Search for dark matter produced with an energetic jet or a hadronically decaying W or Z boson at sqrt(s) = 13 TeV

A search for dark matter particles is performed using events with large missing transverse momentum, at least one energetic jet, and no leptons, in proton-proton collisions at sqrt(s) = 13 TeV collected with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 12.9 inverse femtobarns. The search includes events with jets from the hadronic decays of a W or Z boson. The data are found to be in agreement with the predicted background contributions from standard model processes. The results are presented in terms of simplified models in which dark matter particles are produced through interactions involving a vector, axial-vector, scalar, or pseudoscalar mediator. Vector and axial-vector mediator particles with masses up to 1.95 TeV, and scalar and pseudoscalar mediator particles with masses up to 100 and 430 GeV respectively, are excluded at 95% confidence level. The results are also interpreted in terms of the invisible decays of the Higgs boson, yielding an observed (expected) 95% confidence level upper limit of 0.44 (0.56) on the corresponding branching fraction. The results of this search provide the strongest constraints on the dark matter pair production cross section through vector and axial-vector mediators at a particle collider. When compared to the direct detection experiments, the limits obtained from this search provide stronger constraints for dark matter masses less than 5, 9, and 550 GeV, assuming vector, scalar, and axial-vector mediators, respectively. The search yields stronger constraints for dark matter masses less than 200 GeV, assuming a pseudoscalar mediator, when compared to the indirect detection results from Fermi-LAT.


Introduction
Astrophysical observations have provided compelling evidence for the existence of dark matter (DM) in the universe [1][2][3].However, there is no compelling experimental evidence for nongravitational interactions between the DM and standard model (SM) particles.Most current models of DM assume that it consists of weakly interacting massive particles (WIMPs) [2].If such particles exist, direct pair production of WIMPs may occur in TeV-scale collisions at the CERN LHC [4].If DM particles are produced at the LHC, they would not generate directly observable signals in the detector.However, if they recoil against a jet radiated from the initial state, they may produce an apparent, large transverse momentum imbalance in the event.This is termed the 'monojet' final state [5,6].The DM particles may also be produced in association with an electroweak boson, resulting in the 'mono-V' signature, where V represents the W or Z boson [7][8][9].Observation of these final states could be interpreted as evidence for DM particles.Additionally, the Higgs boson [10][11][12] could be a mediator between DM and SM particles [13][14][15][16][17].The monojet and mono-V signatures can be used to set a bound on the invisible branching fraction of the Higgs boson.
Several previous searches at the LHC have exploited the mono-V and monojet signatures.Results from earlier searches [18][19][20] have typically been interpreted using effective field theories that model contact interactions between the DM and SM particles.Recent search results [21][22][23] have been interpreted in terms of simplified DM models [24][25][26][27][28][29][30].The invisible branching fraction of the Higgs boson, B(H → inv), has been constrained by several searches at the LHC [20,[31][32][33][34], with the ATLAS and CMS Collaborations setting upper limits of 0.25 and 0.24, at 95% confidence level (CL), respectively, through direct searches [35,36].Precise measurements of the Higgs boson couplings from a combination of 7 and 8 TeV data sets, collected by the ATLAS and CMS experiments, provide indirect constraints on additional contributions to the Higgs boson width from non-SM decay processes.The resulting indirect upper limit on the Higgs boson branching fraction to non-SM decays is 0.34, at 95% CL [37].This paper presents the results of a search for DM in the mono-V and monojet channels using a data set of proton-proton collisions at √ s = 13 TeV, collected with the CMS detector in the first half of 2016, and corresponding to an integrated luminosity of 12.9 fb −1 .In the case of the mono-V signature, a hadronic decay of a W or Z boson reconstructed as a single largeradius jet is considered.The results of the search are interpreted using simplified DM models in which the interaction between the DM and SM particles is mediated by a spin-1 particle such as a Z boson, as shown in Fig. 1, or a spin-0 particle (S), as shown in Fig. 2. The results are also interpreted in terms of B(H → inv).The Feynman diagrams for the production of the SM Higgs boson and its decay to invisible particles resulting in the monojet and mono-V final states are similar to those shown for a spin-0 mediator in Fig. 2. q ¯ q q Z 0 q q ¯ W/Z q q q Z 0 Figure 1: Leading order Feynman diagrams of monojet (left) and mono-V (right) production and decay of a spin-1 mediator.
Figure 2: Leading order Feynman diagrams of monojet (left) and mono-V (right) production and decay of a spin-0 mediator.

The CMS detector
The CMS detector is a multi-purpose apparatus designed to study a wide range of physics processes in proton-proton and heavy ion collisions.Its central feature is a superconducting solenoid of 6 m internal diameter that produces a magnetic field of 3.8 T parallel to the beam direction.A silicon pixel and strip tracker is contained inside the solenoid and measures the momentum of charged particles up to a pseudorapidity of |η| = 2.5.The tracker is surrounded by a lead tungstate crystal electromagnetic calorimeter (ECAL) and a sampling hadron calorimeter (HCAL) made of brass and scintillator, which provide coverage up to |η| = 3.The steel and quartz-fiber Čerenkov hadron forward calorimeter extends the coverage to |η| = 5.The muon system consists of gas-ionization detectors embedded in the steel flux-return yoke of the solenoid, and covers |η| < 2.4.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. [38].
The particle-flow (PF) event algorithm [39,40] reconstructs and identifies each individual particle with an optimized combination of information from the various elements of the CMS detector.The energy of photons is directly obtained from the ECAL measurement.The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track.The energy of muons is obtained from the curvature of the corresponding track.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 zero-suppression effects and for the response function of the calorimeters to hadronic showers.Finally, the energy of neutral hadrons is obtained from the corresponding ECAL and HCAL energies.
The missing transverse momentum vector ( p miss T ) is computed as the negative vector sum of the transverse momenta (p T ) of all the PF candidates in an event, and its magnitude is denoted as E miss T .Jets are reconstructed by clustering PF candidates using the anti-k T algorithm [41].Jets clustered with distance parameters of 0.4 and 0.8 are referred to as AK4 and AK8 jets, respectively.The primary vertex with the largest sum of p 2 T of the associated tracks is chosen as the vertex corresponding to the hard interaction in an event.All charged PF candidates originating from any other vertex are ignored during the jet reconstruction.Jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be within 5 to 10% of the true momentum, over the whole p T spectrum and detector acceptance.An offset correction is applied to jet energies to take into account the contribution from additional proton-proton interactions within the same or adjacent bunch crossings (pileup).Jet energy corrections are derived from simulation and are confirmed with in situ measurements of the energy balance in dijet and γ+jet events [42].These are also propagated to the E miss T calculation [43].

Event simulation
The Monte Carlo generators used to simulate various signal and background processes are listed in Table 1.Simulated samples of background events are produced for the Z+jets and γ+jets processes at leading order (LO) with up to four partons in the final state, using MAD-GRAPH5 aMC@NLO 2.2.3 [44].This generator is also used to simulate the W( ν)+jets process at next-to-leading order (NLO), with up to two partons in the final state, and the quantum chromodynamics (QCD) multijet background at LO.The tt and single top quark background samples are produced using POWHEG 2.0 [45][46][47], and a set of diboson samples is produced with PYTHIA 8.205 [48].The monojet DM signal is simulated at NLO for spin-1 mediators, and at LO for spin-0 mediators with the resolved top quark loop calculations carried out using POWHEG [29,49].The mono-V DM signal samples are produced at LO with the JHUGEN 5.2.5 generator [50][51][52] for the scalar mediator, and with MADGRAPH5 aMC@NLO for the spin-1 mediators.Standard model Higgs boson signal events produced through gluon fusion and vector boson fusion are generated using POWHEG, while SM Higgs boson production in association with W or Z bosons is simulated using the JHUGEN generator.
Events produced by the MADGRAPH5 aMC@NLO, POWHEG, and JHUGEN generators are further processed with PYTHIA using the CUETP8M1 tune [53] for the simulation of fragmentation, parton shower, hadronization, and the underlying event.In the case of the MAD-GRAPH5 aMC@NLO samples, jets from the matrix element calculations are matched to the parton shower description, following the FxFx matching prescription [54] for the NLO samples and the MLM scheme [55] for the LO ones.The NNPDF 3.0 [56] parton distribution functions (PDFs) are used for all generated samples.Interactions of final-state particles with the CMS detector are simulated with GEANT4 [57].Simulated events include the effects of pileup, and are weighted to reproduce the distribution of reconstructed primary vertices observed in data.

Event selection
Candidate events are selected using triggers that have thresholds of 90, 100, or 110 GeV applied equally to both E miss T,trig and H miss T,trig , where E miss T,trig is computed as the magnitude of the vector sum of the p T of all the particles reconstructed at the trigger level, and H miss T,trig is the magnitude of the vector p T sum of jets reconstructed at the trigger level.Jets used in the H miss T,trig computation are required to have p T > 20 GeV and |η| < 5.0.The energy fraction attributed to neutral hadrons in these jets is required to be less than 0.9.This requirement removes jets reconstructed from detector noise.The values of E miss T,trig and H miss T,trig are calculated without including muon candidates, allowing the same triggers to be used for selecting events in the muon control samples used for background estimation.The trigger efficiency is measured to be about 95% for events passing the analysis selection with E miss T ≈ 200 GeV.The triggers become fully efficient for events with E miss T > 350 GeV.Events considered in this search are required to have E miss T > 200 GeV, which ensures that the trigger efficiency is higher than 95%.The leading AK4 jet in the event is required to have p T > 100 GeV and |η| < 2.5.Unlike earlier searches performed by the CMS Collaboration in this final state [19,21], there is no requirement on the number of reconstructed jets in the event.The leading AK4 jet must have at least 10% of its energy associated with charged hadrons, and less than 80% of its energy coming from neutral hadrons.These requirements, along with quality filters applied to tracks, muon candidates, and other objects, reduce the background due to large misreconstructed E miss T [43].
The dominant backgrounds in this search are the Z(νν)+jets and W( ν)+jets processes.The Z(νν)+jets process constitutes the largest background and is irreducible.The W( ν)+jets background is suppressed by vetoing events that contain at least one isolated electron or muon with p T > 10 GeV, or a hadronically decaying τ lepton with p T > 18 GeV.Electron candidates must have |η| < 2.5, and are required to satisfy identification criteria based on the shower shape of the energy deposit in the ECAL, the matching of a track to the ECAL energy cluster, and the consistency of the electron track with the primary vertex [58].Muon candidates must have |η| < 2.4, and are required to be identified as muons by the PF algorithm.The isolation sum of the transverse momenta of particles in a cone of radius 0.4 (0.3) around the muon (electron), corrected for the contribution of pileup, is required to be less than 25% (14%) of the muon (electron) transverse momentum.The τ lepton identification criteria [59] require a jet with an identified subset of particles whose invariant mass is consistent with that of a hadronically decaying τ lepton, and for which the pileup-corrected isolation sum of the p T of particle candidates within a cone of radius 0.3 around the jet axis is less than 5 GeV.Events are vetoed if they contain an isolated photon with p T > 15 GeV that satisfies identification criteria based on its ECAL shower shape [60].This reduces electroweak backgrounds with a photon radiated from the initial state to about 1% of the total background.The top quark background is suppressed by vetoing events in which a b-jet with p T > 15 GeV is identified using the combined secondary vertex algorithm with the medium working point [61,62], which has a 60% efficiency for tagging jets originating from b quarks, and a 1% probability of misidentifying a light-flavor jet as a b-jet.Lastly, in order to suppress the QCD multijet background in which large E miss T arises from a severe mismeasurement of the jet momenta, the minimum azimuthal angle between p miss T and the directions of each of the four highest p T AK4 jets with p T > 30 GeV is required to be greater than 0.5 radians.The QCD multijet background is reduced to about 1% of the total background after this requirement.
After these criteria are applied, events are classified into mono-V or monojet categories.If a V boson has p T > 250 GeV, its hadronic decay is more likely to be reconstructed as a single AK8 jet than as two AK4 jets.An event is categorized as a mono-V event if it has E miss T > 250 GeV, and the leading AK8 jet in the event has p T > 250 GeV and |η| < 2.4, and also passes requirements used to identify jets arising from hadronic decays of Lorentz-boosted V bosons.Jets arising from hadronic decays of a V boson are identified using the N-subjettiness variable τ N [63].Low values of τ N are indicative of an N-prong decay.In particular, the ratio τ 2 /τ 1 discriminates the two-prong decays of a V boson from QCD jets, and the leading AK8 jet is required to have τ 2 /τ 1 < 0.6.Additionally, the invariant mass of the jet is required to be between 65 and 105 GeV in order to be consistent with the mass of the W or Z boson.The jet mass is computed after pruning [64], which involves reclustering of the jet constituents using the Cambridge-Aachen algorithm [65,66] and removing the soft constituents in every recombination step, thereby improving the jet mass resolution.The requirements on the τ 2 /τ 1 ratio and the jet mass result in a 70% efficiency for tagging jets originating from V bosons, and a 5% probability of misidentifying a QCD jet as a V jet.If an event fails any of these mono-V selection requirements, it is assigned to the monojet category.The selection requirements for the mono-V and monojet categories are listed in Table 2.

Background estimation
The Z(νν)+jets and W( ν)+jets processes constitute about 90% of the total background in this search.These background contributions are estimated using data from dimuon, dielectron, single-muon, single-electron, and γ+jets control samples.Events in each of these control samples are further classified into the monojet and mono-V categories, resulting in ten mutually exclusive control samples.The E miss T in the control samples is redefined by excluding the leptons and the photons from the calculation.The p T of the resulting hadronic recoil system resembles the E miss T distribution of the electroweak backgrounds in the signal region.Therefore, the hadronic recoil p T is used as a proxy for E miss T in the control regions.
The dimuon and single-muon events are selected with the same E miss T triggers that are used to select the signal events.The dimuon events are required to contain exactly two oppositely charged muons, each with p T > 10 GeV.Events are vetoed if there is an additional muon or electron with p T > 10 GeV.At least one of the two muons is required to have p T > 20 GeV and to pass tight identification requirements based on the number of measurements in the tracker and the muon system, the quality of the muon track fit, and the consistency of the muon track with the primary vertex.The isolation sum of the p T of particles in a cone of radius 0.4 around the muon, corrected for the contribution of pileup, is required to be less than 15% of the muon p T .The invariant mass of the dimuon system is required to be between 60 and 120 GeV, in order to be consistent with a Z boson decay.The single-muon events are required to contain exactly one tightly identified and isolated muon with p T > 20 GeV.No additional muon or electron with p T > 10 GeV is allowed, and the transverse mass of the muon-E miss T system is required to be less than 160 GeV.The transverse mass (m T ) is computed as , where p µ T is the p T of the muon, and ∆φ is the angle between p µ T and p miss T .The dimuon and single-muon events are further required to satisfy all other selection requirements imposed on the signal events with the E miss T replaced by the p T of the hadronic recoil system.The distribution of the hadronic recoil p T is then used to estimate the Z(νν)+jets and W( ν)+jets backgrounds in the signal region.
The dielectron control sample is constructed using events with exactly two oppositely charged electrons with p T > 10 GeV, and no additional muon or electron.The invariant mass of the dielectron system is required to be between 60 and 120 GeV, as in the case of the dimuon events.A single-electron trigger with a p T threshold of 27 GeV is used to select these events.If the Z boson has p T > 600 GeV, the two electrons produced in its decay typically have a small angular separation, and are likely to be included in each other's isolation cones.This effect results in some inefficiency for the single-electron trigger, which imposes isolation requirements on electron candidates.In order to overcome this inefficiency, events are also accepted if they pass a single-electron trigger that has a p T threshold of 105 GeV and no isolation requirements on the electron candidate.Furthermore, in order to improve the efficiency of the electron triggers in the early part of the data taking, additional events passing a trigger with a threshold of 800 GeV on the total sum of the p T of jets (H T ) reconstructed at the trigger level are also included.The same set of triggers is also used for selecting events in the single-electron control sample.At least one of the two electrons in the dielectron control sample is required to have p T > 40 GeV, and is required to pass tight identification requirements on the shower shape of its ECAL energy deposit, the matching of a track to the ECAL energy cluster, and the consistency of the electron track with the primary vertex.The isolation sum of the p T of particles in a cone of radius 0.3 around this electron, corrected for the contribution of pileup, is required to be less than 3.5% of the electron p T for electrons within the ECAL barrel (|η| < 1.48), and less than 6.5% of the electron p T for electrons within the ECAL endcaps (1.48 < |η| < 2.50).The singleelectron events are required to contain exactly one tightly identified and isolated electron with p T > 40 GeV.No additional muons or electrons with p T > 10 GeV are allowed.The QCD background in the single-electron control sample is suppressed by requiring E miss T > 50 GeV, and m T < 160 GeV.
The γ+jets control sample is constructed using events with one high-p T photon that are selected using single-photon triggers with p T thresholds of 165 or 175 GeV.As in the case of the electron control samples, additional events passing the H T trigger with a threshold of 800 GeV are also included.The photon p T is required to be larger than 175 GeV, which ensures that the trigger efficiency is greater than 98%.The photon candidate is required to be reconstructed in the ECAL barrel, and is required to pass identification and isolation criteria that ensure an efficiency of 80% in selecting prompt photons, and a sample purity of 95% [60].
The procedure for estimating the Z(νν)+jets and W( ν)+jets backgrounds relies on transfer factors derived from simulation that connect the yields of electroweak processes in the control samples with the background estimates in the signal region, for a given range of E miss T .The transfer factors for the dilepton control samples relate the yields of Z(µ + µ − ) and Z(e + e − ) events to the Z(νν) background in the signal region by taking into account the difference in the branch-ing fractions of Z(νν) and Z( + − ) decays and the effect of lepton acceptance and selection efficiencies.In the case of dielectron events these transfer factors also account for the difference in efficiencies of the electron and E miss T triggers.The transfer factor for the γ+jets control sample takes into account the difference in the cross sections of the γ+jets and Z(νν)+jets processes, the effect of photon acceptance and efficiency, and the difference in the efficiencies of the photon and E miss T triggers.Transfer factors are also defined between the W(µν) and W(eν) event yields in the single-lepton control samples and the W( ν)+jets background estimate in the signal region.These take into account the effect of lepton acceptance, lepton selection efficiencies, τ lepton veto efficiency, and the difference in trigger efficiencies in the case of the singleelectron control sample.Finally, a transfer factor is also defined to connect the Z(νν)+jets and W( ν)+jets background yields in the signal region.The photon transfer factor relies on an accurate estimate of the ratio of the γ+jets and Z+jets cross sections.Similarly, the transfer factor between the Z(νν)+jets and W( ν)+jets backgrounds relies on an accurate prediction of the ratio of the W+jets and Z+jets cross sections.Therefore, the LO simulations for the Z+jets and γ+jets processes are corrected using p T -dependent NLO QCD K-factors derived using MADGRAPH5 aMC@NLO, and the Z+jets, W+jets, and γ+jets processes are corrected using p T -dependent NLO electroweak K-factors from theoretical calculations [67][68][69].
The Z(νν)+jets and W( ν)+jets background yields are determined through a maximum likelihood fit, performed simultaneously across all the bins of hadronic recoil p T in the ten control samples and E miss T in the two signal regions.The likelihood function L k for each of the two event categories k, corresponding to the monojet and mono-V selections, is defined as where Poisson(x|y) = y x e −y /x!.The symbols , and d i denote the observed number of events in each bin i of the γ+jets, dimuon, dielectron, single-muon, and singleelectron control samples, and the signal region, respectively.The symbol f i denotes the transfer factor between the Z(νν)+jets and W( ν)+jets backgrounds in the signal region, and represents a constraint between these backgrounds.The symbols represents the yield of the Z(νν)+jets background in each bin i of E miss T in the signal region, and this parameter is left floating in the fit.The likelihood also includes a term for the signal region in which B i represents all the backgrounds apart from Z(νν)+jets and W( ν)+jets, S i represents the nominal signal prediction, and µ denotes the signal strength parameter.The systematic uncertainties are modeled as nuisance parameters (θ).
The uncertainties in the Z(νν)+jets and W( ν)+jets backgrounds enter the likelihood as constrained perturbations of the transfer factors , R e i and f i .These include theoretical uncertainties in the γ+jets to Z+jets, and W+jets to Z+jets differential cross section ratios from the choice of the renormalization (10-15%) and factorization (1-10%) scales [21], and the PDF modeling uncertainty, which is found to be negligible.The effect of missing higher-order electroweak corrections to the γ+jets, W+jets, and Z+jets processes is covered by propagating the full NLO electroweak correction as a function of the boson p T as the uncertainty.The resulting uncertainty varies within 2-14% and 1-9% for the γ+jets to Z+jets and W+jets to Z+jets differential cross section ratios, respectively, and it is conservatively considered to be uncorrelated across the bins of hadronic recoil p T .Uncertainties in the reconstruction efficiencies of leptons (1% per muon or electron); in selection efficiencies of leptons (2% per muon or electron), photons (2%), and hadronically decaying τ leptons (3%); in the purity of photons in the γ+jets control sample (2%); and in the efficiency of the electron (2%), photon (2%), and E miss T (1%) triggers, are included and their correlations across all the bins of hadronic recoil p T are taken into account.Figures 3-5 show the results of the combined fit in the ten control samples and the two signal regions assuming the absence of any signal.Data in the control samples are compared to the pre-fit predictions from simulation and the post-fit estimates obtained after performing the fit.The control samples with larger yields dominate the fit results.     in the signal region.The filled histogram indicates all processes other than W( ν)+jets.Ratios of data and the pre-fit background prediction (red points) and postfit background prediction (blue points) are shown for both the monojet and mono-V signal categories.The gray band indicates the overall post-fit uncertainty.The last bin includes all events with hadronic recoil p T larger than 1160 (750) GeV in the monojet (mono-V) category.contribute to the total event yield in the signal region.These include QCD multijet events that have little genuine E miss T .However, jet mismeasurement and instrumental effects can give rise to high E miss T tails.A ∆φ extrapolation method [70] is used to estimate this background.In this method, a background-enriched control sample is obtained by selecting events that fail the ∆φ requirement between jets and E miss T , but pass the remaining event selection criteria.An estimate of the multijet background in the signal region is obtained by applying E miss T dependent transfer factors, derived from simulated QCD multijet events, to this control sample.The overall uncertainty in the multijet background estimate, based on the variations of the jet response and the statistical uncertainties in the transfer factors, ranges from 50 to 150%, depending on the event category and the E miss T region.
The remaining background sources include top quark and diboson processes, which are estimated directly from simulation.The p T distribution of the top quark in simulation is corrected to match the observed p T distribution in data [71].A systematic uncertainty of 10% is assigned to the prediction of the top quark background cross section [72].An additional 10% uncertainty is assigned to the top quark background normalization to take account of the modeling of the top quark p T distribution in simulation.The overall normalization of the diboson background has an uncertainty of 20% [73,74].These uncertainties in the top quark and diboson backgrounds are correlated across the signal and control samples.Several experimental sources of uncertainty are associated with the backgrounds estimated from simulation.An uncertainty of 6.2% in the integrated luminosity measurement [75] is propagated to the background yields.The uncertainty in the efficiency of the b-jet veto is estimated to be 6% for the top quark background and 2% for the diboson background.The uncertainty in the efficiency of the V tagging requirements is estimated to be 13% in the mono-V category.The uncertainty in the modeling of E miss T in simulation [76] is dominated by the jet energy scale uncertainty, and is estimated to be 5%.

Results and interpretation
Figure 6 shows the E miss T distributions in the monojet and mono-V signal regions.The background prediction is obtained from a combined fit in all the control samples, excluding the signal region.Data are found to be in agreement with the SM prediction.Tables 3 and 4 show the estimated yields of background processes in the monojet and mono-V signal regions, respectively, along with the observed event yields in the two signal regions.The correlations between the uncertainties across all the E miss T bins in the two signal regions are reported in Appendix A. These results can be used with the simplified likelihood approach detailed in Ref. [77] for reinterpretations in terms of models not studied in this paper.
Figure 7 shows the E miss T distributions where the background estimates have been computed after including events from the signal region in the fit, but assuming the absence of any signal.The comparison of this fit with an alternative fit assuming the presence of signal is used to set limits on the DM signal cross section.

Dark matter interpretation
The results of the search are interpreted in terms of simplified DM models for the monojet and mono-V final states, assuming a vector, axial-vector, scalar, or pseudoscalar mediator decaying into a pair of fermionic DM particles.These results supersede those from the earlier CMS publications in the same final states [19,21].distribution in the monojet (left) and mono-V (right) signal regions compared with the background expectations for various SM processes evaluated after performing a combined fit to the data in all the control samples, but excluding the signal region.The last bin includes all events with E miss T > 1160 (750) GeV for the monojet (mono-V) category.Expected signal distributions for a 125 GeV Higgs boson decaying exclusively to invisible particles, and for a 1.6 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.The ratio of data and the post-fit background prediction is shown for both the monojet and mono-V signal regions.The gray bands in these ratio plots indicate the post-fit uncertainty in the background prediction.Finally, the distributions of the pulls, defined as the difference between data and the post-fit background prediction relative to the post-fit uncertainty in the prediction, are also shown in the lower panels.

The mediators are assumed to interact with the pair of DM particles with coupling strength
g DM = 1.The spin-1 mediators are assumed to interact with SM quarks with coupling strength g q = 0.25.The spin-0 mediators are assumed to couple to the quarks through SM-like Yukawa interactions with the coupling strength modifier g q = 1.The width of the mediators is determined assuming they interact only with the SM particles and the DM particle.The choice of all the signal model parameters follows the recommendations from Ref. [78] (Sec.2.1 and 2.2).Uncertainties of 20 and 30% are assigned to the inclusive signal cross section in the case of the spin-1 and spin-0 mediators, respectively.These include the renormalization and factorization scale uncertainties, and the PDF uncertainty.
Upper limits are computed at 95% CL on the ratio of the signal cross section to the predicted cross section, denoted by µ = σ/σ th , with the CL s method [79,80], using the asymptotic approximation [81].Limits are obtained as a function of the mediator mass, m med , and the DM mass, m DM .In the case of the vector, axial-vector and scalar mediators, limits are computed on the combined cross section due to the monojet and mono-V signal processes.In the case of the pseudoscalar mediator, limits are computed assuming only the monojet signal process.The mono-V signal process (Fig. 2, right), in which a pseudoscalar mediator couples directly to vector bosons, is ill-defined without making additional assumptions [82] and therefore is not included.Figure 8 shows the exclusion contours in the m med -m DM plane for the vector and Table 3: Expected event yields in each E miss T bin for various background processes in the monojet signal region.The background yields and the corresponding uncertainties are obtained after performing a combined fit to data in all the control samples, but excluding data in the signal region.The observed event yields in the monojet signal region are also reported.bin for various background processes in the mono-V signal region.The background yields and the corresponding uncertainties are obtained after performing a combined fit to data in all the control samples, excluding data in the signal region.The observed event yields in the mono-V signal region are also reported.axial-vector mediators.Mediator masses up to 1.95 TeV and DM masses up to 750 and 550 GeV are excluded for the vector and axial-vector models, respectively, at 95% CL. Figure 9 shows the exclusion contours in the m med -m DM plane for the scalar and pseudoscalar mediators.For scalar mediators, masses up to 100 GeV and DM masses up to 35 GeV are excluded at 95% CL, and no exclusion is expected or observed considering only the monojet signal process.Pseudoscalar mediator masses up to 430 GeV and DM masses up to 170 GeV are excluded at 95% CL. Figure 10 shows the limits for the spin-0 models as a function of the mediator mass, assuming the DM mass to be 1 GeV.In the case of the scalar mediator limits are computed for the monojet signal process, and for the combination of the monojet and mono-V signal processes.
Figures 8 and 9 also show the constraints from the observed cosmological relic density of DM as determined from measurements of the cosmic microwave background by the Planck satellite experiment [83].The expected DM abundance is estimated using the thermal freeze-out mechanism implemented in the MADDM [84] package, and compared to the observed cold DM distribution in the monojet (left) and mono-V (right) signal regions compared with the background expectations for various SM processes evaluated after performing a combined fit to the data in all the control samples, as well as in the signal region.The fit is performed assuming the absence of any signal.The last bin includes all events with E miss T > 1160 (750) GeV for the monojet (mono-V) category.Expected signal distributions for a 125 GeV Higgs boson decaying exclusively to invisible particles, and for a 1.6 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.The ratio of data and the post-fit background prediction is shown for both the monojet and mono-V signal regions.The gray bands in these ratio plots indicate the post-fit uncertainty in the background prediction.Finally, the distributions of the pulls, defined as the difference between data and the post-fit background prediction relative to the post-fit uncertainty in the prediction, are also shown in the lower panels.
density Ω c h 2 = 0.12 [85], where Ω c is the DM relic abundance and h is the Hubble constant, under the assumption that a single DM particle describes DM interactions in the early universe and that this particle only interacts with SM particles through the considered simplified model [86,87].
The limits obtained using the simplified DM models may be compared to the results from direct and indirect DM detection experiments, which are usually expressed as 90% CL upper limits on the DM-nucleon scattering cross sections.The approach outlined in Refs.[30,88,89] is used to translate the exclusion contours into the m DM vs. σ SI/SD plane where σ SI/SD are the spinindependent/spin-dependent DM-nucleon scattering cross sections.These limits are shown in Fig. 11 for the vector and axial-vector mediators, and in Fig. 12 (left) for the scalar mediator.For the scalar mediator model, only the contributions from heavy quarks (charm, bottom, and top) are taken into account while evaluating the limit on the DM-nucleon cross section, as done in Ref. [21].When compared to the results from direct detection experiments, the limits obtained from this search provide stronger constraints for dark matter masses less than 5, 9, and 550 GeV, assuming vector, scalar, and axial-vector mediators, respectively.In the case of the pseudoscalar mediator, the 95% CL upper limits are compared in Fig. 12 (right) with the indirect detection results in terms of the velocity-averaged DM annihilation cross section from Figure 8: Exclusion limits at 95% CL on the signal strength µ = σ/σ th in the m med -m DM plane assuming vector (left) and axial-vector (right) mediators.The limits are shown for m med between 150 GeV and 2.5 TeV, and m DM between 50 GeV and 1.2 TeV.While the excluded area is expected to extend below these minimum values of m med and m DM , the axes do not extend below these values as the signal simulation was not performed in this region.The solid (dotted) red (blue) line shows the contour for the observed (expected) exclusion.The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation theoretical uncertainties in the signal cross section and the combination of the statistical and experimental systematic uncertainties, respectively.Constraints from the Planck satellite experiment [83] are shown with the dark green contours and associated hatching.The hatched area indicates the region where the DM density exceeds the observed value.
the Fermi-LAT Collaboration [90], and provide stronger constraints for DM masses less than 200 GeV.

Invisible decays of the Higgs boson
The results of this search are also interpreted in terms of an upper limit on the product of the cross section and branching fraction B(H → inv), relative to the predicted cross section (σ SM ) of the Higgs boson assuming SM interactions, where the Higgs boson is produced through gluon fusion (ggH) along with a jet; in association with a vector boson (ZH, WH); or through vector boson fusion (VBF).The predictions for the Higgs boson production cross section and the corresponding theoretical uncertainties are taken from the recommendations of the LHC Higgs cross section working group [101].If the production cross section of the Higgs boson is assumed to be the same as σ SM , this limit can be used to constrain the invisible branching fraction of the Higgs boson.The observed (expected) 95% CL upper limit on the invisible branching fraction of the Higgs boson, σB(H → inv)/σ SM , is found to be 0.44 (0.56).The limits are summarized in Fig. 13.Table 5 shows the individual limits for the monojet and mono-V categories.While these limits on B(H → inv) are not as strong as the combined ones from Ref. [36], they are obtained from an independent data sample and therefore will contribute to future combinations.

Summary
A search for dark matter (DM) is presented using events with jets and large missing transverse momentum in a √ s = 13 TeV proton-proton collision data set corresponding to an integrated luminosity of 12.9 fb −1 .The search also exploits events with a hadronic decay of a W or Z bo-Figure 9: Exclusion limits at 95% CL on signal strength the µ = σ/σ th in the m med -m DM plane assuming scalar (left) and pseudoscalar (right) mediators.The limits are shown for m med between 50 and 500 GeV, and m DM between 0 and 300 GeV.While the excluded area is expected to extend below the minimum value of m med , the axis does not extend below this value as the signal simulation was not performed in this region.The red line shows the contour for the observed exclusion.The solid red contours around the observed limit represent one standard deviation theoretical uncertainties in the signal cross section.The dashed blue contour in the case of the scalar mediator shows the −1σ deviation due to the combination of the statistical and experimental systematic uncertainties.Constraints from the Planck satellite experiment [83] are shown with the dark green contours and associated hatching.The hatched area indicates the region where the DM density exceeds the observed value.Table 5: Expected and observed 95% CL upper limits on the invisible branching fraction of the Higgs boson.Limits are tabulated for the monojet and mono-V categories separately, and for their combination.The one standard deviation uncertainty range on the expected limits is listed.The signal composition in terms of gluon fusion, vector boson fusion, and an associated production with a W or Z boson is also provided.

Category
Expected Observed ±1 s.d.son reconstructed as a single large-radius jet.No significant excess is observed with respect to the standard model backgrounds.Limits are computed on the DM production cross section using simplified models in which DM production is mediated by spin-1 or spin-0 particles.Vector and axial-vector mediators with masses up to 1.95 TeV are excluded at 95% confidence level, assuming a coupling strength of 0.25 between the mediators and the standard model fermions, and a coupling strength of 1.0 between the mediators and the DM particles.The results of this search provide the strongest constraints on DM pair production through vector and axial-vector mediators at a particle collider.Scalar and pseudoscalar mediators with masses up to 100 and 430 GeV, respectively, are excluded at 95% confidence level, assuming the coupling of the spin-0 mediators with DM particles to be 1.0 and the coupling of the spin-0 mediators with standard model fermions to be the same as the standard model Yukawa interactions.When compared to the direct detection experiments, the limits obtained from this search provide stronger constraints for dark matter masses less than 5, 9, and 550 GeV, assuming vector, scalar, and axial-vector mediators, respectively.The search yields stronger constraints for  Figure 11: Exclusion limits at 90% CL in the m DM vs. σ SI/SD plane for vector (left) and axialvector (right) mediator models.The solid (dotted) red line shows the contour for the observed (expected) exclusion in this search.Limits from the CDMSLite [91], LUX [92], PandaX-II [93], and CRESST-II [94] experiments are shown for the vector mediator.Limits from the PICO-2L [95], PICO-60 [96], IceCube [97], and Super-Kamiokande [98] experiments are shown for the axial-vector mediator.Exclusion limits at 90% CL in the m DM vs. σ SI/SD plane for the scalar mediator model (left).The observed exclusion in this search (red line) is compared to the results from the CDM-SLite [91], LUX [92], PandaX-II [93], and CRESST-II [94] experiments.For the pseudoscalar mediator (right), limits at 95% CL are compared to the velocity-averaged DM annihilation cross section upper limits from Fermi-LAT [90].There are no comparable limits from direct detection experiments as the scattering cross section between DM particles and SM quarks is suppressed at nonrelativistic velocities for a pseudoscalar mediator [99,100].dark matter masses less than 200 GeV, assuming a pseudoscalar mediator, when compared to the indirect detection results from Fermi-LAT.The search also yields an observed (expected) 95% confidence level upper limit of 0. Tables 3 and 4 provide the estimates of various background processes in the monojet and mono-V signal regions, respectively, that are obtained by performing a fit across all the control samples.The resulting correlations between the uncertainties in the estimated background yields across all the E miss T bins of the monojet and mono-V signal regions are shown in Fig. 14 and 15, respectively.

Figure 3 :
Figure 3:  Comparison between data and Monte Carlo simulation in the γ+jets control sample before and after performing the simultaneous fit across all the control samples and the signal region, assuming the absence of any signal.The left plot shows the monojet category and the right plot shows the mono-V category.The hadronic recoil p T in γ+jets events is used as a proxy for E miss T in the signal region.The filled histogram indicates the multijet background.Ratios of data and the pre-fit background prediction (red points) and post-fit background prediction (blue points) are shown for both the monojet and mono-V signal categories.The gray band indicates the overall post-fit uncertainty.The last bin includes all events with hadronic recoil p T larger than 1160 (750) GeV in the monojet (mono-V) category.In addition to the Z(νν)+jets and W( ν)+jets processes, several other sources of background

Figure 4 :
Figure 4: Comparison between data and Monte Carlo simulation in the dilepton control samples before and after performing the simultaneous fit across all the control samples and the signal region, assuming the absence of any signal.Plots on the upper left and right correspond to the monojet and mono-V categories, respectively, in the dimuon control sample.Plots on the bottom left and right correspond to the monojet and mono-V categories, respectively, in the dielectron control sample.The hadronic recoil p T in dilepton events is used as a proxy for E miss T in the signal region.The filled histogram indicates all processes other than Z( + − )+jets.Ratios of data and the pre-fit background prediction (red points) and post-fit background prediction (blue points) are shown for both the monojet and mono-V signal categories.The gray band indicates the overall post-fit uncertainty.The last bin includes all events with hadronic recoil p T larger than 1160 (750) GeV in the monojet (mono-V) category.

Figure 5 :
Figure 5:  Comparison between data and Monte Carlo simulation in the single-lepton control samples before and after performing the simultaneous fit across all the control samples and the signal region, assuming the absence of any signal.Plots on the upper left and right correspond to the monojet and mono-V categories, respectively, in the single-muon control sample.Plots on the bottom left and right correspond to the monojet and mono-V categories, respectively, in the single-electron control sample.The hadronic recoil p T in single-lepton events is used as a proxy for E miss T

Figure 6 :
Figure 6: Observed E miss T

Figure 7 :
Figure 7: Observed E miss T

Figure 10 :
Figure10: Expected (dotted black line) and observed (solid black line) 95% CL upper limits on the signal strength µ as a function of the mediator mass for the spin-0 models.The horizontal red line denotes µ = 1.Limits for the scalar model on the combined cross section of the monojet and mono-V processes (upper left).Limits for the scalar (upper right) and pseudoscalar (bottom) models, respectively, assuming only the monojet signal process.
Figure12: Exclusion limits at 90% CL in the m DM vs. σ SI/SD plane for the scalar mediator model (left).The observed exclusion in this search (red line) is compared to the results from the CDM-SLite[91], LUX[92], PandaX-II[93], and CRESST-II[94] experiments.For the pseudoscalar mediator (right), limits at 95% CL are compared to the velocity-averaged DM annihilation cross section upper limits from Fermi-LAT[90].There are no comparable limits from direct detection experiments as the scattering cross section between DM particles and SM quarks is suppressed at nonrelativistic velocities for a pseudoscalar mediator[99,100].

Figure 13 :
Figure 13: Expected (dotted black line) and observed (solid black line) 95% CL upper limits on the invisible branching fraction of a 125 GeV SM-like Higgs boson.Limits are shown for the monojet and mono-V categories separately, and also for their combination.

Figure 14 :
Figure 14: Correlations between the uncertainties in the estimated background yields in all the E miss T bins of the monojet signal region.The boundaries of the E miss T bins, expressed in GeV, are shown at the bottom and on the left.

Figure 15 :
Figure 15: Correlations between the uncertainties in the estimated background yields in all the E miss T bins of the mono-V signal region.The boundaries of the E miss T bins, expressed in GeV, are shown at the bottom and on the left.

Table 1 :
Monte Carlo generators used for simulating various signal and background processes.

Table 2 :
Selection requirements for the mono-V and monojet event categories.
and R e i are the transfer factors from the γ+jets, dimuon, dielectron, single-muon, and single-electron control samples, respectively, to the signal region; the contributions from other background processes in these control samples are denoted by B γ i , B µµ i , B ee i , B µ i , and B e i , respectively.The parameter µ Z(νν) i

Table 4 :
Expected event yields in each E miss T 44 (0.56) on the invisible branching fraction of a standard model-like 125 GeV Higgs boson, assuming the standard model production cross section.tion Office, Hungary; the Department of Atomic Energy and the Department of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and National Research Foundation (NRF), Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and University of Malaya (Malaysia); the Mexican Funding Agencies (BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundac ¸ão para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, the Russian Foundation for Basic Research and the Russian Competitiveness Program of NRNU "MEPhI"; the Ministry of Education, Science and Technological Development of Serbia; the Secretaría de Estado de Investigaci ón, Desarrollo e Innovaci ón, Programa Consolider-Ingenio 2010, Plan de Ciencia, Tecnología e Innovaci ón 2013-2017 del Principado de Asturias and Fondo Europeo de Desarrollo Regional, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation.Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Scientific and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus programme of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); and the Welch Foundation, contract C-1845.