Searches for heavy diboson resonances in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Searches for new heavy resonances decaying to $WW$, $WZ$, and $ZZ$ bosons are presented, using a data sample corresponding to 3.2 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13$ TeV collected with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting $\nu\nu qq$, $\ell\nu qq$, $\ell\ell qq$ and $qqqq$ final states are combined, searching for a narrow-width resonance with mass between 500 and 3000 GeV. The discriminating variable is either an invariant mass or a transverse mass. No significant deviations from the Standard Model predictions are observed. Three benchmark models are tested: a model predicting the existence of a new heavy scalar singlet, a simplified model predicting a heavy vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2 graviton. Cross-section limits are set at the 95% confidence level and are compared to theoretical cross-section predictions for a variety of models. The data exclude a scalar singlet with mass below 2650 GeV, a heavy vector-boson triplet with mass below 2600 GeV, and a graviton with mass below 1100 GeV. These results significantly extend the previous limits set using $pp$ collisions at $\sqrt{s}=8$ TeV.


Introduction
Diboson resonances are predicted in several extensions to the Standard Model (SM), such as composite Higgs models [1,2], technicolour [3][4][5], warped extra dimensions [6][7][8], Two-Higgs-doublet models (2HDM) [9], and Grand Unified Theories [10][11][12][13]. The search for high-mass resonances decaying into vector bosons benefits greatly from the increase in centre-of-mass energy of proton-proton collisions at the Large Hadron Collider (LHC) from √ s = 8 TeV (Run 1) to 13 TeV (Run 2). This would result in more abundant production of new particles with masses significantly in excess of a TeV, in processes initiated by gg, gq or qq. 1 This paper reports a search for a charged or neutral resonant state, with a mass between 500 GeV and 3 TeV, decaying to WW, ZZ or WZ bosons, with subsequent decays of the W and Z bosons to quarks or leptons. Four different decay modes are considered: the fully hadronic mode (qqqq), and the semileptonic modes ( qq, νqq and ννqq). Decays of the W or Z bosons to quarks are reconstructed as single jets with a large radius parameter. These jets are required to have features characteristic of a two-body decay, and are identified as W or Z bosons using the jet mass and jet substructure [14,15].
Three specific signal models are used to assess the sensitivity of the search, to optimise the event selection, and to search for local excesses in the observed data. The first is an extension of the SM with an additional heavy, CP-even, scalar singlet decaying to longitudinally polarised bosons [16]. The second is the Heavy Vector Triplet (HVT) parameterisation [17], predicting W → WZ and Z → WW processes. The third model, known as a bulk Randall-Sundrum (RS) graviton model, features a spin-2 graviton (G * ) decaying to WW or ZZ. The G * is the first Kaluza-Klein mode in a RS model [6,18] with a warped extra dimension with curvature κ, where the SM fields are allowed to propagate in the bulk of the extra dimension [19][20][21].
Both ATLAS and CMS have searched for heavy diboson resonances in various final states in the √ s = 7 TeV and 8 TeV datasets [22][23][24][25][26][27][28][29][30][31]. As an example, CMS set a lower limit of 1.7 TeV at the 95% confidence level (CL) on the mass of a W boson predicted by an Extended Gauge Model (EGM) [32] using the fully hadronic channel [26]. The qqqq, qq, νqq channels were combined by ATLAS using the bulk RS G * model and the EGM W boson as benchmarks [31]. Observed lower limits at 95% CL of 1.81 TeV on the EGM W mass and of 810 GeV on the bulk G * mass were obtained, assuming κ/M Pl = 1 (whereM Pl is the reduced Planck mass) for the bulk G * signal hypothesis. The largest deviation from the predicted background in that analysis was a 2.5σ local excess close to a mass of 2 TeV.

ATLAS detector and data sample
The ATLAS detector [33] is a general-purpose particle detector used to investigate a broad range of physics processes. It includes inner tracking devices surrounded by a superconducting solenoid, electromagnetic (EM) and hadronic calorimeters, and a muon spectrometer inside a system of toroid magnets. The inner detector (ID) consists of a silicon pixel detector including the newly installed Insertable B-Layer [34], a silicon microstrip detector and a straw tube tracker. It is situated inside a 2 T axial magnetic field from the solenoid and provides precision tracking of charged particles with pseudorapidity 2 |η| < 2.5. The straw tube tracker also provides transition radiation measurements for electron identification. The calorimeter system covers the pseudorapidity range |η| < 4.9. It is composed of sampling calorimeters with either liquid argon or scintillator tiles as the active medium. The muon spectrometer (MS) provides muon identification and measurement for |η| < 2.7 and detectors for triggering in the region |η| < 2.4. The ATLAS detector has a two-level trigger system to select events for offline analysis [35].
The data used in this analysis were recorded with the ATLAS detector during the 2015 run and correspond to an integrated luminosity of 3.2±0.2 fb −1 of proton-proton collisions at √ s = 13 TeV. The measurement of the integrated luminosity is derived, following a methodology similar to that detailed in Ref. [36], from a preliminary calibration of the luminosity scale using x-y beam-separation scans performed in August 2015. The data are required to satisfy a number of conditions ensuring that the detector was operating well while the data were recorded.

Signal and background simulation
The Monte Carlo (MC) simulation of three benchmark signal models is used to optimise the sensitivity of the search and to interpret the results.
The first model extends the SM by adding a new, heavy, neutral Higgs boson, using the narrow-width approximation (NWA) benchmark [37,38]. Results are then interpreted within a model of a CP-even scalar singlet S [16]. The model is parameterised by: an energy scale Λ = 1 TeV; a coefficient c H scaling the coupling of S to the Higgs boson; and a coefficient c 3 scaling the coupling of S to gluons. Two benchmark scenarios are considered, one in which c 3 is set via naive dimensional analysis (NDA) to be 2 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Rapidity is also defined relative to the beam axis as y = 0.5 ln[(E + p z )/(E − p z )]. Angular distance is measured in units of ∆R ≡ (∆η) 2 + (∆φ) 2 . 2 , with c H = 0.9; and another in which the coupling to gluons is Unsuppressed and c 3 = 1/8π, with c H = 0.5. The value of c 3 determines the production cross-section and the decay width to gluons, while decays to W or Z bosons account for the remaining decay width. In the Unsuppressed scenario considered in this paper, the total branching ratio to WW, ZZ or HH increases from 59% at 500 GeV, to 70% at 2 TeV and to 73% at 5 TeV. For the NDA scenario, this branching ratio is always above 99%. The ratio of WW:ZZ:HH partial widths is approximately 2:1:1 in both scenarios, and couplings to fermions and transversely polarised bosons are set to zero.
The second model is based on the HVT phenomenological Lagrangian which introduces a new triplet of heavy vector bosons that contains three states with identical masses: the two electrically charged W bosons and the electrically neutral Z boson. The Lagrangian parameterises the couplings of the new HVT with the SM fields in a generic manner. This parameterisation allows a large class of models to be described, in which the new triplet field mixes with the SM vector bosons. The coupling between the new triplet and the SM fermions is given by the combination of parameters g 2 c F /g V , where g is the SM S U(2) L gauge coupling, c F is a multiplicative factor that modifies the coupling to fermions, and  Table 1 shows the resonance width and the product of cross-sections and branching ratios for the various models.  m of the resonances for a representative benchmark for the spin-0,  spin-1 and spin-2 cases. The table shows the predictions by the CP-even scalar model (Λ = 1 TeV, c H = 0.9, c 3 = 1/16π 2 ), by model-B of the HVT parameterisation (g V = 3), and by the graviton model (κ/M Pl = 1). In the case of the scalar and HVT models, the alternate benchmarks (Unsuppressed scenario, model-A) correspond to a different cross-section but similar resonance width and ratios between the branching ratios into WW/WZ/ZZ. . For all top-quark processes, top-quark spin correlations are preserved; for t-channel production, top-quarks are decayed using MadSpin [61]. The parton shower, fragmentation, and the underlying event are simulated using Pythia 6.428 [62] with the CTEQ6L1 [63] PDF sets and the set of tuned parameters known as the "Perugia 2012 tune" [64]. The top-quark mass is assumed to be 172.5 GeV. The EvtGen v1.2.0 program [65] is used for the bottom-and charm-hadron decays.
The cross-sections calculated at next-to-next-to-leading order (NNLO) accuracy for W/Z+jets [66] and at NNLO+NNLL (next-to-next-to-leading-logarithm) accuracy for tt production [67] are used to normalise the samples for the optimisation studies, but the final normalisations of these dominant backgrounds are determined by fitting kinematic distributions to the data. For single-top-quark production, cross-sections are taken from Ref. [68].
Diboson processes with one boson decaying hadronically and the other decaying leptonically are simulated using the Sherpa 2.1.1 generator. They are calculated for up to one (ZZ) or no (WW, WZ) additional partons at NLO, and up to three additional partons at LO using the Comix and OpenLoops ME generators. They are merged with the Sherpa PS using the ME+PS@NLO prescription. The CT10 PDF set is used in conjunction with a dedicated parton-shower tuning developed by the Sherpa authors. Cross-section values from the generator, which are at NLO accuracy, are used.
The dominant background in the fully hadronic final state is from multi-jet events. While the background in this search is estimated directly from data, samples of simulated dijet events are produced, using Pythia 8.186 with the NNPDF23LO PDFs and the parton-shower parameter set known as the "A14 tune" [69], to characterise the invariant mass distribution of the dijet final state and optimise the sensitivity of the search. The EvtGen v1.2.0 program is used for the bottom-and charm-hadron decays.
All simulated MC samples include the effect of multiple proton-proton interactions in the same and neighbouring bunch crossings (pile-up) by overlaying simulated minimum-bias events, generated with Pythia 8.186, on each generated signal or background event. The generated samples are processed through the Geant4-based ATLAS detector simulation [70,71]. Simulated events are reconstructed with the standard ATLAS reconstruction software used for collision data. Table 2 summarises the background MC samples used.

Object reconstruction and selection
Electrons are reconstructed from clusters of energy deposits in the EM calorimeter that match a track reconstructed in the ID. The electrons used are required to have transverse momentum p T > 7 GeV and |η| < 2.47. They are identified using a likelihood identification criterion described in Ref.
[72]. The levels of identification are categorised as "loose", "medium" and "tight", which correspond to approximately 96%, 94% and 88% identification efficiency for an electron with transverse energy (E T ) of 100 GeV, where E T is defined in terms of the energy E and of the polar angle θ as E T = E sin θ.
Muons are reconstructed by combining ID and MS tracks. They are classified as "medium" if they satisfy identification requirements based on the number of hits in the different ID and MS subsystems and on the compatibility of track curvature measurements in the two subsystems [73]. An additional sample of "loose" muons is constructed including all medium muons, muons identified by combining an ID track with at least one track segment reconstructed in the MS, and muons reconstructed in the |η| < 0.1 region, where the MS is lacking coverage, by associating an ID track to an energy deposit in the calorimeters compatible with a minimum-ionising particle. Muons are required to have p T > 7 GeV and |η| < 2.7. The loose and medium muons have average efficiencies of about 98% and 96% for |η| < 2.5, respectively.
In order to ensure that leptons originate from the interaction point, requirements of |d BL 0 |/σ d  3 and θ is the polar angle of the track. Lepton isolation criteria are defined based on low values for the scalar sum of transverse momenta of tracks with p T > 1 GeV within a ∆R cone around the lepton, whose size depends upon its p T , and excluding the track associated with the lepton (track isolation). These criteria are optimised for a uniform efficiency of 99% in the (p T , η) plane for leptons from Z → decays in Z + jets events. Calorimeter isolation is also used for the νqq channel, using an isolation variable constructed from calorimeter activity within a cone of radius ∆R = 0.2 around the lepton candidate. The isolation criteria depend on both p T and η, and accept 95% of Z → events while maximising the rejection of leptons originating in jets.
Jets are reconstructed from three-dimensional topological clusters of energy deposits in the calorimeter calibrated at the EM scale [74], using the anti-k t algorithm [75] with two different radius parameters of R = 1.0 and R = 0.4, hereafter referred to as large-R jets (denoted by "J") and small-R jets (denoted by " j"), respectively. The four-momenta of the jets are calculated as the sum of the four-momenta of the clusters, which are assumed to be massless.
The p T of small-R jets are corrected for losses in passive material, the non-compensating response of the calorimeter, and contributions from pile-up [76]. They are required to have p T > 20 GeV and |η| < 2.4. For small-R jets with p T < 50 GeV, a jet vertex tagger (JVT) [77] discriminant, based on tracking and vertexing information, is required to be larger than 0.64, where the JVT is a multivariate tagger used to identify and remove jets with a large contribution from pile-up. In addition, small-R jets are discarded if they are within a cone of size ∆R < 0.2 around an electron candidate, or if they have less than three associated tracks and are within a cone of size ∆R < 0.2 around a muon candidate. However, if a small-R jet with three or more associated tracks is within a cone of size ∆R < 0.4 around a muon candidate, or any small-R jet is within a region 0.2 < ∆R < 0.4 around an electron candidate, the corresponding electron or muon candidate is discarded. Small-R track-jets are defined by applying the same jet reconstruction algorithms to inner-detector tracks treated as having the pion mass, and used to avoid overlap between qqqq sideband regions and searches for Higgs boson pair production, as discussed in Section 6.
For the large-R jets, the original constituents are calibrated using the local cluster weighting algorithm [78] and reclustered using the k ⊥ algorithm [79] with a radius parameter of R sub-jet = 0.2, to form a collection of sub-jets. A sub-jet is discarded if it carries less than 5% of the p T of the original jet. The constituents in the remaining sub-jets are then used to recalculate the large-R jet four-momentum, and the jet energy and mass are further calibrated to particle level using correction factors derived from simulation [80]. The resulting "trimmed"[81] large-R jets are required to have p T > 200 GeV and |η| < 2.0. Large-R jets are required to have an angular separation of ∆R > 1.0 from electron candidates.
The large-R jets are used to reconstruct the hadronically decaying W/Z ("V") boson. A boson tagger [14, 15, 82, 83] is subsequently used to distinguish the boosted hadronically decaying V boson from jets originating from quarks (other than the top-quark) or gluons. The tagger is based on the mass of the jet m J and a variable D (β=1) 2 , defined in Ref. [82], that is sensitive to the compatibility of the large-R jet with a two-prong decay topology. The large-R jet is identified by the boson tagger as a W (Z) candidate with its mass within 15 GeV of the expected W (Z) mass peak, which is estimated from simulated events to be 83.2 GeV (93.4 GeV). Large-R jets with mass within 15 GeV from both the W and Z peaks are assigned both hypotheses. For context, the resolution ranges from 8 GeV to 15 GeV in the jet p T range used in the analysis. Additionally, a p T -dependent selection on the D (β=1) 2 variable is configured so that 3 If more than one vertex is reconstructed, the one with the highest sum of p 2 T of the associated tracks is regarded as the primary vertex. the average identification efficiency for longitudinally polarised, hadronically decaying W or Z bosons is 50%. This selection rejects more than 90% of the background. Large-R track-jets are defined by applying the same jet reconstruction and filtering algorithms to inner-detector tracks treated as having the pion mass. These jets are ghost-associated to large-R jets and used for the evaluation of systematic uncertainties, as discussed in Section 7.
Small-R jets and small-R track-jets containing b-hadrons are identified using the MV2 b-tagging algorithm [84], which has an efficiency of 85% in simulated tt events. The jets thus selected are referred to as b-jets in the following. The corresponding misidentification rate for selecting b-jet candidates originating from a light quark or gluon is less than 1%. The misidentification rate for selecting c-jets as b-jet candidates is approximately 17%.
The missing transverse momentum, E miss T , with magnitude E miss T , is calculated as the negative vectorial sum of the transverse momenta of calibrated objects, such as electrons, muons, and small-R jets. Chargedparticle tracks compatible with the primary vertex and not matched to any of those objects are also included in the E miss T reconstruction [85,86] . For multi-jet background rejection, a similar quantity, p miss T , is computed using only charged-particle tracks originating from the reconstructed primary vertex to substitute for the calorimeter-based measurements of jet four-momenta. Its magnitude is denoted by p miss T . Both tiers of the ATLAS trigger system also reconstruct E miss T . The triggers used in this paper reconstruct E miss T based on calorimeter information, and do not include corrections for muons.
The identification efficiency, energy scale, and resolution of jets, leptons and b-jets are measured in data and correction factors are derived, which are applied to the simulation to improve the modelling of the data.

Event selection
This analysis focuses on identifying diboson events in which at least one vector boson V decays hadronically, and is performed in four different channels identified by the decay of the other vector boson: qqqq, ννqq, νqq and qq. Event selection criteria are chosen to guarantee the statistical independence of the channels. The criteria are summarised in Table 3, and described in more detail below. Events are selected at trigger level by requiring at least one large-R jet with p T > 360 GeV in the qqqq channel, large E miss T in the ννqq channel, large E miss T or at least one electron in the νqq channel, and at least one electron or muon in the qq channel. All trigger requirements guarantee full efficiency in the kinematic region considered in the analysis. A primary vertex is required to be reconstructed from at least three charged-particle tracks with p T > 400 MeV.
At least one large-R jet is required, with p T > 200 GeV, |η| < 2.0 and m J > 50 GeV. Events are then divided by different pre-selection criteria into different channels according to the number of "baseline" and "good" leptons that are reconstructed. A baseline lepton is a loose muon or electron candidate with p T > 7 GeV and |η| < 2.7 or |η| < 2.47, respectively, which passes a relaxed set of track-isolation and impact parameter requirements. A good lepton has p T > 25 GeV and is either a muon with |η| < 2.5, or an electron with |η| < 2.47 excluding the transition region between barrel and endcap calorimeters (1.37 < |η| < 1.52), which passes identification and isolation requirements as discussed in Sec. 4.
Events with no reconstructed baseline lepton and with E miss T > 250 GeV are assigned to the ννqq channel. Events are assigned to the qqqq channel if they have no good leptons, E miss T < 250 GeV, an additional large-R jet meeting the same selection criteria as the other large-R jet, and if the large-R jet with leading p T satisfies a requirement of p T > 450 GeV to ensure full trigger efficiency. Events with exactly one good lepton which satisfies tight track and calorimeter isolation requirements, and which is either a medium muon or tight electron, or a medium electron with p T > 300 GeV, are assigned to the νqq channel. Events with exactly two same-flavour good leptons where one meets medium selection criteria, the invariant mass of the dilepton system passes a Z boson mass window selection of 83 < m ee / GeV < 99 or 66 < m µµ / GeV < 116, and, in the case of muons, the two leptons are oppositely charged, are assigned to the qq channel.
Additional event topology requirements are applied to pre-selected events in order to suppress backgrounds. In the ννqq channel, contributions from non-collision backgrounds and multi-jet production are suppressed by requiring p miss T > 30 GeV, |∆φ(E miss T , p miss T )| < π/2 and by requiring that the minimum azimuthal separation between E miss T and any small-R jet is greater than 0.6.
In the qqqq channel, the separation in rapidity between the two large-R jets, |y J 1 − y J 2 |, is required to be below 1.2, and their transverse momentum asymmetry, (p T,J 1 − p T,J 2 )/(p T,J 1 + p T,J 2 ), is required to be below 0.15. To further reduce the multi-jet background, large-R jets are required to have N trk < 30 charged-particle tracks with p T > 500 MeV, where the tracks must be consistent with the primary vertex and be matched to the calorimeter jet [87]. The matching is made prior to trimming, and is determined by representing each track by a collinear "ghost" constituent with negligible energy during jet reconstruction ("ghost association").
In the νqq channel, events are required to have no small-R jet identified as a b-jet outside a cone of radius ∆R = 1.0 around the selected large-R jet to reject backgrounds from tt production, and to have E miss T > 100 GeV in order to reject multi-jet background. The leptonically decaying W candidate is required to have p T, ν > 200 GeV, where the neutrino is assigned transverse momentum E miss T and its momentum along the z-axis, p z , is obtained by imposing a W boson mass constraint to the -E miss T system. 4 A new resonance with mass m νJ decaying into two bosons, both at fairly central rapidity, would often impart significant transverse momentum to the bosons relative to the resonance mass. The p T of the two vector-boson candidates is therefore required to have p T,J /m νJ > 0.4 and p T, ν /m νJ > 0.4. In the qq channel, similar requirements on the p T of the two vector-boson candidates are applied, namely p T,J /m J > 0.4 and p T, /m J > 0.4.
Events are classified as WW, WZ, or ZZ by applying the corresponding selection criteria to the two boson candidates. If the number of boson-tagged jets exceeds the number of hadronically decaying bosons required by the decay channel, the leading-p T jets are used. The final discrimination between resonant signal and backgrounds is done in a one-dimensional distribution either of mass or of transverse mass. In the qqqq channel, the invariant mass of the jet pair, m JJ , is used in the fiducial region 1 TeV < m JJ < 3.5 TeV whose lower bound is chosen to guarantee full trigger efficiency. In the ννqq channel, the transverse mass In the νqq channel, m νJ is used. In the qq channel, the p T of the dilepton system is scaled event-by-event by a single multiplicative factor to set the dilepton invariant mass m to the mass of the Z boson (m Z ) in order to improve the diboson mass resolution. The invariant mass m J is used as the discriminant. Table 3 shows a summary of the event selection criteria in the four channels. The combined acceptance times efficiency for a heavy resonance decaying to dibosons is as large as 18% for W → WZ and also for The electron, if over 300 GeV in p T , need only be medium.
Z → WW in the HVT model-A benchmark assuming g V = 1. In the bulk RS benchmark with κ/M Pl = 1, it reaches up to 17% for G * → WW, and 14% for G * → ZZ. The acceptance times efficiency is estimated with respect to the branching ratio of the signal benchmarks to the specific diboson final state and takes into account the W and Z boson branching ratios. Figure 1 summarises the acceptance times efficiency for the different channels as a function of the scalar, HVT, and G * masses, considering only decays of the resonance into VV. The mass ranges used in the different channels are reflected in the figure. After all selection criteria are applied, reconstructed diboson mass resolutions for a W with a mass of 2 TeV, decaying to WZ, are 3% for qq, 5.5% for νqq, and 6% for qqqq.

Background estimation
The background contamination in the signal regions is different for each of the channels studied. Different background estimation strategies are used for the fully hadronic and semileptonic channels.
In the qqqq channel, the dominant background originates from multi-jet events, with significantly smaller contributions due to SM W/Z + jet, diboson, tt and single-top-quark production. As all of these processes are expected to produce a smoothly falling m JJ spectrum, the overall background is modelled in terms of a probability density function where x = m JJ / √ s, p 2 and p 3 are dimensionless shape parameters, ξ is a constant whose value is chosen to minimise the correlation between p 2 and p 3 , and N is an overall normalisation factor. The functional form in Eq. (1) is validated using background simulation and validation regions in data, defined to be similar to the signal region but with a few differences. Instead of selecting events where the mass of the large-R jet is consistent with the mass of the W or Z boson, events are selected to have a large-R jet with a mass in the sideband regions, 110−140 GeV or 50−65 GeV, and without applying the requirement on the track multiplicity. Specifically, it is required that either both jets have a mass in the range 110 − 140 GeV and there are less than two b-tagged track-jets matched by ghost-association to either jet, or that one jet has a mass in the range 110 − 140 GeV and the other in the range 50 − 65 GeV. These regions are defined  Figure 1: Signal acceptance times efficiency as a function of the resonance mass, for the different channels contributing to the searches for (a) a scalar resonance decaying to WW and ZZ, (b) HVT decaying to WW and WZ and (c) bulk RS gravitons decaying to WW and ZZ. The branching ratio of the new resonance decaying to dibosons is included in the denominator of the efficiency calculation. The coloured bands represent the total statistical and systematic uncertainties. In the case of the qqqq channel, only signals with resonance masses beyond 1.2 TeV, for which the mass peak is fully reconstructed in the fiducial m JJ region, are considered. such that the kinematic properties of the selected events are similar to the signal region, and overlap with searches for Higgs boson pair production is avoided.
In the ννqq channel, the dominant background is Z + jets production with significant contributions from W + jets, tt, and SM diboson production. In the νqq channel, the dominant backgrounds are W + jets and tt production. In the qq channel, where two same-flavour leptons with an invariant mass close to the Z mass are selected, Z + jets production is by far the dominant background. All three channels also have contributions at the level of a few percent from single-top-quark and diboson production. The single-top-quark process contributes 15% of the total top-quark background in the νqq channel, 10% in the the ννqq, and a negligible amount for the qq channel. The multi-jet background enters the signal regions of the semileptonic channels through semileptonic hadron decays and through jets misidentified as leptons, and this background is found to be negligibly small in all three channels.
In the ννqq, νqq, and qq channels, the modelling of W/Z+jets backgrounds is constrained using dedicated control regions. A region enriched in W + jets events is used to control the W + jets background normalisation in the ννqq and νqq channels; events in this region are required to fall in the sidebands of the m J distribution and to have one reconstructed good muon. A region enriched in Z + jets events is used to control the Z + jets backgrounds in the ννqq and qq channels; events in this region are also required to fall in the sidebands of the m J distribution, but to have two reconstructed good leptons.
The tt background is estimated in the ννqq and νqq channels using a control region enriched in top-quark pairs. This control region is defined as the W + jets control region, without the m J sideband criterion and with the added requirement of at least one additional b-jet with a separation ∆R > 1 from the large-R jet. The tt background for the qq channel is estimated from MC simulation.
The W, Z and tt control regions are included in the combined profile likelihood fit described in Section 8 to help constrain the W+jets, Z+jets and tt normalisation in the signal regions.
The diboson contributions to the ννqq, νqq and qq channels are estimated using MC simulation. Single-top-quark production is constrained by the tt control region using the same normalisation factor as for tt.

Systematic uncertainties
The most important sources of systematic uncertainty are those related to the energy scale and resolution of the large-R jet p T , mass, and D scale are 5%, 6% and 10%, respectively.
The resolution of each of these large-R jet observables is determined as the standard deviation of a Gaussian fit to the distribution of the observable response defined as the ratio of the calorimeter-jet observable to a simulated-particle-level jet observable. The relative uncertainties in these resolutions are estimated based on previous studies with √ s = 7 TeV data and √ s = 13 TeV simulation. For the large-R jet p T [80] and mass resolution a 20% uncertainty is assigned, while for the D (β=1) 2 resolution a 10% uncertainty is assigned. The large-R jet mass resolution uncertainty is estimated from variations in data and simulation in the widths of the W-jet mass peaks in tt events [80]. The D (β=1) 2 resolution uncertainty is estimated by comparing 13 TeV simulation samples from different generators and shower simulations [14].
Other subdominant experimental systematic uncertainties include those in the lepton energy and momentum scales, in lepton identification efficiency, in the efficiency of the trigger requirements, and in the small-R jet energy scale and resolution. All experimental systematic uncertainties are treated as fully correlated among all channels.
Uncertainties are also taken into account for possible differences between data and the simulation model that is used for each process.
In the ννqq channel, an uncertainty on the shape of the m T spectrum for the W + jets and Z + jets backgrounds is extracted by comparing the nominal shape obtained with Sherpa to the one obtained with an alternative sample generated with MadGraph5_aMC@NLO.
In the νqq channel, an uncertainty on the shape of the m νJ distribution of the dominant W + jets background is obtained by comparing the m νJ shape in simulation and in data in the W + jets control region after the expected tt and diboson contributions are subtracted. The ratio of the data distribution to that predicted by MC is fitted with a first-order polynomial and its deviation from unity is used as a modelling uncertainty.
In the qq channel, an uncertainty on the shape of the m J spectrum for the Z + jets background is assessed by comparing the shape difference between the Sherpa predictions and the data-driven estimate using events in the Z control region.
The data and simulation agree very well for events in the top-quark control region. The uncertainty in the shape of the mass distributions for the ννqq, νqq and qq channels from the tt background is estimated by comparing a sample generated using aMC@NLO [52] interfaced with Pythia 8.186 to the nominal tt sample. Additional systematic uncertainties in parton showering and hadronisation are evaluated by comparing the nominal sample showered with Pythia to one showered with Herwig [88]. Samples of tt events generated with the factorisation and renormalisation scales doubled or halved are compared to the nominal sample, and the largest difference observed in the mass discriminants is taken as an additional uncertainty arising from the QCD scale uncertainty.
Theoretical uncertainties in the SM diboson production cross-section, including the effect of PDF and scale uncertainties, are taken into account and amount to about 10% [89]. An uncertainty in the shape of the predicted diboson m J spectrum in the qq channel is derived by comparing MC samples generated by Sherpa and POWHEG BOX. Shape uncertainties are found to have negligible impact in the ννqq and νqq channels.
The uncertainties in the modelling of the Z + jets and W + jets backgrounds are treated as uncorrelated since they are evaluated differently in each channel. For the tt background, the modelling uncertainty is treated as correlated between the νqq and qq channels, and uncorrelated with the modelling uncertainty in the ννqq channel. The diboson normalisation uncertainty is taken as correlated among the ννqq, νqq and qq channels.
Uncertainties in the signal acceptance arise from the choice of PDF and from the amount of initialand final-state radiation present in simulated signal events. The PDF-induced uncertainties in the signal acceptance for semileptonic decay channels are derived using the PDF4LHC recommendations [90]; in all channels the resulting uncertainty is at most 4%. PDF-induced uncertainties are not evaluated for the qqqq channel, where they are subdominant to other acceptance effects. The uncertainty in the integrated luminosity has an impact of 5% on the signal normalisation. All signal acceptance uncertainties are treated as fully correlated across all search channels.
The uncertainty in modelling background distribution shapes in the qqqq channel is found to be negligible compared to statistical uncertainties in the background fit parameters. An additional uncertainty in the signal normalisation is introduced in the qqqq channel to take into account potentially different efficiencies of the N trk < 30 requirement in data and simulation. This uncertainty is estimated in a data control sample enriched in W/Z+jets events, where the W/Z bosons decay to quarks. This control sample is obtained by applying the D (β=1) 2 selection only to the highest-p T large-R jet in dijet events. The m J distribution is fitted in subsamples with different track multiplicity selections to obtain the rates of W/Z decays in each sample. From these the uncertainty from the track multiplicity cut is estimated to be 6%.
For all the considered signal hypotheses, the impact of each source of uncertainty on the search is evaluated in terms of the corresponding contribution to the total uncertainty in the fitted number of signal events, as obtained after the statistical procedure described in the next section. The dominant contribution is due to large-R jet scale uncertainties and amounts to about 35% of the total uncertainty. Additional contributions are due to uncertainties in the modelling and normalisation of backgrounds in the ννqq, νqq and qq channels (about 20%), and small-R jet energy scale uncertainties (about 10%). Sub-leading contributions have an overall impact of less than about 15%.

Statistical analysis
In the combined analysis to search for a scalar resonance decaying to WW or ZZ, HVT decaying to WW or WZ, and bulk G * decaying to WW or ZZ, all four individual channels are used. Table 4 summarises the signal region and mass range in which the individual channels contribute to the search.
The statistical interpretation of these results uses the data modelling and handling toolkits RooFit [91], RooStats [92] and HistFactory [93]. It proceeds by defining the likelihood function L(µ, θ) for a particular model, with an implicit signal description, in terms of the signal strength µ, and the additional set of nuisance parameters θ which can be related to both background and signal. The likelihood function is computed considering in each channel bins of the discriminating variable; the binning is chosen based on the expected mass resolution and statistical uncertainty, as estimated from simulation. The nuisance parameters are either free to float, as in the case of the p 2 and p 3 parameters used in the qqqq channel to estimate the background, or constrained from external studies represented by Gaussian terms. The likelihood for the combination of the four search channels is the product of the Poisson likelihoods for the individual channels, except in the case of common nuisance parameters, The terms n obs c i represent the number of events observed, and the terms n sig c i , n bkg c i , the number of events expected from signal or background in bin i of the discriminant from channel c. The term f k (θ k |θ k ) represents the set of constraints on θ from auxiliary measurements θ k : these constraints include normalisation and shape uncertainties in the signal and background models, and, except for the qqqq channel, include the statistical uncertainties of the simulated bin content. The W + jets normalisation is a free parameter in the combined likelihood fit in all the channels. The normalisation of the Z + jets background in the qq and ννqq channels is a free parameter in the combined likelihood fit. In the νqq channel, where the contribution from Z + jets is small, the normalisation obtained from MC simulation is used instead, with an 11% systematic uncertainty assigned. The tt normalisation in the νqq and ννqq channels is a free parameter in the combined likelihood fit. In the qq channel, where the tt background contribution is small, its normalisation is based on the theoretical cross-section with a 10% systematic uncertainty assigned.
The likelihood function L(µ, θ) is used to construct the profile-likelihood-ratio test statistic [94], defined as: whereμ andˆ θ are the values of the parameters that maximise the likelihood function L(µ, θ) globally, and θ(µ) are the values of θ which maximise the likelihood function given a certain value of µ. The parameter µ is required to be non-negative. This test statistic is used to derive the statistical results of the analysis.
For calculating p-values, which test the compatibility of the data with the background-only model, the numerator of Eq. (3) is evaluated for the background-only hypothesis, i.e. signal strength µ = 0. In extracting upper limits, the calculation is modified such that ifμ > µ, λ(µ) is taken to be 1; this ensures that a signal larger than expected is not taken as evidence against a model. The asymptotic distributions of the above test statistic are known and described in Ref. [95], and this methodology is used to obtain the results in this paper.
Upper limits on the production cross-section times branching ratio to diboson final states for the benchmark signals are set using the modified-frequentist CL s prescription [96], where the probability of observing λ to be larger than a particular value, is calculated using a one-sided profile likelihood. The calculations are done using the lowest-order asymptotic approximation, which was validated to better than 10% accuracy using pseudo-experiments. All limits are set at the 95% confidence level (CL). Table 5: Expected and observed yields in signal and control regions for the W → WZ signal hypothesis. Yields and uncertainties are evaluated after a background-only fit to the data. The background for the qqqq channel is evaluated in situ and only the total background yield is indicated. The W+jets background for the Z+jets control region and the qq signal region is negligible. The uncertainty in the total background estimate can be smaller than the sum in quadrature of the individual background contributions due to anti-correlations between the estimates of different background sources.

Results
The background estimation techniques described in Section 6 are applied to the selected data, and the results in the four different analysis channels are shown in Figure 2 for the channels relevant to the HVT (WZ, WW) search and in Figure 3 for those relevant to the scalar resonance and bulk RS G * → WW, ZZ searches, respectively. Both figures represent background-only fits to the data. The total yields in the different signal and control regions for the HVT WZ channel are also shown in Table 5. Good agreement is found between the data and the background-only hypothesis. The most significant excess over the expected background is observed in the scalar selection for a mass of 1.6 TeV, with a p-value equivalent to a local significance of 2.5 standard deviations. Upper limits at the 95% CL are set on the production cross-section times the branching ratio of new resonances decaying to diboson final states. Figure 4 shows the observed and expected 95% CL model-independent limits on the production crosssection times branching ratio of a narrow-width scalar resonance, as a function of its mass, in the WW and ZZ channels combined. The constraints are compared with the CP-even scalar singlet model described in Section 3, for the NDA and Unsuppressed scenarios. Masses below 2650 GeV are excluded for the Unsuppressed scenario. Figure 5 shows the exclusion contours in the (c H /Λ, c 3 /Λ) parameter space, derived from the cross-section limits for three sample masses. Figure 6 shows the observed and expected limits obtained in the search for an HVT decaying to WW or WZ states as a function of the mass of the HVT, compared to the theoretical predictions for the HVT model A assuming g V = 1 and the HVT model-B assuming g V = 3. For HVT model-B, new gauge bosons with masses below 2600 GeV are excluded at the 95% CL. Results are also shown in Figure 7 in terms of exclusion contours in the HVT parameter space (g 2 c F /g V , g V c H ) for different resonance masses [97].
Similarly, in Figure 8 the observed and expected limits obtained in the search for a bulk G * decaying to WW or ZZ final states are shown and compared to the theoretical prediction for the bulk RS G * model assuming κ/M Pl = 1. Bulk RS G * decaying to WW or ZZ in this model are excluded if their mass is below 1100 GeV. including corrections for the difference in beam energy and the line-shape of the resonance. This study shows that the current analysis is more sensitive to the HVT model A for triplet masses above 1.6 TeV, and that the ratio of the expected cross-section limit to the theoretical cross-section improves by a factor two for triplet masses of 2 TeV. TeV. The region inside each green ellipse indicates, for the corresponding assumed mass, the part of the parameter space in which the ratio of the resonance's total width Γ to its mass m is below 5%, which is comparable to the experimental mass resolution. Points inside the ellipse, but where the absolute values of the c H /Λ and c 3 /Λ parameters are larger than at the exclusion contour, are considered to be excluded at a CL greater than 95%. The solid lines correspond to results for a resonance mass of 3 TeV; the long-dashed lines correspond to a resonance mass of 2 TeV; the short-dashed lines correspond to a resonance mass of 1 TeV. Parameters for the Unsuppressed and NDA benchmark models are also shown.   Figure 7: Observed 95% CL exclusion contours in the HVT parameter space (g 2 c F /g V , g V c H ) for resonances of mass 1 TeV, 2 TeV and 3 TeV. Parameters for the benchmark models-A and -B are also shown. The grey area indicates the part of the parameter space in which the ratio of the resonance's total width Γ to its mass m is higher than 5%, which is comparable to the experimental mass resolution.

Conclusion
A search is performed for resonant WW, WZ or ZZ production in final states with at least one hadronically decaying vector boson, using 3.2 fb −1 of proton-proton collisions at √ s = 13 TeV recorded in 2015 by the ATLAS detector at the LHC. No significant excesses are found in data compared to the SM predictions. Limits on the production cross-section times branching ratio into vector-boson pairs are obtained as a function of the resonance mass for resonances arising from a model predicting the existence of a new heavy scalar singlet, from a simplified model predicting a heavy vector-boson triplet, or from a bulk Randall-Sundrum model with a heavy spin-2 graviton. A scalar resonance with mass below 2650 GeV predicted by the Unsuppressed model, a heavy vector-boson triplet predicted by model-B with g v = 3 of the HVT parameterisation with mass below 2600 GeV, and a graviton in the bulk Randall-Sundrum model (κ/M Pl = 1) with mass below 1100 GeV are excluded at the 95% confidence level. Limits are also expressed in terms of the parameters characterising the simplified models considered. [72] ATLAS Collaboration, Electron efficiency measurements with the ATLAS detector using the 2012 LHC proton-proton collision data, (2014), url: http://cds.cern.ch/record/1706245. [74] ATLAS Collaboration, Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1,   [85] ATLAS Collaboration, Performance of missing transverse momentum reconstruction for the ATLAS detector in the first proton-proton collisions at √ s = 13 TeV, (2015