Search for dark matter particles in W + W − events with transverse momentum imbalance in proton-proton collisions at √ s = 13 TeV

A search for dark matter particles is performed using events with a pair of W bosons and large missing transverse momentum. Candidate events are selected by requiring one or two leptons ( ℓ = electrons or muons). The analysis is based on proton-proton collision data collected at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC and corresponding to an integrated luminosity of 138 fb − 1 . No significant excess over the expected standard model background is observed in the ℓ ν qq and 2 ℓ 2 ν final states of the W + W − boson pair. Limits are set on dark matter production in the context of a simplified dark Higgs model, with a dark Higgs boson mass above the W + W − mass threshold. The dark matter phase space is probed in the mass range 100–300 GeV, extending the scope of previous searches. Current exclusion limits are improved in the range of dark Higgs masses from 160 to 250 GeV, for a dark matter mass of 200 GeV. Submitted to the Journal of High Energy Physics


Introduction
Astrophysical and cosmological observations [1][2][3][4] provide abundant evidence that dark matter (DM) exists.However, this evidence is based only on gravitational interactions, and whether DM has nongravitational interactions with standard model (SM) particles is still one of the major questions of fundamental physics.Many theories of new physics at the scale of electroweak (EW) symmetry breaking [5] propose viable candidates for DM and are able to accommodate the observed relic density of DM particles in the universe [6,7].Compelling contenders for DM are weakly interacting massive particles (WIMPs, denoted as χ) [8], which could be produced at high-energy colliders such as the Large Hadron Collider (LHC) at CERN.A favored DM signature in collider searches consists of one or more SM particles, X, that are produced and detected, recoiling against a pair of noninteracting DM particles that escape detection, resulting in missing transverse momentum (p miss T ).Previous searches at the LHC took X to be a light quark producing a jet [9,10], a heavy-flavor (bottom or top) quark [11,12], a photon [13,14], or a W, Z, or Higgs boson [10,[15][16][17][18]].
An approach to probe DM at the LHC is based on a scenario in which the DM particle acquires mass through its interaction with a dark Higgs field [19].The signal model used as a benchmark in this search posits a Majorana DM particle that transforms under a new U(1) local gauge symmetry yielding an additional massive spin-1 vector boson Z ′ and a new physical dark Higgs boson s which is a singlet of the SM gauge groups.The Z ′ mediator could be responsible for establishing thermal equilibrium between the visible and the dark sector in the early universe and could provide the annihilation and creation processes that set the DM relic abundance via thermal freeze-out.Current results constrain the parameter space in which the DM particles can acquire their relic abundance from direct annihilation into SM final states [20].This limitation can be significantly relaxed if the DM particle is not isolated as the lightest state in the dark sector.The dark Higgs boson can be lighter than the DM particle χ, in which case the observed relic abundance can readily be achieved through χχ → ss annihilation.Even if s is not strictly lighter than the DM candidate, the limitation can be evaded by the χχ → sZ ′ annihilation channel if m s is low enough [21].The dominant Born-level Feynman diagrams contributing to the s+χχ signature are shown in Fig. 1 and involve a Z ′ boson or χ intermediate state.The relevant model parameters are the DM mass m χ , the Z ′ mass m Z ′ , the dark Higgs boson mass m s , the Z ′ couplings to quarks (g q ) and to DM particles (g χ ), and the mixing angle (θ) between the SM and the dark Higgs bosons.
In this paper, a DM search is described using data recorded with the CMS detector at √ s = 13 TeV in 2016-2018, corresponding to an integrated luminosity of 138 fb −1 .The X plus p miss T signature is targeted, where X refers to the dark Higgs boson decaying to a W + W − vector boson pair.For this paper, the signatures in which the W bosons both decay to charged leptons (ℓ = electrons or muons) and neutrinos (2ℓ2ν), or in which one decays to a charged lepton and a neutrino and the other decays to a pair of quarks (ℓνqq), are considered.For m s > 160 GeV, the W + W − channel has the largest branching fraction [22].This is the first search addressing such a dark Higgs model performed by the CMS Collaboration.Limits on this model have been published by the ATLAS Collaboration at √ s = 13 TeV using WW and ZZ channels, with the vector bosons decaying hadronically [23] or decaying to one lepton and jets [24].This paper is organized as follows.A brief introduction to the CMS detector is given in Section 2. The data and simulated event samples are described in Section 3. The event reconstruction is detailed in Section 4. The analysis strategy and the event selections are detailed in Sections 5 and 6, respectively.Section 7 describes the background estimation and Section 8 the systematic uncertainties.Finally, the results are presented in Section 9, and the final summary is The dominant Born-level Feynman diagrams for the benchmark signal model considered in this paper: qq → Z ′ → sχχ, and s → W + W − .
given in Section 10.Tabulated results are provided in the HEPData record for this analysis [25].

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungsten crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors.Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.The first level of the CMS trigger system [26], composed of custom hardware processors, is designed to select the most interesting events within a time interval of less than 4 µs, using information from the calorimeters and muon detectors, with an output rate of up to 100 kHz.The high-level trigger processor farm further reduces the event rate to about 1 kHz before data storage.A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [27].

Data and simulated samples
The proton-proton (pp) collision data used in this search were collected at √ s = 13 TeV during 2016, 2017, and 2018, with integrated luminosities of 36.3, 41.5, and 59.8 fb −1 , respectively [28][29][30].The average number of multiple pp interactions per bunch crossing (pileup) is approximately 23 for the 2016 data, and 32 for the 2017-2018 data.
Events are stored if they satisfy the selection criteria of online triggers requiring one or two leptons with a minimum transverse momentum (p T ) requirement.The lowest p T thresholds for the double-lepton triggers are 23 GeV for the leading lepton (ℓ max ) and 12 GeV for the nextto-leading lepton (ℓ min ).The single-lepton triggers in the 2016 data set have p T thresholds of 25 GeV for |η| < 2.1 and 27 GeV for 2.1 < |η| < 2.5 for electrons, and of 24 GeV for muons.In the 2017 data set, the thresholds are increased to 35 for electrons and 27 GeV for muons, while in the 2018 data set they are reduced to 32 and 24 GeV, respectively.The trigger efficiency is measured using Z+jets events and is larger than 90% for both electrons and muons over the given η range.
Monte Carlo (MC) simulated events are used for modeling both signal and background processes.Event samples for 2016, 2017, and 2018 data sets are simulated separately to account for the differences in the detector and pileup conditions.Different parton distribution functions (PDFs) and underlying event (UE) tunes are used for the different simulated data sets.In all simulations, the PYTHIA [31] 8.226 (8.230) library is used for parton showering, hadronization, and the UE simulation, using the CUETP8M1 [32] (CP5 [33]) tune for 2016 (2017-2018).Similarly, the NNPDF 3.0 [34,35] PDF set is used for the 2016 data set, while the NNPDF 3.1 [36] set is used for the 2017-2018 data sets.
Signal samples are generated at leading order (LO) in perturbative quantum chromodynamics (QCD) using the MADGRAPH5 aMC@NLO v2.6.5 generator [37], applying the PYTHIA CP5 tune for all three years.A scan in the (m s , m Z ′ , m χ ) parameter space is performed on 672 points between 160 < m s < 400 GeV, 200 < m Z ′ < 2500 GeV, and 100 < m χ < 300 GeV, while the other model parameters are fixed to g χ = 1.00, g q = 0.25, and sin θ = 0.01.The Z ′ and s boson widths vary slightly depending on the selected parameters and are confirmed to be below 1% of their respective masses.The chosen values for these parameters correspond to those recommended as a benchmark in the LHC Dark Matter Working Group (LHC DM WG) [19,38].
Continuum W + W − production background via qq annihilation is generated with POWHEG v2 at next-to-LO (NLO) precision [39], while gg → WW events are generated at LO using MCFM v7.0 [40,41].The simulated qq → WW events are reweighted to match the p T distribution of the WW-system (p WW T ) from the p T -resummed calculation at next-to-NLO plus next-to-nextto-leading logarithmic precision [42,43], and to account for the higher-order EW effects [44].The LO gg → WW cross section, obtained from MCFM, is scaled to next-to-NLO precision via a K factor of 1.4 [45].The different Higgs boson production modes are generated with POWHEG v2 [46][47][48][49][50][51][52] and the H → W + W − decay with JHUGEN [53].Single top quark, tt, WZ, and Wγ * background processes are generated at NLO with POWHEG v2.To further improve the modelling of tt production, the simulated samples are reweighted based on the p T of each top quark [54].Production of a single W boson in association with jets is simulated at LO using MADGRAPH5 aMC@NLO v2.2.2 and v2.6.5 for 2016 and 2017-2018 samples respectively.The description of the W+jets process is improved by scaling the events to kinematic distributions computed at NLO EW precision [55].The QCD K factors are derived from NLO samples as a function of the generated p T of the W boson. Variations of up to 12% of the simulated event yields due to different generator versions and settings across the sample years are compensated for with an additional K factor depending on the reconstructed dijet mass, and treated as uncertainties.Drell-Yan (DY) production of Z/γ * , and other multiboson processes, such as Wγ, ZZ, and VVV (V = W or Z), are generated at NLO using MADGRAPH5 aMC@NLO.All samples are normalized to the latest available theoretical cross sections with at least NLO precision [40,56].For all the processes, the detector response is simulated using the GEANT4 toolkit [57].

Event reconstruction
The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [58].
A particle-flow (PF) algorithm [59] aims to reconstruct and identify individual particles in an event with an optimized combination of information from the various elements of the CMS detector.The energy of photons is obtained from the ECAL measurement.The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the response function of the calorimeters to hadronic showers.The energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.
Electrons are reconstructed using information from the pixel detector, the silicon strip tracker, and the ECAL in the interval |η| < 2.5.The track is required to be consistent with originating from the PV.The electron momentum is estimated by combining the energy measurement in the ECAL, the momentum measurement in the tracker, and the energy sum of all bremsstrahlung photons spatially compatible with the electron track.The efficiency to reconstruct and identify electrons ranges between 60-80% depending on the electron p T and η.The momentum resolution for electrons with p T ≈ 45 GeV, measured in Z → ee decays, ranges from 1.7-4.5%,depending on the η region and on the bremsstrahlung energy emitted by the electron as it traverses the material in front of the ECAL [60].
Muons are reconstructed in the interval |η| < 2.4 using the information from the muon chambers and the silicon tracker, and they are required to be consistent with the reconstructed PV.The efficiency to reconstruct and identify muons is greater than 96%.The relative p T resolution for muons with p T up to 100 GeV is 1% in the barrel and 3% in the endcaps [61,62].
Both electrons and muons are required to be isolated.In the case of an electron, the scalar p T sum of other PF candidates within a cone of size ∆R = √ (∆η) 2 + (∆ϕ) 2 < 0.3 (where ϕ is the azimuthal angle in radians) around its direction is required to be less than 6% of the electron p T .Only those PF candidates associated with the PV are included in the isolation sum.In case of a muon, the p T sum is evaluated for PF candidates in a cone ∆R < 0.4 and is required to be less than 15% of the muon p T .
Jets in each event are clustered from the neutral and charged PF candidates associated with the PV, using the anti-k T algorithm [63,64] with a distance parameter of R = 0.4.The expected average contribution from pileup is subtracted from the reconstructed jet energy [59].Additional selection criteria are applied to each jet with p T > 15 GeV and |η| < 4.7 to remove those potentially dominated by anomalous contributions from various subdetector components or reconstruction failures [65].For the 2017 data sets, jets in the range 2.5 < |η| < 3.0 are excluded to eliminate spurious jets caused by the detector noise.The jet energy resolution typically amounts to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV [66].
The identification of jets containing hadrons with bottom (b) quarks is referred to as b tagging.For each reconstructed jet, a b tagging score is calculated through a multivariate analysis of jet properties using a fully-connected deep neural network based algorithm, DeepCSV [67].Jets are considered b tagged if the DeepCSV b tag output score is above a threshold set to achieve ≈80% efficiency for b quark jets in tt events.For this threshold, the probability of misidentifying a jet as b quark jet in tt events is ≈11% for light-flavor or gluon jets and ≈41% for charm quark jets.
The vector (⃗ p miss T ), with magnitude p miss T , is defined as the negative vector p T sum of all the PF candidates in an event [68], weighted by their estimated probability to originate from the primary interaction vertex.The pileup-per-particle identification algorithm [69] is employed to calculate this probability.Energy scale corrections to the reconstructed jets are taken into account in this computation.

Analysis strategy
This analysis exploits the dependence of the kinematic properties of the final-state objects (the decay products of the W + W − boson pair and a substantial amount of p miss T from DM) on the three parameters m s , m Z ′ and m χ , which enables the separation of signal events from the main background events.
For the 2ℓ2ν channel, the observable chosen to test the dark Higgs model is the transverse mass of the ℓ min plus p miss T system, the distribution of which is more sensitive to the predicted dark Higgs signal than other observables based on the kinematic properties of the lepton or p miss T .This transverse mass is defined as: where p is the magnitude of the p T vector of the ℓ min candidate, and ∆ϕ(⃗ p ) is the azimuthal angle between ⃗ p ℓ min T , and the ⃗ p miss T .The signal is extracted from a two-dimensional profiled maximum likelihood fit to the invariant mass of the dilepton system, m ℓℓ and the m ℓ min ,p miss T T observable with a signal-plus-background hypothesis using the ROOSTATS Project tools [70].The asymptotic approximation of the profile likelihood ratio [71] is used as a test statistic.
For the ℓνqq channel, because of the relatively low expected cross section of the signal processes and the large irreducible W+jets background, the variables that show most promising separation of signal and background are combined in a boosted decision tree (BDT) to produce a single discriminator.From the initial set of 23 candidate variables, a subset of 13 variables is selected by comparing intermediate BDTs in terms of background rejection and signal selection efficiency.An overview of all selected variables and their descriptions is given in Table 1.The resulting discriminator returns values between −1, the background-like extreme, and 1, the most signal-like.It has been cross-checked that events with values at the lower end are predominantly background, while signal events accumulate at higher values.The final analysis results are obtained from a fit to the binned BDT discriminator distribution, as described in Section 9.

Event selection 6.1 The 2ℓ2ν channel
The main feature of the s → W + W − decay in the 2ℓ2ν channel is the presence of two oppositely charged and isolated leptons with relatively large p T , recoiling against ⃗ p miss T .The analysis imposes a set of requirements on kinematic and topological quantities aimed at defining a phase space enriched in s → W + W − events.
In addition to the requirement of opposite charge, the leptons are required to be well-identified, isolated, and have different flavors.In order to reduce the contamination from the DY process, final states with same-flavor leptons are excluded in this analysis.The p ℓ max T is required to be greater than 25 GeV and the p ℓ min T has to be greater than 20 GeV, to ensure a good reconstruction and identification efficiency.The dilepton system is required to have a minimum invariant mass m ℓℓ of 20 GeV in order to eliminate low-mass DY.The transverse momentum of the lepton pair p ℓℓ T must be greater than 30 GeV, to reduce background contributions from leptons that do ∆η and ∆ϕ between the lepton and the dijet system ∆η j,j and ∆ϕ j,j ∆η and ∆ϕ between the W candidate jets |η ℓ | The absolute value of the lepton pseudorapidity ∆ϕ ℓ,⃗ p miss T ∆ϕ between the lepton and ⃗ p miss  , which is taken to be massless not originate from the PV (nonprompt leptons).To minimize the impact of multilepton contributions from WZ and ZZ backgrounds, events that include a third lepton, which is subjected to less strict selection criteria compared to the lepton identification used for the two high-p T leptons, are rejected if its p T is larger than 10 GeV.Events with one or more b-tagged jets with transverse momentum p b T > 20 GeV are rejected.This selection reduces the background from top quark production by ≈86% while losing less than 10% of signal events.
To further suppress DY background, a minimum value of the transverse mass of the dilepton system plus p miss T is required, m ℓℓ,p miss T T > 50 GeV, and a selection on the quantity p miss,proj T [72] is introduced.This quantity is defined as the component of ⃗ p miss T in the direction of the nearest lepton if the lepton is situated within the azimuthal angular cone of ±π/2 from the ⃗ p miss T direction, or the p miss T otherwise.A selection using this variable efficiently rejects Z/γ * → ℓℓ background events in which the ⃗ p miss T is preferentially aligned with leptons.Since the p miss T resolution is degraded by pileup, a quantity is defined as the smaller of the two p ).This quantity is required to be larger than 20 GeV.These selection requirements remove ≈95% of the DY background and less than 5% of the signal.
A summary of the event selection is shown in Table 2, and the m ℓ min ,p miss T T distribution for signal and leading backgrounds is shown in Fig. 2.
To account for the dependence of the kinematic properties of the final-state objects on the mass of the dark Higgs boson, the events that pass the event selection described above are categorized into three signal regions (SRs).The split is based on a proxy of the Lorentz boost of the dark Higgs boson recoiling against the DM system by considering the distance between the two leptons in the (η,ϕ) plane, ∆R ℓℓ .An optimized division is achieved in SR1: ∆R ℓℓ < 1.0 (high-boost); SR2: 1.0 < ∆R ℓℓ < 1.5 (medium-boost); and SR3: 1.5 < ∆R ℓℓ < 2.5 (low-boost) by carefully balancing the signal efficiency and background rejection.Approximately 33% of   distribution in the 2ℓ2ν channel for a signal with m s = 160 GeV, m χ = 100 GeV, m Z ′ = 500 GeV (black), after the event selection criteria are applied.Predictions for the two main backgrounds of the analysis, WW and t production, are shown as blue and yellow solid lines respectively.The last bin includes the overflow.The t production sample consists of approximately 79% t quark pair production and 21% single t processes.the background is rejected by selecting events with ∆R ℓℓ < 2.5, with a negligible effect on the signal.

The ℓνqq channel
The main feature in the ℓνqq channel of the s → W + W − decay is the presence of one wellreconstructed and isolated lepton and at least two jets recoiling against ⃗ p miss T .Different lepton preselections are used for each data set to comply with the varying trigger selection thresholds; they are listed in Table 3. Events containing a second loosely-defined lepton with p T > 10 GeV are vetoed.
When more than two jets are available, the pair having an invariant mass closest to the W These two kinematic requirements are especially effective in decreasing the amount of nonpromptlepton and DY background.Another feature of the signal events is that the visible particles tend to cluster azimuthally in the direction opposite to ⃗ p miss T .For these reasons, ∆R ℓ,jj is required to be smaller than 3.0, ∆ϕ ℓ,jj is required to be below 1.8, ∆ϕ ℓjj,⃗ p miss T must be above 2.0, and p ℓjj T must be above 60 GeV.
These additional topological requirements remove ≈97% of the background (≈97% for W+jets, ≈94% for t production, and ≈99% for nonprompt-lepton events) while keeping between 60-80% of signal events.An optimal differentiation of signal and background events is accomplished using a BDT for which these variables are inputs.A summary of the event selection criteria for the ℓνqq channel is shown in Table 4.

Background estimation
All background processes, except those with nonprompt leptons, are modeled using MC simulations.The nonprompt-lepton background is estimated from data by examining events selected with less stringent lepton selection criteria.These loose leptons have a relative high probability to originate from jets that have been incorrectly categorised.By measuring the rate of these misidentified loose leptons erroneously passing the SR criteria and the efficiency of correctly reconstructing and identifying a lepton, the nonprompt contribution to the SR can be estimated.Details of this method are given in Ref. [72].The validity of this background estimation is checked in a validation region.For the 2ℓ2ν selection, this region is defined by requiring two same-sign leptons while keeping the other selection criteria the same as those listed in Table 2.In the ℓνqq case, the requirements p miss T < 30 GeV and m ℓ,p miss T T < 30 GeV replace the corresponding selections of Table 4, exploiting the fact that events with a nonprompt lepton do not necessarily have a neutrino, resulting in a relatively small p miss T .The normalizations of the most important background processes are determined from the observed data in certain control regions (CRs).The main backgrounds consist of the W + W − and DY processes for the 2ℓ2ν channel, W+jets events for the ℓνqq channel, and t production for both.One CR is defined for each process: • The t production CR is defined by requiring the presence of at least one b-tagged jet, thereby inverting the b-veto.
• In the 2ℓ2ν channel, the DY CR is defined by inverting the m • In the ℓνqq channel, the W+jets CR is defined by inverting the m jj selection, i.e., m jj < 65 or > 105 GeV.
The event yields in these four CRs are fitted simultaneously with the SRs, letting the W + W − , DY, W+jets and t production normalizations float freely in all CRs and SRs.A possible signal contribution in the CRs is also taken into account.

Systematic uncertainties
Experimental and theoretical sources of systematic uncertainty are described in this section.Effects from experimental uncertainties are studied by scaling and/or smearing the reconstructed objects in simulation and propagating the effect to the kinematic variables used in the analysis.
There are several sources of experimental systematic uncertainties, including the lepton reconstruction and identification efficiencies, the lepton momentum scales, the jet energy scale and resolution, the b tagging efficiency for b quark jets, the mistag rate for light-flavor quark and gluon jets, the modeling of p miss T and of pileup in the simulation, the background contributions, and the integrated luminosity.All experimental sources are treated as uncertainties that either change the shapes of the distributions or scale the normalizations of the individual signal and background processes.In the simultaneous fit, the different sources of uncertainty are each represented by single independent nuisance parameters.When combining the uncertainties across processes and data sets, they are treated as correlated or uncorrelated as appropriate.
Lepton efficiency uncertainties are evaluated as functions of the lepton p T and η, using the tag-and-probe method.The impact of the trigger efficiency uncertainty is less than 1 (2)% overall in the 2ℓ2ν (ℓνqq) analysis, while the uncertainties in the reconstruction and identification efficiency cause shape and normalization changes of ≈1.0% (≈1.0%) for electrons and ≈2.0 (≈0.5)% for muons.Changes in lepton momentum scale are at the level of 0.2 (0.4)% for muons and ≈0.6-1.0 (≈0.1-0.8)% for electrons.Those uncertainties are propagated to p miss T resulting in a total variation of 1-10%.For the changes in the jet energy scale, the impact on the normalization is ≈1% for the 2ℓ2ν search, while for the ℓνqq case, the impact can be as large as 10%.
Experimental uncertainties in the estimation of the nonprompt-lepton background are also taken into account.The nonprompt background is affected by the shape uncertainties arising from the dependence on the flavor composition of the jets misidentified as leptons.These shape uncertainties amount to ≈5-10% [72].Statistical fluctuations in the data sets from which the scale factors are determined can be sizable in the ℓνqq analysis, with a 2-40% variation for electrons and 4-25% for muons.For the 2ℓ2ν channel, the trigger conditions are less tight, resulting in larger data sets for estimating efficiencies with negligible statistical uncertainties.In addition, a 30% normalization uncertainty is determined from a closure test performed with simulated samples.
The modeling of pileup depends on the total inelastic pp cross section [73].The pileup uncertainty is evaluated by varying this cross section up and down by 5%.The uncertainty in the integrated luminosity measurement is 1.2, 2.3, and 2.5% for the 2016, 2017, and 2018 data sets, respectively [28][29][30], combining to an overall 1.6% uncertainty across the three years; it contributes directly to the normalization of the MC samples.Luminosity uncertainties are not considered for the top quark, W+jets, W + W − , and the DY background processes as their normalizations are determined by the fit to the data.
Several theoretical uncertainties are pertinent for all simulated event samples.Uncertainties in this category arise from the choice of PDFs and missing higher-order corrections in the perturbative expansion of the simulated cross sections.The PDF uncertainties are estimated, following the PDF4LHC recommendations [74], comparing the value obtained using the set of MC replicas provided by the NNPDF collaboration and PDFs with varied α S values.The estimated uncertainties from missing higher-order corrections in the perturbative QCD expansion are given by the bin-by-bin difference between the nominal and alternative templates, which are constructed from simulated events, where renormalization and factorization scales are shifted up and down by a factor of two.The parton showering scale uncertainties are estimated by varying the initial-state and final-state radiation scales separately by a factor two.An overall 1.5% UE uncertainty is applied to all the simulated samples in order to account for fluctuations obtained from alternative MC simulations with UE tune variations [75].
Theoretical systematic uncertainties specific to individual background processes are also considered.A 15% uncertainty is applied to the relative fraction of the gluon-induced component of the W + W − background [76], while for the qq → WW component, the applied p WW T corrections are varied by changing the renormalization and factorization scales.For the tt component in the t production background samples, the entire p T correction weight (as mentioned in Section 3) is treated as the uncertainty.Furthermore, the entire EW NLO correction to the W+jets samples is considered as an uncertainty, while variations in the QCD NLO corrections are estimated from statistical fluctuations in the sample sizes, and by varying the jet |η| selections in the K factor estimations, resulting in 1 and 2% uncertainties, respectively.Differences in yearby-year setup for the W+jets simulation are addressed with an additional simulation-based nuisance parameter and amount to a ≈12% variation.
Finally, uncertainties arising from the limited statistical precision of the simulation are included for each bin of the discriminant distributions in each independent category [77].In the ℓνqq channel, these typically add an uncertainty of ≈20% in the highest BDT bins.For the 2ℓ2ν channel, the values vary greatly among the different analysis regions, typical values are ≈1-40% in SR1, ≈1-20% in SR2 and ≈1-10% in SR3.

Results
Distributions from the 2ℓ2ν and ℓνqq channels are fitted jointly, and the signal is obtained from the results of the fit.These distributions correspond to both SRs and CRs.
For the 2ℓ2ν channel, the event yields in the CRs are recorded in single-bin histograms.Kinematic information from the SR is contained in two-dimensional distributions of m ℓℓ and m  5.
Table 5: Data and background yields for each analysis region in the 2ℓ2ν channel.Central values and uncertainties for the background contributions are the post-fit values.For the signal prediction from simulation, with the associated uncertainties, values are given for a sample with m s = 160 GeV, m χ = 100 GeV, m Z ′ = 500 GeV.In the ℓνqq channel, the signal and background information is contained in BDT distributions for the SRs and CRs.The binning is set by considering the bin-to-bin significance of dark Higgs boson mass points and by requiring the expected yield to be greater than 10 events in every bin.A coarser binning is obtained for the CRs and also for the 2016 SR ([−1, 0, 0.4, 0.6, 0.
Data/Pred.while a finer binning is obtained for the 2017-2018 SRs ([−1, 0, 0.4, 0.6, 0.7, 0.8, 0.9, 1]).The post-fit distributions of the SRs and CRs are shown in Fig. 4 for the two CRs (upper two plots corresponding to 138 fb −1 ), the 2016 SR (lower left plot, 36.3 fb −1 ) and the combined 2017-2018 SRs (lower right plot, 101 fb −1 ).In the t quark CR and the 2017-2018 SR distributions shown in Fig. 4, a downward slope is visible in the last two bins of the distribution of the ratio of the observed to predicted events.This apparent trend is found to be an artifact of the chosen binning.Table 6 shows the post-fit expected yields of the background processes and the prefit signal for the sample with m s = 160 GeV, m χ = 100 GeV, m Z ′ = 500 GeV, when the BDT discriminator values are above 0.6.Neither the 2ℓ2ν nor the ℓνqq channel show a significant deviation from the SM predictions.
To extract upper limits, a modified frequentist approach was pursued using the CL s crite- rion [78,79].Upper limits at 95% confidence level (CL) on the model production cross section are obtained from the combination of both final-states; these upper limits are displayed in the (m s , m Z ′ ) mass plane in Fig. 5.An interpolation between the signal samples is carried out by reweighting the events using the ratio of dark Higgs boson p T ; the reweighted samples are rescaled according to the respective theoretical cross sections to obtain the correct kinematic distributions.A deficit of data events in the most sensitive bins, namely, the high-m ℓ min ,p miss T T bins in the 2ℓ2ν channel (with a local significance of 1.8 and 2.3 sigma in the highest m ℓℓ bin of SR1 and SR2 ) and the high-BDT bins in the ℓνqq channel (with a local significance of 1.8 sigma in the last SR bin of 2017-2018), leads to an observed limit that is more stringent than the expected one.The differences are not statistically significant, however, and the observed limit falls within two standard deviations of the expected one for most of the scanned parameter space.For m χ = 200 GeV, near m s = 350 GeV and m Z ′ = 700 GeV, the observed exclusion limit is just over two standard deviations above the expected one.
Comparison with the observed DM relic density can indicate the preferred model parameters.Therefore, relic density calculations are performed with the current dark Higgs model assumptions using MADDM [80].When the dark Higgs boson mass is lower than the DM mass, DM annihilation to two s bosons is on-shell, thereby reducing the relic density compared to models with only the Z ′ boson as the mediator.In the case where m s ≈ 2m χ , the WIMPs can be converted to SM particles through an on-shell dark Higgs resonance, strongly reducing the relic density.Gray lines in Fig. 5 indicate where the model parameters produce exactly the current measurement of the observed relic density [7].
In this analysis, only the decay of the dark Higgs boson to a pair of visible W bosons is considered; this decay mode is dominant in the phase space analyzed.In the case where m s > 2m χ , however, the dark Higgs boson decays predominantly to a pair of DM particles.The consequence of this change of decay mode can be seen in Fig. 5: there is a boundary reflecting a sharp drop of sensitivity in the upper left (upper right) plot corresponding to m s equal to twice the DM particle mass of 100 (150) GeV.
This search covers a wider range of DM mass (100-300 GeV) compared to previous analy-ses [23,24].In the (m s , m Z ′ ) plane with m χ = 200 GeV, m Z ′ values up to ≈2200 GeV are excluded for m s close to 160 GeV, extending the lower limit on m Z ′ presented in Ref. [24].In the same plane, the lower limit on m s is ≈350 GeV for m Z ′ around 700 GeV, which is slightly weaker than that of Ref. [24].

Summary
A search for dark matter particles χ produced in association with a dark Higgs boson (s) has been presented.Proton-proton collision data at a center-of-mass energy of 13 TeV are used, corresponding to an integrated luminosity of 138 fb −1 .The decay mode of the dark Higgs boson to a W + W − pair is explored.Results are presented from a combination of the 2ℓ2ν and ℓνqq decay channels of the W + W − pair (where ℓ = electrons or muons).No significant deviation from the standard model prediction is observed.Upper limits at 95% confidence level on the production cross section for dark matter particles are set and translated into bounds on dark Higgs model parameters.This analysis investigates a dark matter mass range 100-300 GeV, which is wider than in previous searches and extends the limit on the Z ′ boson mass m Z ′ in the region of the s mass 160 < m s ≲ 250 GeV for m χ = 200 GeV.The most stringent limit is set for m χ = 200 GeV, excluding m s masses up to ≈350 GeV at m Z ′ = 700 GeV, and up to m Z ′ ≈ 2200 GeV for m s = 160 GeV.

T 2 T 1 T 1 T
∆ϕ ℓjj,⃗ p miss T ∆ϕ between the vectorial sum of the visible particles and ⃗ p )/p miss T Minimum of the lepton p T and the next-to-leading W candidate jet p T , divided by p miss T max(p ℓ T , p j )/p miss T Maximum of the lepton p T and the leading W candidate jet p T , divided by p miss T max(p ℓ T , p j )/m ℓjjp miss T Maximum of the lepton p T and the leading W candidate jet p T , divided by the invariant mass of the system of all visible particles and ⃗ p miss T based on all the PF candidates in the event (p miss,PF proj T ), and the other one based only on the reconstructed tracks originating from the PV (p miss,track proj T

Figure 4 :
Figure 4: Post-fit BDT distributions in the ℓνqq channel for the full data set in the t quark CR (upper left) and W+jets CR (upper right).The SR of the 2016 data set (lower left) and the 2017-2018 data set (lower right).The black line indicates the signal prediction with m s = 160 GeV, m χ = 100 GeV, m Z ′ = 500 GeV.In the lower panel of each plot, the ratio between the data and the background prediction is shown.

Figure 5 :
Figure 5: Observed (expected) exclusion regions at 95% CL for the dark Higgs model in the (m s , m Z ′ ) plane, marked by the solid red (black) line.The expected ±1σ (68% CL) and ±2σ (95% CL) bands are shown as the thinner black lines.The bar on the righthand side of each figure maps the displayed colors to the corresponding limit values.Upper left: m χ = 100 GeV, upper right: m χ = 150 GeV, lower left: m χ = 200 GeV, lower right: m χ = 300 GeV.The gray line indicates were the model parameters produce exactly the observed relic density Ω c h 2 = 0.12 [7].

Table 1 :
Summary of all selected variables considered in the BDT for the ℓνqq channel.

Table 2 :
Summary of the event selection criteria in the 2ℓ2ν channel.

Table 3 :
Selection criteria for the leptons for 2016-2018 data in the ℓνqq channel.The p T thresholds are chosen to be equal to the corresponding single-lepton trigger threshold.selectedas W candidate jets.Both W candidate jets are required to be within the tracker acceptance region (|η| < 2.4) to avoid the high multiplicity of background particles produced in the high-|η| regions.Events with jets that do not originate from a W boson are suppressed by requiring 65 < m jj < 105 GeV.The contribution of top quark background events to the SR is further reduced by removing events with at least one b-tagged jet, with p T > 20 GeV, that is not tagged as a W candidate jet.All background events can be further suppressed by comparing the kinematic variables of the visible particles and p miss T .The presence of DM candidates in an event results in a large p miss T well separated from visible particles as compared to SM processes.Thus, we impose the re-

Table 4 :
Summary of the event selection criteria for the ℓνqq channel.

Table 6 :
Data and background yields for the ℓνqq channel with a BDT discriminator score above 0.6.Central values and uncertainties for the background contributions are the post-fit values.For the signal prediction from simulation, with the associated uncertainties, values are given for a sample with m s = 160 GeV, m χ = 100 GeV, m Z ′ = 500 GeV.