Available on the CERN CDS information server CMS PAS EXO-16-049

CMS Physics Analysis Summary

Contact: cms-pag-conveners-exotica@cern.ch 2018/04/03

Search for dark matter produced in association with a topquark pair at

√s = 13 TeV

The CMS Collaboration

Abstract

A search is performed for dark matter produced in association with a top quark pairin proton-proton collisions at

√s = 13 TeV recorded by the CMS detector at the LHC in

2016. The data correspond to an integrated luminosity of 35.9 fb−1. Combined resultsof final states involving zero, one, or two leptons (electrons or muons) are presented.No significant excess is observed, and the results are interpreted in the context of sim-plified models of dark matter production via spin-0 mediators. Scalar (pseudoscalar)mediators with masses below 165 (223) GeV are excluded at 95% confidence level.These are the most stringent limits at the LHC on dark matter models involving ascalar mediator. Constraints on the coupling strength between dark matter and stan-dard model quarks are also presented.

1. Introduction 1

1 IntroductionAstrophysical observations strongly motivate the existence of dark matter (DM) [1–3], whichmay originate from physics beyond the standard model. In a large class of models, DM consistsof stable, weakly interacting massive particles (χ) [1], which may be pair produced at the CERNLHC via new mediators that couple these DM particles to standard model (SM) quarks. TheDM particles escape detection, thereby creating a transverse momentum imbalance (pmiss

T ) inthe event. A compelling model for tt+χχ production posits that DM couples preferentially tothe top quark via a scalar or pseudoscalar mediator [4–12]. At the LHC, the tt+χχ process canbe probed through the signature of a top quark pair plus pmiss

T [13, 14].

This article presents a search for DM produced with a top quark pair in pp collisions at√

s =

13 TeV with 35.9 fb−1 of data recorded by the CMS experiment in 2016. The analysis builds onthe strategy previously employed in Ref. [15]. The data are categorized into signal regions (SRs)that correspond to different decay modes of the tt system: all-hadronic, lepton+jets (`+jets),and dileptonic. The signal is extracted from a fit to the pmiss

T distributions in these signal regions.Data from control regions (CRs) enriched in tt, W+jets, and Z+jets processes are included inthe fit to constrain these backgrounds.

2 The CMS detector and physics object reconstructionA detailed description of the CMS detector, the coordinate system, and the relevant kinematicvariables is provided in Ref. [16]. Event reconstruction is based on the particle-flow (PF) al-gorithm [17], which reconstructs and identifies individual particles using an optimized com-bination of the detector information. The ~pmiss

T vector is computed as the negative vector sumof the transverse momenta (pT) of all the PF candidates in an event. Jets are formed from PFcandidates using the anti-kT algorithm [18, 19]. Corrections are applied to calibrate the jet mo-mentum [20] and to remove energy from additional collisions in the events (pileup) [21]. Thesecorrections are also propagated to the pmiss

T calculation. Jets in the analysis are required tohave pT > 30 GeV and pseudorapidity (η) within 2.4, and to satisfy identification criteria [22]that minimize spurious detector and reconstruction effects. The combined secondary vertexb tagging algorithm [23, 24] is used to identify jets originating from b quarks. A multivariatediscriminant, the “resolved top tagger” (RTT) [15], based on jet properties and kinematic infor-mation, is used to identify top quarks that decay into three jets. The reconstructed vertex withthe largest value of summed physics-object p2

T is taken to be the primary pp interaction vertex.The physics objects are the jets, clustered using the jet finding algorithm [18, 19] with the tracksassigned to the vertex as inputs, and the associated missing transverse momentum, taken asthe negative vector sum of the pT of those jets.

3 Physics modeling and simulationThe tt+χχ signal results in high-pT jets, bottom quarks, leptons, and significant pmiss

T . Thelargest backgrounds are tt, W+jets, and Z+jets. The tt and single top quark backgrounds aresimulated at next-to-leading order (NLO) accuracy in quantum chromodynamics (QCD) us-ing POWHEG V2 and POWHEG V1 [25], respectively. Samples of Z+ jets, W+ jets, and QCDmultijet events are simulated at leading-order (LO) in QCD using MADGRAPH5 aMC@NLOv2.2.2 [26], with up to four additional partons in the final state. The W+jets and Z+jets sam-ples are corrected with boson pT-dependent QCD NLO/LO K factors computed using MAD-GRAPH5 aMC@NLO , and electroweak corrections obtained from Ref. [27–32]. Samples of

2

tt+W, tt+Z, and diboson processes (WW, WZ, and ZZ) are generated at NLO using eitherMADGRAPH5 aMC@NLO or POWHEG V2. The initial-state partons are modeled with theNNPDF 3.0 [33] parton distribution function (PDF) sets. Generated events are interfaced withPYTHIA 8.205 [34] for parton showering using the CUETP8M1 tune [35]. The simulation of theCMS detector is performed with GEANT4 [36]. Data-based corrections are applied to improvethe accuracy of the simulation.

The signal is simulated using simplified models of DM production [37]. The DM particlesare assumed to be Dirac fermions, and the mediators are spin-0 particles with scalar (φ) orpseudoscalar (a) interactions. The couplings between the mediator and SM quarks are gqq =

gqyq, where yq =√

2mq/v are the SM Yukawa couplings, mq is the quark mass, and v =246 GeV is the Higgs boson field vacuum expectation value. The gq parameter is assumed tobe 1 for all quarks. The coupling strength of the mediators to DM, gχ, is assumed to be 1. Themodel does not account for any mixing between φ and the SM Higgs boson [38]. The tt+χχsignal is generated at LO using MADGRAPH5 aMC@NLO with up to one additional partonin the final state, and the mediator is forced to decay to a pair of DM fermions. The mediatorwidth is computed assuming no additional interactions apart from those described here; it iscalculated from the partial-width formulas given in Ref. [39]. The signal is normalized to thecross section computed at NLO with no additional partons in the Born process.

4 Event selectionData are collected by triggering on events containing large pmiss

T or high-pT leptons. The triggerused for searching in the all-hadronic final state is based on the amount of pmiss

T and HmissT

reconstructed with a coarse version of the PF algorithm. The HmissT variable is defined as the

magnitude of the pT vector sum of all jets passing the loose identification requirements withpT > 20 GeV and |η| < 5.0. The pmiss

T and HmissT requirements for this trigger range from 90

to 120 GeV, with the thresholds increasing with higher instantaneous luminosity during the2016 data taking. Events in the `+jets (` = e, µ) final state are obtained using single leptontriggers that require an electron (muon) with pT > 27 GeV (24 GeV). Events in the dilepton finalstate are obtained using single lepton and dilepton (ee, eµ, µµ) triggers. The trigger thresholdson the higher-pT and lower-pT electrons (muons) are 23 GeV (17 GeV) and 12 GeV (8 GeV),respectively.

Using additional selection requirements, two all-hadronic, one `+jets, and four dilepton SRsare defined. Several CRs enriched in SM processes are used to improve the simulation-basedbackground estimates for the SRs. At least one signal selection requirement is inverted to en-hance background yields in the CRs and to prevent event overlaps with the SRs. Together, theSRs and CRs associated with the individual tt+χχ final states are referred to as “channels”. Allthree tt+χχ channels are used in a simultaneous fit of pmiss

T distributions to extract a potentialDM signal. The fit allows the background-enriched CRs to constrain the contributions of tt,W+jets, and Z+jets processes within the CRs and SRs of each channel.

4.1 All-hadronic channel

The all-hadronic SRs require pmissT > 200 GeV, and four or more jets, of which at least one must

be b tagged. Any event with a loosely identified lepton with pT > 10 GeV is vetoed. Followingthese selection requirements, the dominant background consists of tt decays to `+jets, referredto as tt(1`), where the lepton is not identified. In contrast, both the top quarks of selected sig-nal events typically decay hadronically. The RTT is employed to define a category of eventswith two tagged hadronic top quark decays (2RTT), which suppresses the tt(1`) background,

4. Event selection 3

and a category with less than two top quark tags (0,1RTT) and at least two b-tagged jets. Spu-rious pmiss

T can arise in multijet events due to jet energy mismeasurement. In such cases, thereconstructed ~pmiss

T tends to align with a jet. The multijet background is suppressed by re-quiring the smallest azimuthal angle between the directions of ~pmiss

T and each jet in the event,∆j ≡ min ∆φ(~p j

T,~pmissT ), be greater than 0.4 (1.0) radians in the 2RTT (0,1RTT) category. The ∆j

requirement also helps to reduce the tt(1`) background, for which ~pmissT can align with a b-jet.

The CRs targeting the tt(1`) background are defined by selecting events with exactly one iden-tified lepton with pT > 30 GeV, and by requiring the transverse mass, MT, calculated from ~pmiss

Tand the lepton momentum (~p`T) as

MT =√

2p`T pmissT (1− cos ∆φ(~p`T,~pmiss

T )), (1)

to be less than 160 GeV, in order to avoid overlaps with the SR of the `+jets search channel.

The all-hadronic SRs also contain significant background contributions from Z(νν)+jets, andW(`ν)+jets where the lepton is not identified. Control regions enriched in both W+jets andZ+jets are formed by modifying the SR selections to require zero b-tagged jets. In addition,dedicated W+jets CRs are defined by requiring the presence of an isolated, identified leptonwith pT > 30 GeV and MT < 160 GeV. A CR dedicated to Z+jets is defined by requiring twowell-identified, oppositely charged, same-flavor leptons, where the dilepton mass falls between60 and 120 GeV. The pmiss

T observable in the hadronic SRs is emulated by ignoring the leptonmomenta in the pmiss

T calculation.

4.2 The `+jets channel

Events in the `+jets SR are selected by requiring pmissT > 160 GeV, exactly one lepton, and three

or more jets, of which at least one must satisfy the b tagging criteria. The lepton is required tohave pT > 30 GeV, and to pass the tight identification criteria [40, 41]. Events must not containadditional loosely identified leptons with pT > 10 GeV. A selection of MT > 160 GeV is im-posed to reduce the tt(1`) and W+jets backgrounds. Following these selections, the remainingbackground events primarily consist of dileptonic tt decays, referred to as tt(2`) events, whereone of the leptons is not identified. This background is suppressed by requiring that for thetwo highest pT jets in the event, ∆j1,2 ≡ min ∆φ(~p j1,2

T ,~pmissT ) > 1.2, and the MW

T2 variable [42] belarger than 200 GeV. The defining feature of the MW

T2 distribution is that it ideally lies below thetop quark mass for tt(2`) events.

The CR targeting the tt background is defined by requiring an additional lepton with respectto the SR selection, and by removing the selections on MT, MW

T2, and ∆j1,2 . To reduce the signalcontamination and avoid overlap with the dileptonic signal region, the M``

T2 variable [43–45] isrequired to be less than 110 GeV. A W+jets CR for the `+jets channel is defined by requiringzero b-tagged jets. The MT > 160 GeV selection from the SR selection is maintained, however,the requirements on MW

T2 and ∆j1,2 are removed.

4.3 Dilepton channel

Events in the dilepton SRs are selected by requiring exactly two oppositely charged leptonswith pT > 25 GeV and pT > 15 GeV, two or more jets, at least one b-tagged jet, and pmiss

T >50 GeV. The dilepton mass is required to be greater than 20 GeV, and at least 15 GeV away fromthe Z boson pole mass for dielectron and dimuon events. Separate categories are consideredfor events with same-flavor and different-flavor lepton pairs, and for events with M``

T2 greater

4

or less than 110 GeV. The SRs with large M``T2 have significantly higher signal purity. In the

categories with low M``T2, events that would also pass the dileptonic CR of the `+jets channel

are excluded.

A correction to the Drell–Yan background estimate in the same-flavor SRs is obtained by com-paring data and simulation for events within 15 GeV of the Z boson pole mass. The back-ground from misidentified leptons is estimated using events from data with pairs consisting ofone identified lepton and a lepton object that fails identification requirements, but still passesa looser selection. The number of such combinations is scaled by the misidentification rate,which is measured in a jet-enriched control sample, to obtain the background estimate; thecontribution from events with multiple candidates is negligible.

5 Signal extractionThe DM signal, which would be observed as an excess of events compared to the predictedbackground at high pmiss

T , is extracted via a simultaneous fit to the binned pmissT distributions of

the signal and backgrounds, obtained from simulation, in the SRs and associated CR. The fit isperformed using the ROOSTATS statistical package [46]. The template shapes and normaliza-tions are allowed to vary in the fit, and are constrained by nuisance parameters representingthe effects of uncertainties in the signal and background predictions.

Within each channel, uncertainties are correlated across SRs and CRs. Across channels, com-mon sources of uncertainty are correlated. These common sources include the integrated lu-minosity, b tagging efficiency, lepton efficiency, trigger efficiency, pileup simulation, jet energyscale and resolution, PDF, and the uncertainty on the modeling of top quark pT in tt simu-lation [47]. Jet energy scale uncertainties have the largest impact on the `+jets and dileptonchannels, while in the all-hadronic channel the top quark pT modeling and pmiss

T trigger uncer-tainties are more important.

Within the all-hadronic and `+jets search channels, additional nuisance parameters scale theyields of the tt, W+jets, and Z+jets backgrounds independently in each pmiss

T bin across the SRsand CRs of a given channel. For example, in each bin of pmiss

T a single parameter is associatedwith the contribution of the W+jets process in the all-hadronic SRs and CRs across both 2RTTand 0,1RTT categories, while another set of parameters, distinct from those of the all-hadronicchannel, is associated with the W+jets background in the `+jets SRs and CRs. These nuisanceparameters allow the data in the CRs to constrain the estimates of the dominant backgroundprocesses in the corresponding SRs. Signal yields in all the SRs and CRs are scaled simulta-neously by the signal strength parameter (µ), defined as the ratio of the measured signal crosssection to the theoretical cross section at NLO precision in QCD, µ = σ/σTH.

6 Results and interpretationThe fit is performed across all search channels, and no significant excess is observed. This isreflected in Fig. 1, which shows the pmiss

T distributions obtained after a background-only fitassuming the absence of any signal. Upper limits are set on the tt+χχ production cross sectionusing a modified frequentist approach (CLs) with a test statistic based on the profile likelihoodin the asymptotic approximation [48–50]. For each signal hypothesis, 95% confidence level (CL)upper limits on µ are determined.

Several SR pmissT distributions obtained from the background-only fit are shown in Fig. 1. The

all-hadronic channel provides the best sensitivity. The dileptonic channel is competitive with

6. Results and interpretation 5

the all-hadronic channel for scalar mediator masses less than about 50 GeV, where the signalhas a soft pmiss

T spectrum, but is typically the least sensitive channel in other regions of theparameter space.

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Figure 1: Selected pmissT distributions in SRs: 2RTT SR for the all-hadronic (left), the `+jets (mid-

dle), and the different flavor, M``T2 > 110 GeV SR in dileptonic channel (right). The background

distributions (filled histograms) are obtained after a background-only fit. The expected pmissT

distribution for a signal corresponding to a 100 GeV pseudoscalar is overlaid (solid red line).The last bin contains overflow events. The lower panel shows the ratio of the observed data tothe fitted distribution (points), and the ratio of the pre-fit background expectation to the fitteddistribution (dashed magenta line). The horizontal bars indicate the bin width.

The limits are shown as a function of ma/φ and mχ in Fig. 2. The contours enclose the regionwhere the upper limit on µ is less than 1. Due to the narrow width of the mediator, the signalcross section drops rapidly across the ma/φ = 2mχ line, from the on-shell to the off-shell region.Therefore, the exclusion contour runs close to the ma/φ = 2mχ line but does not cross it. Theobserved (expected) upper limits on µ exclude scalar and pseudoscalar masses of 165 (240)and 223 (318) GeV, respectively, at 95% CL. The observed exclusion is weaker than expectedmainly due to the all-hadronic channel, where the degree of over-prediction a priori in the CRsis markedly greater than in the SRs.

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Figure 2: The exclusion limits at 95% CL on the signal strength µ computed as a function ofthe mediator and DM mass, assuming a scalar (left) and pseudoscalar (right) mediator. Themediator couplings are assumed to be gq = gχ = 1.

The limits on µ are also expressed in terms of the mediator coupling strength to quarks in Fig. 3.These results are obtained by fixing gχ = 1, and then finding the value of gq that corresponds

6

to the upper limit on the cross section. This limit translation procedure is valid because thekinematic properties of the signal do not vary appreciably with gq.

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Figure 3: The 95% CL upper limits on the coupling strength of the mediator to the SM quarksunder the assumption that gχ = 1. A DM particle with mass of 1 GeV is assumed.

7 SummaryIn summary, a comprehensive search for dark matter produced in association with a top quarkpair yields no significant excess over the predicted background. The results presented in thisarticle significantly extend the reach of the previous CMS result [15], and provide 30 − 60%better sensitivity compared to earlier searches targeting the same signature [51–53].

AcknowledgmentsWe congratulate our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC and thank the technical and administrative staffs at CERN and at otherCMS institutes for their contributions to the success of the CMS effort. In addition, we grate-fully acknowledge the computing centers and personnel of the Worldwide LHC ComputingGrid for delivering so effectively the computing infrastructure essential to our analyses. Fi-nally, we acknowledge the enduring support for the construction and operation of the LHCand the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus-tria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria);CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia);RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Ger-many); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI(Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM(Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (NewZealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON,RosAtom, RAS, RFBR and RAEP (Russia); MESTD (Serbia); SEIDI and CPAN (Spain); SwissFunding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thai-land); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom);DOE and NSF (USA).

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