Search for heavy resonances decaying to Z($\nu\bar{\nu}$)V(qq') in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search is presented for heavy bosons decaying to Z($\nu\bar{\nu}$)V(qq'), where V can be a W or a Z boson. A sample of proton-proton collision data at $\sqrt{s} =$ 13 TeV was collected by the CMS experiment during 2016-2018. The data correspond to an integrated luminosity of 137 fb$^{-1}$. The event categorization is based on the presence of high-momentum jets in the forward region to identify production through weak vector boson fusion. Additional categorization uses jet substructure techniques and the presence of large missing transverse momentum to identify W and Z bosons decaying to quarks and neutrinos, respectively. The dominant standard model backgrounds are estimated using data taken from control regions. The results are interpreted in terms of radion, W' boson, and graviton models, under the assumption that these bosons are produced via gluon-gluon fusion, Drell-Yan, or weak vector boson fusion processes. No evidence is found for physics beyond the standard model. Upper limits are set at 95% confidence level on various types of hypothetical new bosons. Observed (expected) exclusion limits on the masses of these bosons range from 1.2 to 4.0 (1.1 to 3.7) TeV.


Introduction
The search for physics beyond the standard model (SM) using proton-proton (pp) collisions produced by the CERN LHC is a key goal of the CMS physics program. The apparent large hierarchy between the electroweak scale and the Planck scale, the nature of dark matter, and the possibility of a unification of the gauge couplings at high energies, are among the outstanding problems in particle physics not addressed within the SM. New bosons are predicted in many beyond-the-SM theories, which attempt to answer some of these questions. New spin-0 and spin-2 particles are predicted in the Randall-Sundrum (RS) models of warped extra dimensions [1,2], which arise from radion and graviton fields. Spin-1 W and Z bosons can also arise in these models [3][4][5], as well as in left-right symmetric theories [6], and little Higgs models [7][8][9]. When the interaction strength between a new boson and the SM boson field is large, such as in the bulk RS models [10,11], searches for diboson resonances are motivated, either via weak vector boson fusion (VBF) or strong production processes. This paper presents a search for new bosons (X) decaying either to a pair of Z bosons or to a W and a Z boson, as shown in Fig. 1. In addition to VBF production, we consider gluon-gluon fusion (ggF) production of spin-0 and spin-2 particles, and Drell-Yan (DY) production of spin-1 particles. The targeted final state is one in which one Z boson decays into a neutrino pair, while the other vector boson decays hadronically into jets. Searches for similar signatures have been presented by the ATLAS [12] and CMS [13] Collaborations with the LHC data recorded in 2015 and 2016. Compared to earlier CMS publications, this paper includes additional data, new interpretations in terms of radion models, and extends the analysis to new search regions by including event categories that identify forward jets consistent with VBF production. An analysis similar to the one presented here was published by the ATLAS Collaboration using data recorded in 2015-2018 [14]. In that analysis, no significant deviations from the SM were observed.
In the present work, proton-proton collisions at √ s = 13 TeV recorded during 2016-2018 with the CMS detector are analyzed. The data set corresponds to an integrated luminosity of 137 fb −1 . Events are selected that have a high-mass jet and a significant amount of missing transverse momentum (p miss T ), which is the signature of the Z → νν decay. Events are categorized by the presence or absence of jets at large pseudorapidity (forward jets). Events that include forward jets are typical of VBF production. Events without forward jets more commonly occur in ggF or DY processes. For sufficiently heavy new bosonic states, the decaying vector bosons will have high momenta and, when decaying hadronically, will appear in the detector as single jets. As a result, we employ jet substructure techniques to identify these objects. Contributions from the dominant backgrounds are determined using control samples in data.  Figure 1: Representative Feynman diagrams for various production modes of a heavy resonance X. These modes are: a ggF-produced spin-0 or spin-2 resonance decaying to ZZ → qq νν (left), a DY-produced spin-1 resonance decaying to WZ → qq νν (center), and a VBF-produced spin-1 resonance decaying to WZ → qq νν (right).
This paper is organized as follows. Section 2 gives a brief description of the CMS detector and its components relevant to this work. Section 3 summarizes the simulated data sets used in this analysis. Algorithms for the reconstruction of physics objects and the selection criteria applied to these objects are described in Sections 4 and 5, respectively. Section 6 discusses methods used for estimating the SM backgrounds. The systematic uncertainties relevant to this analysis are described in Section 7. The final results are presented in Section 8, along with their statistical interpretations. A summary of the work is presented in Section 9. Tabulated results are provided in the HEPData record [15] for this analysis.

The CMS detector
The central feature of the CMS detector 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, and a brass and scintillator hadron calorimeter. Each of these systems is composed of a barrel and two endcap sections. The tracking detectors cover the pseudorapidity range |η| < 2.5. For the electromagnetic and hadronic calorimeters, the barrel and endcap detectors together cover the range |η| < 3.0. Forward calorimeters extend the coverage to |η| < 5.0. Muons are measured and identified in both barrel and endcap systems, which together cover the pseudorapidity range |η| < 2.4. The detection planes are based on three technologies: drift tubes, cathode strip chambers, and resistive-plate chambers, which are embedded in the steel flux-return yoke outside the solenoid. The detector is nearly hermetic, permitting accurate measurements of p miss T . Events of interest are selected using a two-tiered trigger system [16,17]. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a fixed time interval of less than 4 µs. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [18].  [19][20][21][22]. The V+jets (tt+jets) samples are generated with leading order (LO) precision in the perturbative expansion of quantum chromodynamics (pQCD) and contain up to four (three) additional partons in the matrix element calculations. The t-channel and tW single top quark events, and WW events for 2016 (2017 and 2018) are generated using POWHEG v1.0 (v2.0) [23][24][25][26][27] at next-to-LO (NLO) precision in pQCD. All other SM background samples are generated using MADGRAPH5 aMC@NLO at NLO precision in pQCD. The signal samples used for interpretation of the results are also generated using MAD-GRAPH5 aMC@NLO with LO precision in pQCD.

Simulated event samples
The parton showering and hadronization step in all simulations is performed with two versions of PYTHIA [28]. The 2016 (2017 and 2018) simulation uses the CUETP8M1 [29] (CP5 [30]) underlying event tune with PYTHIA v8.212 (v8.230). The parton distribution functions (PDFs) used in the 2016 (2017 and 2018) simulated data samples are NNPDF3.0 LO or NLO [31] (NNPDF3.1 NNLO [32]). The simulation of the particle interactions and the CMS detector is performed with GEANT4 [33]. The effects due to additional pp interactions in the same or adjacent bunch crossings (pileup) are also simulated and the events are weighted to match the pileup distribution in data.
The cross sections used to normalize different SM processes correspond to NLO or next-to-NLO (NNLO) accuracy [19,26,27,[34][35][36][37][38][39][40][41][42]. The V+jets samples are weighted based on the transverse momentum (p T ) of the W and Z bosons. Weights are derived from comparisons of LO simulations and simulations at NNLO precision in pQCD interactions and NLO precision in electroweak interactions [43].  When diboson signatures are produced through VBF, correlations between the spin of initialand final-state bosons cause event kinematic distributions to depend on the hypothesized resonance spin. These correlations are manifested in the decay angle, θ * , of the vector bosons, defined in Ref. [44]. Figure 2 shows the distribution of the cosine of the decay angles in the rest frame of X for each spin configuration and production mechanism we consider, given a parent particle mass of 2 TeV. Scalar resonances have no correlation between initial-and final-state spins, which translates to a flat cos θ * distribution. Spin-1 and spin-2 particles can have strong correlations, especially when produced via VBF, where vector bosons are preferentially produced in the forward direction (cos θ * ±1). Such correlations are caused by the production of longitudinally or transversely polarized vector bosons [45]. The decay angle is correlated with the p T of the resonance's decay products. Thus, the spectral features explored here are different from typical diboson searches because the final state is only partially reconstructed. We explore the sensitivity of the analysis to the assumed spin by considering three different production models: radions (spin 0), W bosons (spin 1), and gravitons (spin 2). In each case, we consider both VBF and ggF or DY production, and masses between 1.0 and 4.5 TeV in steps of 200 (500) GeV for masses less (greater) than 2.0 TeV.
To interpret the data in terms of spin-0 and spin-2 signals, radions and gravitons arising from models of warped extra dimensions [1,2], and specifically from bulk scenarios [10,11], are used as representative models. The warped extra dimension model has several free parameters, including the mass of the lowest excited state of the graviton, the radion mass, the parameter kr c π, where k and r c are the curvature and the compactification scale of the extra dimension respectively, the dimensionless coupling k = k/M Pl , where M Pl is the reduced Planck mass, and the energy scale associated with radion interactions (Λ R ). These parameters and the corresponding cross sections are described in Ref. [45]. We assume k = 0.5, kr c π = 35, and Λ R = 3 TeV, which results in decay widths for gravitons and radions smaller than 10% of their mass. The predicted cross sections for radions and gravitons produced via ggF (VBF) are accurate to NLO (LO) in pQCD.
To interpret data in terms of spin-1 signals, W bosons within the heavy vector triplet (HVT) framework [6] are used. The interactions between W bosons and SM particles are parameterized in terms of c H , g V , and c F couplings and the mass of the HVT W boson. Together with the SM SU(2) L gauge coupling, g, these parameters determine the couplings between the HVT bosons and the SM Higgs boson, SM vector bosons, and SM fermions, respectively, according to Ref. [6]. We consider two specific cases of these model parameters: those corresponding to model B (c H = −0.98, g V = 3, and c F = 1.02) in Ref. [6] and model C (c H = g V = 1 and c F = 0). Model B suppresses the fermion couplings, enhancing decays to SM vector bosons. Model C removes direct couplings to fermions, ensuring that only VBF production is possible. The predicted cross sections for W bosons are accurate to LO in pQCD.

Triggers and event reconstruction
Samples of collision data are selected using several p miss T triggers whose thresholds vary between 90 and 140 GeV, depending on the data-taking period. The p miss T trigger efficiencies were studied using samples of events selected with single-lepton triggers. The lepton triggers isolate events with neutrinos produced via W boson decays, which serve as a good proxy for both the signal and the dominant backgrounds. The single-lepton triggers required electrons with p T > 27-32 GeV, depending on the data-taking period, or muons with p T > 24 GeV. The efficiencies of the triggers for selecting events with large p miss T (>200 GeV) were measured as functions of p miss T . The differences between the efficiencies determined using electron events and muon events were found to be less than 1.4% and are assigned as systematic uncertainties. For all data-taking periods, the trigger efficiency is found to reach 95% for p miss T > 250 GeV and plateaus around 98% for p miss T > 300 GeV. At p miss T = 200 GeV, the efficiency is found to be greater than 75%. The trigger efficiencies measured using single-lepton data are applied to the simulated data as functions of the reconstructed p miss T . The dependence of these efficiencies on other kinematic variables has been investigated and the associated effects found to be less than the assigned uncertainties.
The event reconstruction proceeds from particles identified by the particle-flow (PF) algorithm [46], which uses information from the silicon tracking system, calorimeters, and muon systems to reconstruct PF candidates as electrons, muons, charged or neutral hadrons, or photons. The candidate vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The physics objects used for this determination are jets, formed by clustering tracks assigned to candidate vertices using the anti-k T jet finding algorithm [47,48] with a distance parameter of 0.4, and the associated p miss T , taken as the negative vector p T sum of those jets.
Electrons are reconstructed by associating a charged-particle track with an electromagnetic calorimeter supercluster [49]. The resulting electron candidates are required to have p T > 10 GeV and |η| < 2.5, and to satisfy identification criteria designed to reject light-parton jets, photon conversions, and electrons produced in the decays of heavy-flavor hadrons. Muons are recon-structed by associating tracks in the muon system with those found in the silicon tracker [50]. Muon candidates are required to satisfy p T > 10 GeV and |η| < 2.4.
Leptons (e, µ) are required to be isolated from other PF candidates to select preferentially those originating from W and Z boson decays and suppress backgrounds in which leptons are produced in the decays of hadrons containing heavy quarks. Isolation is quantified using an optimized version of the mini-isolation variable originally introduced in Ref. [51]. The isolation variable, I mini , is calculated by summing the p T of the charged and neutral hadrons, and photons with ∆R ≡ √ (∆φ) 2 + (∆η) 2 < R 0 of the lepton momentum vector, p , where φ is the azimuthal angle and R 0 depends on the lepton p T . The three values of R 0 used are: 0.2 for p T ≤ 50 GeV; (10 GeV)/p T for 50 < p T < 200 GeV; and 0.05 for p T ≥ 200 GeV. Electrons (muons) are then required to satisfy I mini /p T < 0.1 (0.2). In order to mitigate the effects from pileup in an event, charged hadron candidates are required to originate from the primary vertex of the given event.
Events are vetoed in which muon or electron candidates are identified that satisfy isolated track requirements, |η| < 2.4, and p T > 5 GeV, but do not satisfy the kinematic requirements just described for isolated leptons. Hadronically decaying τ leptons can produce isolated hadron tracks. Events in which an isolated hadron track is identified that satisfies |η| < 2.4 and p T > 10 GeV are also vetoed.
Events with one or more photons are vetoed. Photon candidates are required to have p T > 100 GeV, |η| < 2.4, and be isolated from neutral hadrons, charged hadrons, and electromagnetic particles, excluding the photon candidate itself. The isolation criterion is calculated using a cone with ∆R < 0.2 around the photon [52].
Jets are reconstructed by clustering charged and neutral PF candidates using the anti-k T algorithm. Two collections of jets are considered clustered with distance parameters R = 0.4 and 0.8, as implemented in the FASTJET package [48]. Depending on the distance parameter used, these jets are referred to as AK4 and AK8 jets, respectively. Jet energies are corrected using a p T -and η-dependent jet energy calibration [53]. To mitigate contributions to jet reconstruction from pileup, we utilize the charged-hadron subtraction method for AK4 jets and the pileupper-particle identification (PUPPI) method [54,55] for AK8 jets.
Jets are required to satisfy p T > 30 (200) GeV, |η| < 5.0 (2.4), and jet quality criteria [56,57] for AK4 (AK8) jets. The mass of AK8 jets and information about the pattern of energy deposited in various detectors are used to reconstruct massive vector bosons. To further reduce the dependence on pileup and to help reduce the effect of wide-angle soft radiation, the soft-drop algorithm [58,59] is used to remove constituents from the AK8 jets. Corrections are applied to AK8 jets to ensure that the reconstructed jet mass reproduces the pole masses of the SM bosons. Corrections are derived using W bosons from tt production to account for known differences between measured and simulated jet mass scale and jet mass resolution [60]. Finally, jets having PF constituents matched to an isolated lepton are removed from the jet collection.
The N-subjettiness [61] technique is used to distinguish between AK8 jets originating from the hadronic decay of W or Z bosons and those originating from quantum chromodynamics (QCD). In hadronic boson decays, the resulting jet is likely to have two substructure components, which results in a smaller N-subjettiness ratio, τ 21 . For QCD jets, τ 21 tends to be higher. We require AK8 jets to satisfy τ 21 < 0.75. There is a loss of about 36% in background events due to this requirement. Negligible loss of efficiency is observed due to this requirement in a signal sample of VBF-produced gravitons (VBFG) with a mass of 1 TeV. The efficiency for tagging W bosons in simulated data sets is validated against collision data using tt events [60]. Scale factors are applied to simulated data sets to account for observed differences.
The AK4 jets are tagged as originating from the hadronization of b quarks using the deep combined secondary vertex algorithm [62]. For the medium working point chosen here, the signal efficiency for identifying b jets with p T > 30 GeV in tt events is about 68%. The probability of misidentifying jets in tt events arising from c quarks is approximately 12%, while the probability of misidentifying jets associated with light-flavor quarks or gluons as b jets is approximately 1%.
The vector p miss T is defined as the negative vector p T sum of all PF candidates and is calibrated taking into account the jet energy corrections. Its magnitude is denoted by p miss T . Dedicated event filters designed to reject instrumental noise are applied to improve the correspondence between the reconstructed and the genuine p miss T [63]. To suppress SM backgrounds, we use the quantity m T , defined as the transverse mass of the system consisting of the highest p T AK8 jet (p J T ) and p miss T . The value of m T is computed as where ∆Φ is the difference between the azimuthal angle of the AK8 jet's momentum and p miss T . The m T variable in Eq. 1 assumes that the new state decays into much lighter daughter particles.

Event selection
The reconstructed objects (defined in Section 4) are used to define signal regions (SRs) and control regions (CRs). These are all subsets of a baseline phase space where at least one AK8 jet and p miss T > 200 GeV are required. Events are rejected if they contain a reconstructed electron, muon, photon, isolated track, or an AK4 jet which has been identified as a b jet. Events are vetoed if any jet passes the p T and η requirements, but fails the jet quality criteria. Events are also vetoed if p miss T is aligned with the transverse projection of any of the four highest p T AK4 jets, defined as ∆φ(j i , p miss T ) < 0.5. The baseline phase space is split into two sets of regions, VBF and ggF/DY. The VBF regions require at least two AK4 jets, each required to be separated by ∆R > 0.8 from the AK8 jet. The two highest-p T AK4 jets are also required to be reconstructed in opposite hemispheres (η 1 η 2 < 0), have a large pseudorapidity separation (∆η > 4.0), and form a large invariant mass (m jj > 500 GeV). These requirements are indicative of VBF production. If any of these conditions is failed, the event is put into the ggF/DY category.
Both the VBF and ggF/DY categories are further separated into high-purity (HP) and lowpurity (LP) categories, depending on the highest p T AK8 jet's value of τ 21 . Events in which the highest p T AK8 jet satisfies τ 21 < 0.35 (0.35 < τ 21 < 0.75) are referred to as HP (LP). The signal (VBFG 1 TeV) selection efficiency with the high (low) purity cut is 69 (31)%. The background selection efficiency with the high (low) purity cut is 32 (68)%.
Each of these four event categories is divided into a number of m T bins. Starting from m T = 400 GeV, each bin has a width of 100 GeV. In the ggF/DY (VBF) HP category, the bin width is constant up to 2200 (1600) GeV, beyond which, bin boundaries correspond to m T = 2200, 2350, 2550, 2750, and 3000 (1600, 1750, and 2075) GeV. In the ggF/DY (VBF) LP category, the bin width is constant up to 2900 (2300) GeV, beyond which bin widths are 200 GeV up to m T = 3500 (2700) GeV. The last bin in each of the categories includes all events with m T above the final quoted bin boundary.
In all m T bins, an SR and a CR is defined based on the mass of the highest p T AK8 jet, m J . The SRs require 65 < m J < 105 GeV, a range which is chosen to accept both W and Z bosons, but reject most hadronically decaying Higgs bosons. The CRs require either 30 < m J < 65 GeV or 135 < m J < 300 GeV, which excludes the SR mass requirement and a window around the Higgs boson mass. The event selections used in the analysis are summarized in Table 1.
The dominant backgrounds are events originating from W+jets and Z+jets production, followed by the W → ν and Z → νν decays. In these events the charged leptons do not pass the reconstruction requirements described in Section 4, while the neutrinos manifest themselves as p miss T . In addition, the massive jets in these events do not arise from hadronically-decaying vector bosons; rather they arise from the tail of a smoothly falling distribution of jet mass. We refer to these and other processes with similar kinematic properties as nonresonant backgrounds. The shape and normalization of nonresonant backgrounds are constrained using data, as described in Section 6.
Subdominant SM contributions come from tt, single top quark, and diboson processes. These processes typically have a hadronically-decaying vector boson. There is a small contribution from the diboson events produced via the vector boson scattering process. These events are expected to contribute less than 10% of the total diboson event yield in the VBF SRs. The contributions from subdominant backgrounds, referred to as resonant backgrounds, are estimated using predictions from simulation.
The reconstructed m T distribution for the signal depends on the spin, mass, and production mechanism. Using events from all signal regions and control regions combined, Fig. 3 shows the m T distributions for the various signal hypotheses considered. These distributions for VBFproduced W and graviton resonances are a reflection of the prevalence for vector bosons production at large η due to correlations between η and cos θ * . When vector bosons have large η, the AK8 jet p T and the p miss T are lower, and in turn, the reconstructed m T is lower. For models with multimodal cos θ * distributions, there is a corresponding distortion in the m T distribution, which tends to produce higher yields at lower values of m T .

Background estimation method
The nonresonant backgrounds populate both the CRs and the SRs, while signal events mainly populate the SRs. The yields observed in the CRs are weighted by a transfer factor, α, to account for known differences between the SR and CR kinematic properties. The transfer factor is derived from simulated data sets. Algebraically, the predictions of the nonresonant backgrounds where N obs CR refers to the observed CR yields, and N non-res (N res ) refers to the nonresonant (resonant) background yields in simulated data sets. In this formula, N res * serves the role of removing the expected contributions from resonant backgrounds, which have a systematically different transfer factor and whose predictions are handled separately. All event yields are derived separately for each m T bin and each event category. Figure 4 shows α as a function of m T in each of the event categories.  The resonant backgrounds are directly estimated using predictions from simulation, with sys-tematic uncertainties evaluated to account for potential data mismodeling. The resonant background yields are used to account for contamination in the CRs before predicting the nonresonant backgrounds and their contribution to the SRs themselves.
The procedures used to predict SM backgrounds have been validated using data from a subset of each CR, which we refer to as the validation SR (vSR). The vSRs have the same selections as the SRs except that the jet mass must satisfy 55 < m J < 65 GeV. The CRs for validation tests are redefined by removing the events in the vSR. The vSR and analogous CRs are used to compute the analog of α, and the full background prediction is evaluated on data. The predicted yields in the vSR are then compared to the observed event yields. This comparison is performed in the corresponding vSR of each of the event categories. The resulting distributions are shown in Fig. 5.  The vSR tests result in a prediction of more events in each of the event categories than observed in the data. The overprediction is as large as 10% in the lowest m T bin. To account for any potential mismodeling of our prediction, we derive a shape uncertainty. The uncertainty is based on a linear fit to the ratio of the prediction and the observation versus m T in the LP ggF/DY vSR. Based on the fit, an uncertainty is assessed that corresponds to 7% in the lowest m T bin, and decreases linearly to -40% in the highest m T bin. This shape uncertainty is applied to each of the four signal regions assuming no correlation between the regions.

Systematic uncertainties
Because the nonresonant backgrounds are estimated from data, several simulation-related systematic uncertainties have little to no effect on the estimation of these backgrounds. However, PDF uncertainties, renormalization (µ R ) and factorization (µ F ) scale uncertainties, and jet energy scale (JES) and resolution (JER) uncertainties have nonnegligible effects on α.
For PDF uncertainties, the distribution of α is evaluated for each recommended PDF variation [31,32]. An envelope of these variations is used to assess an α shape uncertainty. The size of the uncertainty in a given m T bin due to PDFs is as large as 3 (1.5)% for the VBF (ggF/DY) categories. The effects of the scale uncertainties are evaluated by varying the values of µ R and µ F simultaneously up and down by a factor of two. Based on scale variations, an α shape uncertainty is determined, which is less than 2% in any single m T bin. The JES and JER uncertainties are propagated to α, and are not larger than 3%. A summary of all systematic uncertainties related to the nonresonant background prediction is shown in the second and third columns of Table 2.
In addition to those listed in Table 2, we account for uncertainties due to the limited size of simulated data sets. The Poisson uncertainties associated with the observed CR yields are propagated to the nonresonant background predictions in each m T bin. The uncertainties due to the limited size of simulated data sets are treated as uncorrelated across each analysis bin.
The predicted resonant background and signal yield uncertainties are evaluated from a larger list of potential sources. These sources include the integrated luminosity, τ 21 scale factors, pileup modeling, b jet veto efficiency, effects related to inefficiencies due to instrumental effects of the electromagnetic calorimeter trigger (prefiring), modeling of unclustered energy in the calculation of p miss T , jet mass scale (JMS) and resolution (JMR), JES and JER, trigger efficiency modeling, PDF uncertainties, and scale uncertainties. A summary of the impacts these uncertainties have on resonant backgrounds and signal is shown in the fourth through seventh columns of Table 2 and in Table 3. A description of each uncertainty source is provided below.
The measured integrated luminosity uncertainty is propagated to the prediction of the resonant background and signal yields. This uncertainty amounts to 1.6% on the entire data set [64][65][66] and is correlated across all signal regions. The effects of the luminosity uncertainty on signal and nonresonant backgrounds are treated as fully correlated.
Uncertainties associated with the determination of τ 21 efficiency scale factors that correct for systematic differences in simulated and collision data sets are propagated to the predicted signal and resonant background yields. These uncertainties have two components: one that affects the normalization of predictions (τ 21 SF) and another that accounts for p T -dependent differences (τ 21 p T extrap.) in the tagging efficiency, which affects the m T shape of our predicted yields.
Jet energy and jet mass scales are varied within their uncertainties. Effects of JMS uncertainties are treated as anticorrelated between SR and CR regions and correlated across all categories. The magnitudes of JMS uncertainties are assumed to be independent of m T . They are treated as fully correlated across all m T bins and all regions.
Jet masses are smeared to broaden their distribution within measured JMR uncertainties. Jet mass smearing is done for both SR and CR but for simulated data sets only. The effect of jet smearing was at most 10%. The effects of JMR uncertainties are correlated across m T bins and all categories, and between signals and resonant backgrounds.
Similarly to the nonresonant background, the effect of JES and JER uncertainties are propagated to the predicted event yields. These are found to have minimal impact on the m T shape (<1%) within a given category but can cause events to migrate from the ggF/DY to the VBF categories.
Other systematic uncertainties affect the normalization of resonant backgrounds and signals. These include pileup uncertainties, b-tagging scale factor uncertainties, prefiring corrections, unclustered energy scale uncertainties, and trigger uncertainties. These effects are assumed to be correlated across various categories, and between signal and resonant backgrounds.
Finally, the statistical uncertainties due to the limited size of simulated data sets are propagated to all predicted signal and resonant background yields. In this analysis, all the uncertainties quoted are pre-fit values.

Results and interpretations
The final predicted event yields are computed using a simultaneous maximum likelihood fit of event yields in all m T bins, and all SRs and CRs. Each bin is modeled as a marked Poisson model [67] with mean value corresponding to the sum of expected yields for resonant and  We derive both expected and observed 95% confidence level (CL) upper limits on the X → V(qq )Z(νν ) production cross section. A test statistic is used in conjunction with the CL s criterion [68] to set upper limits. The test statistic is defined as q µ = −2 ln(L µ /L max ), where L max refers to the maximum value of the likelihood when all parameters are varied and L µ refers to the likelihood obtained by varying µ while profiling all the other parameters conditioned on its value. Upper limits are computed using the asymptotic approximation [69]. Expected limits are computed by evaluating the test statistic using the post-fit predicted numbers of background events and their uncertainties.
Upper limits on the radion production cross sections times their branching fraction to ZZ versus the radion mass are shown in Fig. 8. Limits are computed assuming radions are produced entirely either through the ggF process or the VBF process. The expected (observed) radion mass exclusion limits are 2.5 (3.0) TeV for ggF-produced states. These are the first mass exclusion limits set by CMS on ggF-produced radions in this final state. Figure 9 shows the expected and observed upper limits on the W boson production cross sections times their branching fraction to WZ, assuming exclusive production through the DY (model B) or VBF process (model C). The expected and observed mass exclusion limits for DY-produced W resonances are found to be 3.7 and 4.0 TeV, respectively. This is an improvement of 0.6 (0.4) TeV in the observed (expected) mass exclusion limit from the previous CMS result. Finally, the upper limits on the graviton production cross sections times their branching fraction to ZZ are shown   in Fig. 10. Limits are set assuming gravitons are produced entirely either through the ggF process or the VBF process. The expected (observed) graviton mass exclusion limit is found to be 1.1 (1.2) TeV, assuming gravitons are produced exclusively through the ggF mechanism. These are the first mass exclusion limits set by CMS on ggF-produced gravitons in this final state. For the VBF-produced models considered here, no masses are excluded. The observed upper limits on σB(X → VZ) vary between 0.2 and 9 fb for radions, 0.5 and 20 fb for W resonances, and 0.3 and 10 fb for gravitons.
The methods used here complement the recent ATLAS search [14] in the same channel by using different jet substructure variables and different VBF tagging requirements. The 95% CL upper limits on these resonance production cross sections times X → Z + W/Z branching fraction from the recent ATLAS results are comparable to those set in this paper.

Summary
A search has been presented for new bosonic states decaying either to a pair of Z bosons or to a W boson and a Z boson. The analyzed final states require large missing transverse momentum and one high-momentum, large-radius jet. Large-radius jets are required to have a mass consistent with either a W or Z boson. Events are categorized based on the presence of large-radius jets passing high-purity and low-purity substructure requirements. Events are also categorized based on the presence or absence of high-momentum jets in the forward region of the detector. Forward jets distinguish weak vector boson fusion (VBF) from other production mechanisms. Contributions from the dominant SM backgrounds are estimated from data control regions using an extrapolation method. No deviation between SM expectation and data is found, and 95% confidence level upper limits are set on the production cross section times branching frac-tion for several signal models. A lower observed (expected) limit of 3.0 (2.5) TeV is set on the mass of gluon-gluon fusion produced radions. The observed (expected) mass exclusion limit for Drell-Yan produced W bosons is found to be 4.0 (3.7) TeV. The observed (expected) mass exclusion limit for gluon-gluon fusion produced gravitons is found to be 1.2 (1.1) TeV. At 95% confidence level, upper observed (expected) limits on the VBF production cross section times X → Z + W/Z branching fraction range between 0.2 and 20 (0.3 and 30) fb. The 95% CL upper limits on these resonance production cross sections times X → Z + W/Z branching fraction from the recent ATLAS results are comparable to those set in this paper.

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 centers and personnel of the Worldwide LHC Computing Grid and other centers 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, the CMS detector, and the supporting computing infrastructure provided by the follow-