFT effects in all sensitive processes at once.It offers maximal control over correlations and systematic uncertainties. However, itrequires the generation of samples including EFT effects up to the detector level.A recent CMS analysis [10] employed this approach for the first time in the topquark sector to constrain a set of 16 relevant operators. It considered EFT effects infive associated production modes of the top quark with gauge and Higgs bosons ( ttZ , ttW , tZq , ttH , tHq ) in multilepton final states. Simulated samples including EFTeffects were passed through a full simulation of the CMS detector, and events werecategorized based on lepton, jet and b jet multiplicities to enhance the separationbetween different processes. The postfit yields are shown for different categories inFig. 1. Both 1D and 2D limits were extracted for each operator, while either settingthe other operators to zero or profiling them. This represents an important steptowards direct measurements including EFT effects in all relevant processes.4 v en t s Postfit (13 TeV) CMS
Preliminary ℓ ss ( + ) ℓ ss ( − ) ℓ ( + ) ℓ ( − ) ℓ ( + ) ℓ ( − ) S FZ S FZ ℓ da t a / p r ed Figure 1: Postfit yields in several multilepton categories from Ref. [10]. The yieldsof five top quark processes are parameterized with 16 different WCs, which get con-strained in a fit to the data.