Search for new physics in final states with an energetic jet or a hadronically decaying W or Z boson and transverse momentum imbalance at $\sqrt{s} = $ 13 TeV

A search for new physics using events containing an imbalance in transverse momentum and one or more energetic jets arising from initial-state radiation or the hadronic decay of W or Z bosons is presented. A data sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV, collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 35.9 fb$^{-1}$, is used. The observed data are found to be in agreement with the expectation from standard model processes. The results are interpreted as limits on the dark matter production cross section in simplified models with vector, axial-vector, scalar, and pseudoscalar mediators. Interpretations in the context of fermion portal and nonthermal dark matter models are also provided. In addition, the results are interpreted in terms of invisible decays of the Higgs boson and set stringent limits on the fundamental Planck scale in the Arkani-Hamed, Dimopoulos, and Dvali model with large extra spatial dimensions.


Introduction
Several astrophysical observations [1][2][3] provide compelling evidence for the existence of dark matter (DM), a type of matter not accounted for in the standard model (SM). To date only gravitational interactions of DM have been observed and it remains unknown if DM has a particle origin and could interact with ordinary matter via SM processes. However, many theoretical models have been proposed in which DM and SM particles interact with sufficient strength that DM may be directly produced with observable rates in high energy collisions at the CERN LHC. While the DM particles would remain undetected, they may recoil with large transverse momentum (p T ) against other detectable particles resulting in an overall visible p T imbalance in a collision event. This type of event topology is rarely produced in SM processes and therefore enables a highly sensitive search for DM. Similar event topologies are predicted by other extensions of the SM, such as the Arkani-Hamed, Dimopoulos, and Dvali (ADD) model [4][5][6][7][8] of large extra spatial dimensions (EDs). This paper describes a search for new physics resulting in final states with one or more energetic jets and an imbalance in p T due to undetected particles. The jets are the result of the fragmentation and hadronization of quarks or gluons, which may be produced directly in the hard scattering process as initial-state radiation or as the decay products of a vector boson V (W or Z). These final states are commonly referred to as 'monojet' and 'mono-V'. Several searches have been performed at the LHC using the monojet and mono-V channels [9][10][11][12][13][14][15]. This analysis makes use of a data sample of proton-proton (pp) collisions at √ s = 13 TeV collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb −1 . This sample is approximately three times larger than the one used in Ref. [14]. The analysis strategy is similar to that of previous CMS searches, and simultaneously employs event categories to target both the monojet and mono-V final states. In an improvement compared to previous searches, in this paper revised theoretical predictions and uncertainties for γ+jets, Z+jets, and W+jets processes based on recommendations of Ref. [16] are used. In addition to interpretations in the context of simplified DM models [17][18][19], in this paper the results are further studied in the context of the fermion portal (FP) dark matter model [20], the light nonthermal DM model [21,22], and the ADD model. In many simplified DM models, DM particles are assumed to be Dirac fermions that interact with SM particles through a spin-1 or spin-0 mediator [18,20,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. These interactions are classified into four different types, depending on whether the mediator is a vector, axial-vector, scalar, or pseudoscalar particle. The spin-0 mediators are assumed to couple to the SM particles via Yukawa couplings. The SM Higgs boson is a specific example of a scalar mediator that may couple to the DM particles. Combined results of the direct searches for invisible Higgs bosons have been presented by both the ATLAS and CMS Collaborations, which respectively obtain observed upper limits of 0.25 and 0.24 on the Higgs boson invisible branching fraction, B(H → inv.), at 95% confidence level (CL) [39,40].
In the FP dark matter model [20], the DM particle, assumed to be either a Dirac or Majorana fermion, couples to a color-triplet scalar mediator (φ u ) and an SM fermion. In the investigated model, the DM candidate is assumed to couple only to up-type quarks, with a coupling strength parameter λ u = 1. In this model, the mediators couple to quarks and the DM candidate, and may be singly produced in association with a DM particle. This associated production yields a monojet signature, while pair production of mediators can be observed in multijet final states with significant p T imbalance, as shown in Fig. 1.
The light nonthermal DM model [21,22] is a minimal extension of the SM where the DM particle is a Majorana fermion (n DM ) that interacts with the up-type quarks via a colored scalar mediator (X 1 ) with a coupling strength parameter λ 2 . This new colored mediator also interacts with the down-type quarks with a coupling strength parameter λ 1 . Baryon number is not conserved in interactions of such mediators, and therefore the nonthermal DM model could explain both the baryon abundance and the DM content of the universe. The DM particle mass in this model must be nearly degenerate with the proton mass to ensure the stability of both the proton and the DM particle. Thus, the latter can be singly produced at the LHC, as shown in Fig. 2. This leads to a final state that includes large p T imbalance and an energetic jet, whose p T distribution is a Jacobian peak at half the X 1 mass. The ADD model of EDs offers an explanation of the large difference between the electroweak unification scale and the Planck scale (M Pl ), at which gravity becomes as strong as the SM interactions. In the simplest ADD model, a number (n) of EDs are introduced and are compactified on an n-dimensional torus of common radius R. In this framework, the SM particles and their interactions are confined to the ordinary 3+1 space-time dimensions, while gravity is free to propagate through the entire multidimensional space. The strength of the gravitational force in 3+1 dimensions is effectively diluted. The fundamental Planck scale M D of this 4+n-dimensional theory is related to the apparent four-dimensional Planck scale according to M Pl 2 ≈ M D n+2 R n . The production of gravitons (G) is expected to be greatly enhanced by the increased phase space available in the EDs. Once produced in proton-proton collisions, the graviton escapes undetected into the EDs and its presence must be inferred from an overall p T imbalance in the collision event, again leading to a monojet signature, as shown in Fig. 3.
For all models, the signal extraction is performed using the distribution of the p T imbalance in each event category. In the context of simplified DM models, the results of the search are reported in terms of excluded values of the masses of the mediator and of the DM particles. In the context of the FP and nonthermal DM models, the results of the search are reported in terms of excluded values of the mass of the mediator particle, and either the DM particle mass or the strength of the coupling between the mediator and the DM or SM particles. The case of q q G g g g G g g q G q Figure 3: Examples of Feynman diagrams of the main production mechanisms of gravitons at the LHC that provide monojet signatures in the ADD model. a Higgs boson decaying to invisible (e.g., DM) particles is also considered, and the results are reported in terms of upper limits on the branching fraction to invisible particles of the Higgs boson with a mass of 125 GeV [41][42][43], assuming SM production cross sections (σ SM ). In the ADD model, the results are reported in terms of limits on the fundamental Planck scale as a function of the number of extra spatial dimensions. This paper is organized as follows. A brief overview of the CMS detector and a description of the event reconstruction is given in Section 2. Information about the event simulation is provided in Section 3 and the event selection is provided in Section 4. Section 5 details the background estimation strategy used in the analysis. Finally, the results of the search are described in Section 6 and summarized in Section 7.

The CMS detector and event reconstruction
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 tungstate 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. 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. [44].
The CMS particle-flow (PF) event algorithm [45] reconstructs and identifies each individual particle with an optimized combination of information from the various elements of the detector. The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects. The energy of muons is obtained from the curvature of the corresponding track. 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 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 corrected ECAL and HCAL energy.
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 p miss T . Hadronic jets are reconstructed by clustering PF candidates using the infrared and collinear safe anti-k T algorithm [46]. Jets clustered with distance parameters of 0.4 and 0.8 are referred to as AK4 and AK8 jets, respectively. The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The physics objects are those returned by a jet finding algorithm [46,47] applied to all charged PF candidates associated with the vertex, plus the corresponding associated p miss T . Jet momentum is determined as the vector 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 full 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 nearby bunch crossings (pileup). Jet energy corrections are derived from simulation, and are confirmed with in situ measurements of the energy balance in dijet, multijet, γ+jet, and leptonic Z+jet events [48]. Additional selection criteria are applied to each event to remove spurious jet-like features originating from isolated noise patterns in certain HCAL regions. Such corrections and selections are also propagated to the p miss T calculation [49,50].
Muons within the geometrical acceptance of |η| < 2.4 are reconstructed by combining information from the silicon tracker and the muon system [51]. The muons are required to pass a set of quality criteria based on the number of spatial points measured in the tracker and in the muon system, the fit quality of the muon track, and its consistency with the primary vertex of the event. The isolation requirements for muons are based on the sum of the energies of the PF candidates originating from the primary vertex within a cone of ∆R < 0.4 around the muon direction, excluding the muons and electrons from the sum. The muon isolation variable is corrected for pileup effects by subtracting half of the p T sum of the charged particles that are inside the isolation cone and not associated with the primary vertex. In this paper, 'loose' muons are selected with an average efficiency of 98% and are used as a condition to veto the events, whereas 'tight' muons are selected with an average efficiency of 95% and are used to tag the events in the control samples.
Electrons within the geometrical acceptance of |η| < 2.5 are reconstructed by associating tracks reconstructed in the silicon detector with clusters of energy in the ECAL [52]. Well-identified electron candidates are required to satisfy additional identification criteria based on the shower shape of the energy deposit in the ECAL and the consistency of the electron track with the primary vertex [53]. Electron candidates that are identified as coming from photon conversions in the detector material are removed. The isolation requirements are separated from electron identification, and are based on the sum of the energies of the PF candidates originating from the primary vertex within a cone of ∆R < 0.3 around the electron direction, excluding the muons and electrons from the sum. The mean energy deposit in the isolation cone of the electron coming from pileup is estimated following the method described in Ref.
[52] and subtracted from the isolation sum. In this paper, 'loose' electrons are selected with an average efficiency of 95% and are used as a condition to veto the events, whereas 'tight' electrons with an average efficiency of 70% are used to select the events in the control samples.
Photon candidates are reconstructed from energy deposits in the ECAL using algorithms that constrain the clusters to the size and shape expected from a photon [54]. The identification of the candidates is based on shower-shape and isolation variables. For a photon to be considered to be isolated, scalar p T sums of PF candidates originating from the primary vertex, excluding the muons and electrons within a cone of ∆R < 0.3 around the photon candidate, are required to be below the bounds defined. Only the PF candidates that do not overlap with the electromagnetic shower of the candidate photon are included in the isolation sums. In this paper, 'loose' photon candidates are required to be reconstructed within |η| < 2.5, whereas 'tight' photon candidates used are required to be reconstructed in the ECAL barrel (|η| < 1.44). The tight photon candidates are also required to pass identification and isolation criteria that ensure an efficiency of 80% in selecting prompt photons, and a sample purity of 95% for the control samples.
Hadronically decaying τ lepton candidates detected within |η| < 2.3 are required to pass identification criteria using the hadron-plus-strips algorithm [55]. The algorithm identifies a jet as a hadronically decaying τ lepton candidate if a subset of the particles assigned to the jet is consistent with the decay products of a τ candidate. In addition, τ candidates are required to be isolated from other activity in the event. The isolation requirement is computed by summing the p T of the PF charged and PF photon candidates within an isolation cone of ∆R = 0.5 and 0.3, respectively, around the τ candidate direction. A more detailed description of the isolation requirement can be found in Ref. [55].

Simulated samples
To model the SM backgrounds, simulated Monte Carlo (MC) samples are produced for the Z+jets, W+jets, γ+jets, and quantum chromodynamics (QCD) multijet processes at leading order (LO) using the MADGRAPH5 aMC@NLO 2.2.2 [56] generator and are generated with up to four additional partons in the matrix element calculations. The samples for the tt and single top quark background processes are produced at next-to-leading order (NLO) using POWHEG 2.0 and 1.0, respectively [57,58], and the set of diboson (WW, WZ, ZZ) samples is produced at LO with PYTHIA 8.205 [59].
Vector and axial-vector monojet and mono-V dark matter signals are simulated at NLO using the DMSIMP models [60,61] with the MADGRAPH5 aMC@NLO generator. Both scalar and pseudoscalar monojet and mono-V production contain gluon-initiated loop processes. In the case of mono-V signals, no direct couplings of the mediator to vector bosons are considered. All samples are generated at LO with one additional parton in the matrix element calculations, taking into account finite top quark mass effects and using the MADGRAPH5 aMC@NLO generator in conjunction with the DMSIMP models.
The SM Higgs boson signal events produced through vector boson fusion and gluon fusion are generated using the POWHEG generator [62,63]; for each sample the cross section is normalized to the next-to-NLO (NNLO) and next-to-NNLO, respectively. The SM Higgs boson production in association with W or Z bosons is simulated at LO using the JHUGENERATOR 5.2.5 generator [64] and normalized to the NNLO cross section.
The ADD ED signal is simulated at LO in QCD using the PYTHIA generator, requiringp T > 80 GeV, wherep T denotes the transverse momentum of the outgoing parton in the partonparton center-of-mass frame. The PYTHIA truncation setting is used to suppress the cross section by a factor of M D 4 /ŝ 2 forŝ > M D 2 , whereŝ is the center-of-mass energy of the incoming partons, to ensure validity of the effective field theory.
Lastly, both the FP dark matter signal and the nonthermal DM signal models are simulated at LO using the MADGRAPH5 aMC@NLO generator. In the FP dark matter signal model, the coupling strength parameter is fixed to be λ u = 1 while, in the nonthermal DM signal model, the mass of the DM particle is fixed to the proton mass to assure the stability of both the proton and the DM particle. In this latter model, coupling ranges of 0.01-1.5 for λ 1 and 0.01-2.0 for λ 2 are considered, to ensure the mediator width is less than about 30% of its mass.
The MC samples produced using MADGRAPH5 aMC@NLO, POWHEG, and JHUGENERATOR generators are interfaced with PYTHIA using the CUETP8M1 tune [65] for the fragmentation, hadronization, and underlying event description. In the case of the MADGRAPH5 aMC@NLO samples, jets from the matrix element calculations are matched to the parton shower description following the MLM [66] (FxFx [67]) prescription to match jets from matrix element calculations and parton shower description for LO (NLO) samples. The NNPDF 3.0 [68] parton distribution functions (PDFs) are used in all generated samples. The propagation of all final-state particles through the CMS detector are simulated with GEANT 4 [69]. The simulated events include the effects of pileup, with the multiplicity of reconstructed primary vertices matching that in data. The average number of pileup interactions per proton bunch crossing is found to be 23 for the data sample used in this analysis [70].

Event selection
Signal region events are selected using triggers with thresholds of 110 or 120 GeV on both p miss T,trig and H miss T,trig , depending on the data taking period. The p miss T,trig corresponds to the magnitude of the vector p T sum of all the PF candidates reconstructed at the trigger level, while the H miss T,trig is computed as the magnitude of the vector p T sum of jets with p T > 20 GeV and |η| < 5.0 reconstructed at the trigger level. The energy fraction attributed to neutral hadrons in these jets is required to be smaller than 0.9. This requirement suppresses anomalous events with jets originating from detector noise. To be able to use the same triggers for selecting events in the muon control samples used for background prediction, muon candidates are not included in the p miss T,trig nor H miss T,trig computation. The trigger efficiency is measured to be 97% for events passing the analysis selection for p miss T > 250 GeV and becomes fully efficient for events with p miss T > 350 GeV.
Candidate events are required to have p miss T > 250 GeV. In the monojet category, the highest p T (leading) AK4 jet in the event is required to have p T > 100 GeV and |η| < 2.4, whereas in the mono-V category, the leading AK8 jet is required to have p T > 250 GeV and |η| < 2.4. In both categories, the leading jet is also required to have at least 10% of its energy coming from charged particles and less than 80% of its energy attributed to neutral hadrons. This selection helps to remove events originating from beam-induced backgrounds. In addition, the analysis employs various event filters to reduce events with large misreconstructed p miss T [49] originating from noncollision backgrounds.
The main background processes in this search are the Z(νν)+jets and W( ν)+jets processes. The Z(νν)+jets process is an irreducible background and constitutes the largest background in the search. In contrast, the background from W( ν)+jets is suppressed by imposing a veto on events containing one or more loose muons or electrons with p T > 10 GeV, or τ leptons with p T > 18 GeV. Events that contain a loose, isolated photon with p T > 15 GeV and |η| < 2.5 are also vetoed. This helps to suppress electroweak (EW) backgrounds in which a photon is radiated from the initial state. To reduce the contamination from top quark backgrounds, events are rejected if they contain a b-tagged jet with p T > 20 GeV and |η| < 2.4. These jets are identified using the combined secondary vertex algorithm (CSVv2) [71,72], adopting a working point corresponding to correctly identifying a jet originating from a bottom quark with a probability of 80% and misidentifying a jet originating from a charm quark (light-flavor jet) with a probability of 40 (10)%. Lastly, QCD multijet background with E miss T arising from mismeasurements of the jet momenta is suppressed by requiring the minimum azimuthal angle between the p miss T direction and each of the first four leading jets with p T greater than 30 GeV to be larger than 0.5 radians.
To select an event in the mono-V category, a leading AK8 jet is identified as a jet arising from hadronic decays of Lorentz-boosted W or Z bosons. Such jets typically have an invariant mass, computed from the momenta of jet's constituents, between 65 and 105 GeV [73]. The mass of the leading AK8 jet is computed after pruning based on the technique [74,75] involving reclustering the constituents of the jet using the Cambridge-Aachen algorithm [76] and removing the soft and wide-angle contributions to jets in every recombination step. The pruning algorithm is controlled by a soft threshold parameter z cut = 0.1 and an angular separation threshold of ∆R > m jet /p jet T . This technique yields improved jet mass resolution owing to reduced effects coming from the underlying event and pileup. The N-subjettiness variable τ N [77] is also employed to further isolate jets arising from hadronic decays of W or Z bosons. This observable measures the distribution of jet constituents relative to candidate subjet axes in order to quantify how well the jet can be divided into N subjets. Therefore, the ratio of the '2-subjettiness' to the '1-subjettiness' (τ 2 /τ 1 ) has excellent capability for distinguishing jets originating from boosted vector bosons from jets originating from light quarks and gluons. The pruned jet mass and N-subjettiness requirements, whose use if referred to as V tagging, result in a 70% efficiency for tagging jets originating from V bosons and a 5% probability of misidentifying a jet as a V jet. Events that do not qualify for the mono-V category are assigned to the monojet category. The common selection requirements for both signal categories are summarized in Table 1, while the category-specific selection requirements are reported in Table 2. >0.5 radians QCD Leading AK4 jet p T and η >100 GeV and |η| < 2.4 All Table 2: Summary of the selection requirements for the mono-V category. Events that fail the mono-V selection are assigned to the monojet category.

Background estimation
The largest background contributions, from Z(νν)+jets and W( ν)+jets processes, are estimated using data from five mutually exclusive control samples selected from dimuon, dielectron, single-muon, single-electron, and γ+jets final states as explained below. The hadronic recoil p T is used as a proxy for p miss T in these control samples, and is defined by excluding identified leptons or photons from the p miss T calculation.

Control sample selection
Dimuon and single-muon control sample events are selected using full signal region criteria with the exception of the muon veto. Events in the dimuon control sample are selected requiring leading (subleading) muon p T greater than 20 (10) GeV and an invariant mass in the range 60 to 120 GeV, compatible with a Z boson decay. Events are vetoed if there is an additional loose muon or electron with p T > 10 GeV. In the single-muon control sample, exactly one tightly identified, isolated muon with p T > 20 GeV is required. No additional loose muons or electrons with p T > 10 GeV are allowed. In addition, the transverse mass (M T ) of the muon-p miss T system is required to be less than 160 GeV and is computed as Dielectron and single-electron control sample events are selected with an isolated single-electron trigger with a p T threshold of 27 GeV. In boosted Z(ee)+jets events, the two electrons produced in the decay typically have so little separation such that their tracks are included in each other's isolation cones. Therefore, to recover efficiency in selecting high-p T Z candidates at the trigger level, a nonisolated single-electron trigger with a p T threshold of 105 GeV is used. Events in the dielectron control sample are required to contain exactly two oppositely charged electrons with leading (trailing) electron p T greater than 40 (10) GeV. Similar to the dimuon control sample case, the invariant mass of the dielectron system is required to be between 60 and 120 GeV to be consistent with a Z boson decay. The events in the single-electron control sample are required to contain exactly one tightly identified and isolated electron with p T > 40 GeV. In addition, the contamination from QCD multijet events in this control sample is suppressed by requiring p miss T > 50 GeV and M T < 160 GeV.
Lastly, the γ+jets control sample is selected using events with one high-p T photon collected using single-photon triggers with p T thresholds of 165 or 175 GeV, depending on the data taking conditions. The photon is required to have p T > 175 GeV and to pass tight identification and isolation criteria, to ensure a high trigger efficiency of 98%.

Signal extraction
A binned likelihood fit to the data as presented in Ref. [14] is performed simultaneously in the five different control samples and in the signal region, for events selected in both the monojet and mono-V categories, to estimate the Z(νν)+jets and W( ν)+jets rate in each p miss T bin. In this likelihood, the expected numbers of Z(νν)+jets events in each bin of p miss T are the free parameters of the fit. Transfer factors, derived from simulation, are used to link the yields of the Z( )+jets, W( ν)+jets and γ+jets processes in the control regions with the Z(νν)+jets and W( ν)+jets background estimates in the signal region. These transfer factors are defined as the ratio of expected yields of the target process in the signal region and the process being measured in the control sample.
To estimate the W( ν)+jets background in the signal region, the transfer factors between the W(µν)+jets and W(eν)+jets event yields in the single-lepton control samples and the estimates of the W( ν)+jets background in the signal region are constructed. These transfer factors take into account the impact of lepton acceptances and efficiencies, lepton veto efficiencies, and the difference in the trigger efficiencies in the case of the single-electron control sample.
The Z → νν background prediction in the signal region is connected to the yields of Z → µ + µ − and Z → e + e − events in the dilepton control samples. The associated transfer factors account for the differences in the branching ratio of Z bosons to charged leptons relative to neutrinos and the impact of lepton acceptance and selection efficiencies. In the case of dielec-tron events, the transfer factor also takes into account the difference in the trigger efficiencies. The resulting constraint on the Z(νν)+jets process from the dilepton control samples is limited by the statistical uncertainty in the dilepton control samples because of the large difference in branching fractions between Z boson decays to neutrinos and Z boson decays to muons and electrons.
The γ+jets control sample is also used to predict the Z(νν)+jets process in the signal region through a transfer factor, which accounts for the difference in the cross sections of the γ+jets and Z(νν)+jets processes, the effect of acceptance and efficiency of identifying photons along with the difference in the efficiencies of the photon and p miss T triggers. The addition of the γ+jets control sample mitigates the impact of the limited statistical power of the dilepton constraint, because of the larger production cross section of γ+jets process compared to that of Z(νν)+jets process.
Finally, a transfer factor is also defined to connect the Z(νν)+jets and W( ν)+jets background yields in the signal region, to further benefit from the larger statistical power that the W( ν)+jets background provides, making it possible to experimentally constrain Z(νν)+jets production at high p miss T . These transfer factors rely on an accurate prediction of the ratio of Z+jets, W+jets, and γ+jets cross sections. Therefore, LO simulations for these processes are corrected using boson p Tdependent NLO QCD K-factors derived using MADGRAPH5 aMC@NLO. They are also corrected using p T -dependent higher-order EW corrections extracted from theoretical calculations [78][79][80][81][82][83]. The higher-order corrections are found to improve the data-to-simulation agreement for both the absolute prediction of the individual Z+jets, W+jets, and γ+jets processes, and their respective ratios.
The remaining backgrounds that contribute to the total event yield in the signal region are much smaller than those from Z(νν)+jets and W( ν)+jets processes. These smaller backgrounds include QCD multijet events which are measured from data using a ∆φ extrapolation method [14,84], and top quark and diboson processes, which are obtained directly from simulation.

Systematic uncertainties
Systematic uncertainties in the transfer factors are modeled as constrained nuisance parameters and include both experimental and theoretical uncertainties in the γ+jets to Z+jets and W+jets to Z+jets differential cross section ratios.
Theoretical uncertainties in V-jets and γ+jets processes include effects from QCD and EW higher-order corrections along with PDF modeling uncertainty. To estimate the theoretical uncertainty in the V-jets and γ+jets ratios due to QCD and EW higher-order effects as well as their correlations across the processes and p T bins, the recommendations of Ref. [16] are employed, as detailed in the following explanation.
Three separate sources of uncertainty associated with QCD higher order corrections are used. One of the uncertainties considered comes from the variations around the central renormalization and factorization scale choice. It is evaluated by taking the differences in the NLO cross section as a function of boson p T after changing the renormalization and factorization scales by a factor of two and a factor of one-half with respect to the default value. These constant scale variations mainly affect the overall normalization of the boson p T distributions and therefore underestimate the shape uncertainties that play an important role in the extrapolation of lowp T measurements to high-p T . A second, conservative shape uncertainty derived from altered boson p T spectra is used to supplement the scale uncertainties and account for the p T dependence of the uncertainties. The modeling of the correlations between the processes assumes a close similarity of QCD effects between all V-jets and γ+jets processes. However, the QCD effects in γ+jets production could differ compared to the case of Z+jets and W+jets productions. In order to account for this variation, a third uncertainty is computed based on the difference of the known QCD K-factors of the W+jets and γ+jets processes with respect to Z+jets production. All QCD uncertainties are correlated across the Z+jets, W+jets, γ+jets processes, and also correlated across the bins of the hadronic recoil p T .
For the V-jets and γ+jets processes, nNLO EW corrections are applied, which correspond to full NLO EW corrections [78][79][80]83] supplemented by two-loop Sudakov EW logarithms [81,[85][86][87]. We also considered three separate sources of uncertainty arising from the following: pure EW higher-order corrections failing to cover the effects of unknown Sudakov logarithms in the perturbative expansion beyond NNLO, missing NNLO effects that are not included in the nNLO EW calculations, and the difference between the next-to-leading logarithmic (NLL) Sudakov approximation at two-loop and simple exponentiation of the full NLO EW correction. The variations due to the effect of unknown Sudakov logs are correlated across the Z+jets, W+jets, and γ+jets processes and are also correlated across the bins of hadronic recoil p T . On the other hand, the other two sources of EW uncertainties are treated as uncorrelated across the V-jet and γ+jets processes, and an independent nuisance parameter is used for each process.
A recommendation that includes a factorized approach to partially include mixed QCD-EW corrections is outlined in Ref. [16]. An additional uncertainty is introduced to account for the difference between the corrections done in the multiplicative and the additive approaches, to account for the non-factorized mixed EW-QCD effects.
The summary of the aforementioned theoretical uncertainties including their magnitude and correlation is outlined in Table 3.
Experimental uncertainties including the reconstruction efficiency (1% per muon or electron) and the selection efficiencies of leptons (1% per muon and 2% per electron), photons (2%), and hadronically decaying τ leptons (5%), are also incorporated. These reconstruction and selection efficiencies further translate into an uncertainty in the lepton veto efficiency of 3%. Uncertainties in the purity of photons in the γ+jets control sample (2%), and in the efficiency of the electron (2%), photon (2%), and p miss T (1-4%) triggers, are included and are fully correlated across all the bins of hadronic recoil p T and p miss T . The uncertainty in the efficiency of the b jet veto is estimated to be 6% (2)% for the contribution of the top quark (diboson) background.
The uncertainty in the efficiency of the V tagging requirements is estimated to be 9% in the mono-V category. The uncertainty in the modeling of p miss T in simulation [50] is estimated to be 4% and is dominated by the uncertainty in the jet energy scale.
A systematic uncertainty of 10% is included for the top quark background associated with the modeling of the top quark p T distribution in simulation [88]. In addition, systematic uncertainties of 10 and 20% are included in the normalizations of the top quark [89] and diboson backgrounds [90,91], respectively, to account for the uncertainties in their cross sections in the relevant kinematic phase space. Lastly, the uncertainty in the QCD multijet background estimate is found to be between 50-150% due to the variations of the jet response and the statistical uncertainty of the extrapolation factors.
Correlated between processes; and in p T

Control sample validation
An important cross-check of the application of p T -dependent NLO QCD and EW corrections is represented by the agreement between data and simulation in the ratio of Z+jets events to both γ+jets events and W+jets events in the control samples, as a function of hadronic recoil p T . Figure 4 shows the ratio between Z( )+jets and γ+jets (left), Z( )+jets and W( ν)+jets (middle), and the one between W( ν)+jets/γ+jets processes (right) as a function of the recoil for events selected in the monojet category. While we do not explicitly use a W( ν)+jets/γ+jets constraint in the analysis, the two cross sections are connected through the Z+jets/γ+jets and Z+jets/W+jets constraints that are explained in Section 5.2. Therefore, it is instructive to examine the data-MC comparison of the W( ν)+jets/γ+jets ratio. Good agreement is observed between data and simulation after the application of the NLO corrections as shown in Fig. 4. The ratio between Z(µµ)+jets and γ+jets, Z(µµ)+jets and W(µν)+jets and the one between W(µν)+jets/γ+jets processes as a function of the boson p T is also studied and the results can be seen in Fig. 19 in Section A.   Figure 6: Comparison between data and MC simulation in the dimuon (upper row) and dielectron (lower row) 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 correspond to the monojet (left) and mono-V (right) categories, respectively, in the dilepton control sample. The hadronic recoil p T in dilepton events is used as a proxy for p miss T in the signal region. The other backgrounds include top quark, diboson, and W+jets processes. The description of the lower panels is the same as in Fig. 5.

Results and interpretation
The search is performed by extracting the signal through a combined fit of the signal and control regions. Figure 8 shows the comparison between data and the post-fit background predictions in the signal region in the monojet and mono-V categories, where the background prediction is obtained from a combined fit performed in all control regions, excluding the signal region. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid. Data are found to be in agreement with the SM prediction.  Tables 4 and 5 for the monojet and mono-V signal regions, respectively. The correlations between the predicted background yields across all the p miss T bins in the two signal regions are shown in Figs. 20 and 21 in Section A. The expected yields together with the correlations can be used with the simplified likelihood approach detailed in Ref. [92] to reinterpret the results for models not studied in this paper. Figure 9 shows a comparison between data and the post-fit background predictions in the signal region in the monojet and mono-V categories, where the fit is performed under the background-only hypothesis including signal region events in the likelihood. The limits on the production cross section of the various models described below is set after comparing this Table 4: Expected event yields in each p 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, excluding data in the signal region. The other backgrounds include QCD multijet and γ+jets processes.The expected signal contribution for a 2 TeV axial-vector mediator decaying to 1 GeV DM particles and the observed event yields in the monojet signal region are also reported. fit with an alternative one assuming the presence of signal.

Dark matter interpretation
The results are interpreted in terms of simplified s-channel DM models assuming a vector, axial-vector, scalar, or pseudoscalar mediator decaying into a pair of fermionic DM particles. The coupling of the mediators to the DM is assumed to be unity for all four types of mediators. The spin-0 particles are assumed to couple to the quarks with a coupling strength (g q ) of 1. In the case of the spin-1 mediators, g q is taken to be 0.25. The choice of all the signal model parameters follows the recommendations from Ref. [93]. 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 estimates include the renormalization and factorization scale uncertainties, as well as the PDF uncertainty.
Upper limits are computed at 95% CL on the ratio of the measured signal cross section to the predicted one, denoted by µ = σ/σ th , with the CL s method [94,95], using the asymptotic approximation [96]. Limits are obtained as a function of the mediator mass (m med ) and the DM mass (m DM ). Figure 10 shows the exclusion contours in the m med -m DM plane for the vector and axial-vector mediators. Mediator masses up to 1.8 TeV, and DM masses up to 700 and 500 GeV are excluded for the vector and axial-vector models, respectively. Figure 11 shows the limits for the scalar mediators as a function of the mediator mass, for a fixed DM mass of 1 GeV and the exclusion contours in the m med -m DM plane for pseudoscalar mediators, respectively. Pseudoscalar mediator (dark matter) masses up to 400 (150) GeV are excluded at 95% CL. A Table 5: Expected event yields in each p miss T 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, but excluding data in the signal region. The other backgrounds include QCD multijet and γ+jets processes. The expected signal contribution for a 2 TeV axial-vector mediator decaying to 1 GeV DM particles and the observed event yields in the mono-V signal region are also reported.  direct comparison of the results for simplified DM models of this paper, to the one presented in Ref. [14] can be seen in Fig. 22 and Fig. 23 in Section A.
The results for vector, axial-vector, and pseudoscalar mediators are compared to constraints Figure 10: Exclusion limits at 95% CL on µ = σ/σ th in the m med -m DM plane assuming vector (left) and axial-vector (right) mediators. The solid (dotted) red (black) 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 due to theoretical uncertainties in the signal cross section and the combination of the statistical and experimental systematic uncertainties, respectively. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.  from the observed cosmological relic density of DM as determined from measurements of the cosmic microwave background by the Planck satellite experiment [97]. The expected DM abundance is estimated, separately for each model, using the thermal freeze-out mechanism implemented in the MADDM [98] framework and compared to the observed cold DM density Ω c h 2 = 0.12 [99], where Ω c is the DM relic abundance and h is the Hubble constant.
In addition to scanning the m med -m DM plane, for a fixed g q value, the analysis interprets the results in the m med -g q plane for a fixed ratio of m med /m DM = 3. The ratio is chosen to ensure a valid relic abundance solution for every allowed g q value scanned for a spin-1 simplified model. Quark couplings down to 0.05 for mediator masses at 50 GeV are excluded for the spin-1 simplified models as shown in Fig. 12. Figure 12: Exclusion limits at 95% CL on µ = σ/σ th in the m med -g q plane assuming vector (left) and axial-vector (right) mediators. The widths shown on the axis correspond to mediator masses above 400 GeV, where the top quark decay channel is fully open. For the mediator masses below the top quark decay channel threshold the width is 9% less. The solid (dotted) black line shows the contour for the observed (expected) exclusion. The solid red contours around the observed limit represent one standard deviation due to theoretical uncertainties in the signal cross section. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.
The exclusion contours obtained from the simplified DM models are translated to 90%CL upper limits on the spin-independent/spin-dependent (σ SI/SD ) DM-nucleon scattering cross sections using the approach outlined in Refs. [19,36,100]. The results for the vector and axial-vector mediators are compared with the results of direct searches in Fig. 13. This search provides the most stringent constraints for vector mediators, for DM particle masses below 5 GeV. For axial-vector mediators, the sensitivity achieved in this search provides stronger constraints up to a DM particle mass of 550 GeV than those obtained from direct searches. For pseudoscalar mediators, the 90%CL upper limits as shown in Fig. 14 are translated to velocity-averaged DM annihilation cross section ( σv ) and are compared to the indirect detection results from the Fermi-LAT Collaboration [101]. The collider results provide stronger constraints for DM masses less than 150 GeV.

Fermion portal dark matter interpretation
The total production cross section in the fermion portal DM model has an exponential (linear) dependence on the mass of the new scalar mediator m φ u (mass of the DM candidate m χ ). The middle diagram shown in Fig. 1 represents the main production mechanism for small m φ u values, whereas the right diagram contributes to the total cross section for m φ u > 1 TeV. The  [102], LUX [103], XENON-1T [104], PANDAX-II [105], and CRESST-II [106] are shown for the vector mediator. Limits from Picasso [107], PICO-60 [108], IceCube [109], and Super-Kamiokande [110] are shown for the axial-vector mediator.  Figure 14: For the pseudoscalar mediator, limits are compared to the the velocity averaged DM annihilation cross section upper limits from Fermi-LAT [101]. 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 [111,112].
region where m φ u < m χ is not considered in the search, because of the reduced production cross section of the model. The upper limits on the signal strength are set as a function of m φ u and m χ . Figure 15 shows the exclusion contours in the m φ u -m χ plane, for which the coupling strength λ u of the interaction between the scalar mediator and up-type quarks is fixed at unity. The results are also compared to constraints from the observed cosmological relic density of DM, obtained by the Planck satellite experiment, for the allowed values of m φ u and m χ [20]. In this search, mediator (dark matter) masses up to 1.4 (0.6) TeV are excluded. Figure 15: The 95% CL expected (black dashed line) and observed (red solid line) upper limits on µ = σ/σ th in the context of the fermion portal DM model, for Dirac DM particles with coupling strengths to the up quark corresponding to λ u = 1 in the m φ u -m χ plane. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

Nonthermal dark matter interpretation
This search is also interpreted in the context of the nonthermal DM model where the DM candidate is not parity protected and therefore could be singly produced. Such production leads to signatures with an energetic jet and large p miss T whose distribution is characterized by a Jacobian-like shape, which exhibits a peak at half of the mediator mass. Therefore, multiple mediator mass points have been studied. The search is restricted to a coupling range of 0.01-1.5 for λ 1 and 0.01-2.0 for λ 2 to ensure the mediator width is less than about 30% of its mass. Within these bounds, no significant excesses were found and limits are reported as a function of coupling strength parameters λ 1 and λ 2 for two reference mediator masses m X 1 of 1 and 2 TeV. Figure 16 shows the exclusion contours in the λ 1 -λ 2 plane.

Invisible decays of the Higgs boson interpretation
The results of this search are further interpreted in terms of an upper limit on the production cross section and branching fraction, B(H → inv.), where the Higgs boson is produced through gluon fusion (ggH) along with a jet; or 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 [113]. The observed (expected) 95% CL upper limit on the invisible branching fraction of the Higgs boson, σ × B(H → inv.)/σ SM , is found to be 53% (40%). The limits are summarized in Fig. 17, while Table 6 shows the individual limits for the monojet and mono-V categories.  Table 6: 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 in the expected limits is listed. The expected composition of the production modes of a Higgs boson with a mass of 125 GeV is summarized, assuming SM production cross sections.

Category
Observed (

The ADD model interpretation
The 95% CL lower limits on the fundamental Planck scale M D of the ADD model are presented as a function of the number of extra spatial dimensions n. The efficiency of the full event selection in the monojet (mono-V) category for this model ranges between 15 (1)% and 20 (1.5)% depending on the values of the parameters M D and n. An upper limit on the signal strength µ = σ/σ th is presented for the ADD graviton production for n = 2 EDs, as a function of M D in Fig. 18. In addition, Fig. 18 shows the observed exclusion on M D which varies from 9.9 TeV for n = 2 to 5.3 TeV for n = 6. The results of this search are also compared to earlier ones obtained by the CMS Collaboration with Run 1 data corresponding to an integrated luminosity of 19.7 fb −1 at a centre-of-mass energy of 8 TeV [10]. The upper limits on the signal production cross section and M D exclusions are also provided in Table 7

Summary
A search for dark matter (DM) particles, invisible decays of a standard-model-like (SM-like) Higgs boson, and extra spatial dimensions is presented using events with one or more energetic jets and large missing transverse momentum in proton-proton collisions recorded at √ s = 13 TeV, using a sample of data corresponding to an integrated luminosity of 35.9 fb −1 . Events are categorized based on whether jets are produced directly in hard scattering as initial-state radiation or originate from merged quarks from a decay of a highly Lorentz-boosted W or Z boson. No excess of events is observed compared to the SM background expectations in either of these two categories.
Limits are computed on the DM production cross section using simplified models in which DM production is mediated by spin-1 and spin-0 particles. Vector and axial-vector (pseudoscalar) mediators with masses up to 1.8 (0.4) TeV are excluded at 95% confidence level. Similarly, limits are also presented for the parameters of the fermion portal DM model and an exclusion up to 1.4 TeV on the mediator mass is observed at 95% confidence level. The first limits on the DM production at a particle collider in the nonthermal DM model are obtained and presented in the coupling strength plane. Furthermore, an observed (expected) 95% confidence level upper limit of 0.53 (0.40) is set for the invisible branching fraction of an SM-like 125 GeV Higgs boson, assuming the SM production cross section. Lower limits are also computed on the fundamental Planck scale M D in the context of the Arkani-Hamed, Dimopoulos, and Dvali model with large extra spatial dimensions, which varies from 9.9 TeV for n = 2 to 5.3 TeV for n = 6 at 95% confidence level, where n is the number of extra spatial dimensions. These limits provide the most stringent direct constraints on the fundamental Planck scale to date.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus   [50] CMS Collaboration, "Performance of the CMS missing transverse momentum reconstruction in pp data at √ s = 8 TeV", JINST 10 (2015) P02006, doi:10.1088/1748-0221/10/02/P02006, arXiv:1411.0511.

A Additional material
Another important cross-check of the application of p T -dependent NLO QCD and EW corrections is represented by the agreement between data and simulation in the ratio of Z+jets events to both γ+jets events and W+jets events in the control samples as a function of boson p T . Figure 19 shows the ratio between Z(µµ)+jets and γ+jets, and the ratio of Z(µµ)+jets and W(µν)+jets events as a function of the boson p T , for the monojet category. While we do not explicitly use a W(µν)+jets/γ+jets constraint in the analysis, the two cross sections are connected through the Z+jets/γ+jets and Z+jets/W+jets constraints. Therefore, it is instructive to examine the data-to-simulation comparison for the W(µν)+jets/γ+jets ratio. This is shown in the same figure. Good agreement is observed between data and simulation after the application of NLO corrections.
The correlations between the predicted background yields across all the p miss T bins in the two signal regions are shown in Figs. 20 and 21. These results can be used with the simplified likelihood approach detailed in Ref. [92] for reinterpretations in terms of models not studied in this paper.
To allow for a direct comparison with the results of Ref.
[14] for simplified DM models, the results are presented for scalar mediators allowing for vector boson couplings simulated at LO in QCD, as shown in Fig. 22. Similarly, results for spin-1 mediators are also presented in Fig. 23, where the mono-V signal is simulated at LO in QCD. The comparison of MC generators are also provided in Table 8.  Figure 19: Comparison between data and Monte Carlo simulation of the Z(µµ)/γ+jets, Z(µµ)/W(µν) and W(µν)/γ+jets ratios, as a function of boson p T , in the monojet category.
In the ratio panel, ratios of data with the pre-fit background prediction are shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.  08 0.10 0.15 0.14 0.10 0.12 0.13 0.10 0.17 0.12 0.02 0.21 0.12 0.05 0.16 -0.03 0.16 1.00   -0.00 0.02 0.07 0.03 0.03 0.15 0.15 0.09 0.04 0.01 -0.01 0.10 0.12 0.01 0.09 -0.01 0.16 0.03 1.00   0.14 0.16 0.15 0.13 0.17 0.24 0.12 0.05 0.17 0.09 0.18 0.05 -0.00 0.15 -0.01 0.07 -0.11 -0.09 0.08 1.00   0.04 0.07 0.07 0.06 0.13 0.09 0.05 0.13 0.20 0.09 0.04 0.11 0.04 0.07 0.06 0.13 0.09 0.04 0.03 0.02 1.00   -0.04 -0.03 0.01 -0.02 -0.01 0.01 0.08 0.03 0.04 0.05 -0.01 0.14 0.04 0.09 0.10 -0.03 0.09 -0.03 0.15 0.09 0.08 1    red (black) 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 due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Expected and observed sensitivity of the previous CMS publication [14] are also presented. Results of the Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant. 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 (right). Figure 23: Exclusion limits at 95% CL on µ = σ/σ th in the m med -m DM plane assuming vector (left) and axial-vector (right) mediators where the the mono-V signal is simulated at LO in QCD. The solid (dotted) red (black) 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 due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant.

B The CMS Collaboration
University of Auckland, Auckland, New Zealand D. Krofcheck