Combination of searches for WW , WZ , and ZZ resonances in pp collisions at √ s = 8 TeV with the ATLAS detector The ATLAS Collaboration

The ATLAS experiment at the CERN Large Hadron Collider has performed searches for new, heavy bosons decaying to WW, WZ and ZZ final states in multiple decay channels using 20.3 fb−1 of pp collision data at √ s = 8 TeV. In the current study, the results of these searches are combined to provide a more stringent test of models predicting heavy resonances with couplings to vector bosons. Direct searches for a charged diboson resonance decaying to WZ in the ν ′ ′ ( = μ, e) , qq̄, νqq̄ and fully hadronic final states are combined and upper limits on the rate of production times branching ratio to the WZ bosons are compared with predictions of an extended gauge model with a heavy W ′ boson. In addition, direct searches for a neutral diboson resonance decaying to WW and ZZ in the qq̄, νqq̄, and fully hadronic final states are combined and upper limits on the rate of production times branching ratio to the WW and ZZ bosons are compared with predictions for a heavy, spin-2 graviton in an extended Randall–Sundrum model where the Standard Model fields are allowed to propagate in the bulk of the extra dimension. c © 2016 CERN for the benefit of the ATLAS Collaboration. Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.


Introduction
The naturalness argument associated with the small mass of the recently discovered Higgs boson [1][2][3][4] suggests that the Standard Model (SM) is conceivably to be extended by a theory that includes additional particles and interactions at the TeV scale. Many such extensions of the SM, such as extended gauge models [5][6][7], models of warped extra dimensions [8][9][10], technicolour [11][12][13][14], and more generic composite Higgs models [15,16], predict the existence of massive resonances decaying to pairs of W and Z bosons.
In the extended gauge model (EGM) [5] a new, charged vector boson (W ′ ) couples to the SM particles. The coupling between the W ′ and the SM fermions is the same as the coupling between the W boson and the SM fermions. The W ′ WZ coupling has the same structure as the WWZ coupling in the SM, but is scaled by a factor c × (m W /m W ′ ) 2 , where c is a scaling constant, m W is the W boson mass, and m W ′ is the W ′ boson mass. The scaling of the coupling allows the width of the W ′ boson to increase approximately linearly with m W ′ at m W ′ ≫ m W and to remain narrow for c ∼ 1. For c = 1 and m W ′ > 0.5 TeV the W ′ width is approximately 3.6% of its mass and the branching ratio of the W ′ → WZ ranges from 1.6% to 1.2% depending on m W ′ . Production cross sections in pp collisions at √ s = 8 TeV for the W ′ boson as well as the W ′ width and branching ratios of W ′ → WZ for a selection of W ′ boson masses in the EGM with scale factor c = 1 are given in Table 1.
Searches for a W ′ boson decaying to ℓν have set strong bounds on the mass of the W ′ when assuming the sequential standard model (SSM) [17,18], which differs from the EGM in that the W ′ WZ coupling is set to zero. For c ∼ 1 the effect of this coupling on the production cross section of the W ′ boson at the LHC is very small, thus the production cross section of the W ′ boson in the SSM and the EGM is very similar. Moreover, due to the small branching ratio of the W ′ → WZ in the EGM with the scale factor c ∼ 1, the branching ratios of the W ′ boson to fermions are approximately the same as in the SSM. Nevertheless, models with narrow vector resonances with suppressed fermionic couplings remain viable extensions to the SM, and thus the EGM provides a useful and simple benchmark in searches for narrow vector resonances decaying to WZ.
The ATLAS and CMS collaborations have set exclusion bounds on the production and decay of the EGM W ′ boson. In searches using the ℓνℓ ′ ℓ ′ (ℓ ≡ e, µ) channel, the ATLAS [19] and CMS [20] collaborations have excluded, at the 95% confidence level (CL), EGM (c = 1) W ′ bosons decaying to WZ for W ′ masses below 1.52 TeV and 1.55 TeV, respectively. In addition the ATLAS Collaboration has excluded EGM (c = 1) W ′ bosons for masses below 1.59 TeV using the ℓℓqq [21] channel, and below 1.49 TeV using the ℓνqq [22] channel. These have also been excluded with masses between 1.3 and 1.5 TeV and below 1.7 TeV by the ATLAS [23] and CMS [24] collaborations, respectively, using the fully hadronic final state.
Diboson resonances are also predicted in an extension of the original Randall-Sundrum (RS) [8][9][10] model with a warped extra dimension. In this extension to the RS model [25][26][27], the SM fields are allowed to propagate in the bulk of the extra dimension, avoiding constraints on the original RS model from flavour-changing neutral currents and from electroweak precision measurements. This so-called bulk-RS model is characterized by a dimensionless coupling constant k/M Pl ∼ 1, where k is the curvature of the warped extra dimension, andM Pl = M Pl / √ 8π is the reduced Planck mass. In this model a Kaluza-Klein excitation of the spin-2 graviton, G * , can decay to pairs of W or Z bosons. For bulk RS models with k/M Pl = 1 and for G * masses between 0.5 and 2.5 TeV, the branching ratio of G * to WW ranges from 34% to 16% and the branching ratio to ZZ ranges from 18% to 8%. The G * width ranges from 3.7% to 6.2% depending on the G * mass. Table 1 lists widths, branching ratio to WW and ZZ for G * , and production cross sections in pp collisions at 8 TeV in these bulk RS models.
The ATLAS Collaboration has excluded, at the 95% CL, bulk G * → ZZ with masses below 740 GeV, using the ℓℓqq channel [21], as well as bulk G * → WW with masses below 760 GeV, using the ℓνqq channel assuming k/M Pl = 1 [22]. The CMS Collaboration has also excluded at the 95% CL the G * of the original RS model, decaying to WW and ZZ with masses below 1. . Due to the large momenta of the bosons from the resonance decay, the resonance in this channel is reconstructed with two large-radius jets, and the fully hadronic channel is hereafter referred to as the JJ channel.
To search for a charged diboson resonance decaying to WZ the ℓνℓ ′ ℓ ′ , ℓℓqq, ℓνqq, and JJ channels are combined. The result of this combination is interpreted using the EGM W ′ model with c = 1 as a benchmark.
To search for neutral diboson resonances decaying to WW and ZZ the ℓℓqq, ℓνqq, and JJ channels are combined, and the result is interpreted using the bulk G * , assuming k/M Pl = 1, as a benchmark.
The ATLAS Collaboration has performed additional searches in which new diboson resonances could manifest themselves as excesses over the background expectation. In the analysis presented in Ref. [29] the ℓℓℓ ′ ℓ ′ , ℓℓνν, ℓℓqq and qqνν final states have been explored in the context of the search for a new, heavy Higgs boson. Also, in the context of searches for dark matter a final state of a hadronically decaying boson and missing transverse momentum [30], and a final state of a leptonically decaying Z boson and missing transverse momentum have been explored [31]. These additional searches are not included in this combination. They are not expected to contribute significantly to the sensitivity of the combined search due to the lower branching ratio in case of the leptonic channels, and the use of only narrow jets in case of the qqνν final state.

ATLAS detector and data sample
The ATLAS detector is described in detail in Ref. [32]. It covers nearly the entire solid angle 1 around the interaction point and has an approximately cylindrical geometry. It consists of an inner tracking detector (ID) placed within a 2 T axial magnetic field surrounded by electromagnetic and hadronic calorimeters and followed by a muon spectrometer (MS) with a magnetic field provided by a system of superconducting toroids.
The results presented in this article use the dataset collected in 2012 by ATLAS from the LHC pp collisions at √ s = 8 TeV, using a single-lepton (electron or muon) trigger [33] with a p T threshold of 24 GeV, or a single large-radius jet trigger with a p T threshold of 360 GeV. The integrated luminosity of this dataset after requiring data quality criteria to ensure that all detector components have been operational during data taking is 20.3 fb −1 . The uncertainty on the integrated luminosity is ±2.8%. It is derived following the methodology detailed in Ref. [34].

Signal and background samples
The acceptance and the reconstructed mass spectra for narrow resonances are estimated with signal samples generated with resonance masses between 200 and 2500 GeV, in 100 GeV steps. The bulk G * signal events are produced by CalcHEP 3.4 [35] with k/M Pl = 1.0, and the W ′ signal samples are generated with Pythia8.170 [36], setting the coupling scale factor c = 1. The factorization and renormalization scales are set to the generated resonance mass. The hadronization and fragmentation are modelled with Pythia8 in both cases, and the CTEQ6L1 [37] (MSTW2008LO [38]) parton distribution functions (PDFs) are used for the G * (W ′ ) signal. The leading-order cross sections and branching ratios for the W ′ and bulk G * signal samples for selected mass points and assumed values of the coupling parameters are provided in Table 1 1 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 upward. 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), and the distance in (φ, η) space as ∆R ≡ (∆φ) 2 + (∆η) 2 .

Object reconstruction and selection
The search channels included in the combination presented in this article use reconstructed electrons, muons, jets and the measurement of the missing transverse momentum. Hadronically decaying vector bosons with low p T ( 450 GeV) are reconstructed using a pair of jets. The jets are formed with the anti-k t algorithm [65] with a radius parameter R = 0.4. These jets are hereafter referred to as small-R jets. Only small-R jets with |η| < 2.8 (2.1) and p T > 30 GeV are considered for the ℓνqq (ℓℓqq) channel. For small-R jets with p T < 50 GeV it is required that the summed scalar p T of the tracks matched to the primary vertex accounts for at least 50% of the scalar summed p T of all tracks matched to the jet. Jets containing hadrons from b-quarks are identified using a multivariate b-tagging algorithm as described in Ref. [66].
Hadronically decaying vector bosons with high p T ( 400 GeV) can be reconstructed as a single jet with a large radius parameter, or large-R jet, due to the collimated nature of their decay products. These large-R jets, hereafter denoted by J, are first formed with the Cambridge-Aachen (C/A) algorithm [67,68] with a radius parameter R = 1.2. After the jet formation a set of criteria is applied to identify the jet as originating from a hadronically decaying boson (boson tagging). A grooming algorithm is applied to the jets to reduce the effect of pile-up and underlying event activity and to identify a pair of subjets associated with the quarks emerging from the vector boson decay. The grooming algorithm, a variant of the massdrop filtering technique [69], is described in detail in Ref.
[23]. The grooming procedure provides a small degree of discriminating power between jets from hadronically decaying bosons and those originating from background processes.
Jet discrimination is further improved by imposing additional requirements on the large-R jet properties. First, in all of the channels using large-R jets, a requirement on the subjet momentum-balance found at the stopping point of the grooming algorithm, √ y > 0.45, 3 is applied to the jet. Second, jets are required to have the groomed jet mass within a selection window. Due to the different backgrounds affecting each of the search channels, different mass windows are used for each channel. In the single lepton and dilepton channels, mass windows of 65 < m J < 105 GeV and 70 < m J < 110 GeV, where m J represents the jet mass, are used for selecting W and Z bosons. In the fully hadronic channel, mass windows of 69.4 < m J < 95.4 GeV and 79.8 < m J < 105.8 GeV, which are ±13 GeV around the expected W or Z reconstructed mass peak, are used for selecting W or Z boson candidates respectively.
The high-p T jets in background events are expected to have a larger charged-particle track multiplicity than the jets emerging from boson decays. This is due to the higher energy scale involved in the fragmentation process of background jets and also due to the larger color charge of gluons in comparison to 2 The primary vertex of the event is defined as the reconstructed primary vertex with highest p 2 T where the sum is over the tracks associated with this vertex. 3 , where m 0 is the mass of the groomed jet at the stopping point of the splitting stage of the grooming algorithm, p T j 1 and p T j 2 are the transverse momenta of the subjets at the stopping point of the splitting stage of the grooming algorithm and ∆R ( j 1 , j 2 ) is the distance in (φ, η) space between these subjets. quarks. Hence, to improve the sensitivity of the search in the fully hadronic channel, a requirement on the charged-particle track multiplicity matched to the large-R jet prior to the grooming, n trk < 30, is used to discriminate between jets originating from boson decays and jets from background processes. Chargedparticle tracks reconstructed with the ID and consistent with particles originating from the primary vertex and with p T ≥ 500 MeV are matched to a large-R jet by representing each track by a "ghost" constituent that is collinear with the track at the perigee with negligible energy during jet formation [70].
The missing transverse momentum E miss T is calculated from the negative vector sum of the transverse momenta of all reconstructed objects, including electrons, muons, photons and jets, as well as calibrated energy deposits in the calorimeter that are not associated to these objects, as described in Ref. [71].

Analysis channels
The selections in the four analysis channels ℓνℓ ′ ℓ ′ , ℓℓqq, ℓνqq and JJ are mutually exclusive and therefore the channels are statistically independent. This independence is enforced by the required lepton multiplicity of the events at a pre-selection stage, with lepton selection criteria looser than those finally applied in the individual channels. The searches in the individual channels are described in detail in their corresponding publications [19, 21-23]. Table 2 summarises the dominant backgrounds affecting each of the individual channels and the methods used to estimate these backgrounds. Summaries of the event selection and classification criteria are given in Tables 3 and 4.
Z+jets MC (Sherpa), normalisation and shape correction data driven ℓνqq W/Z+jets MC (Sherpa), normalisation and shape correction data driven JJ QCD jets data driven The ℓνℓ ′ ℓ ′ analysis channel is described in detail in Ref. [19]. For the purpose of combination the binning of the diboson candidates' invariant mass distribution is adjusted. The ℓνℓ ′ ℓ ′ channel requires exactly three leptons with p T > 25 GeV, of which at least one must be geometrically matched to a lepton reconstructed by a trigger algorithm. Events with additional leptons with p T > 20 GeV are vetoed. At least one pair of oppositely-charged, same-flavour leptons is required to have an invariant mass within the Z mass window |m ℓℓ − m Z | < 20 GeV. If there are two acceptable combinations satisfying this requirement the combination with the mass value closer to the Z boson mass is chosen as the Z candidate. The event is required to have E miss T > 25 GeV. The W candidate is reconstructed from the third lepton, assuming the neutrino is the only source of E miss T and constraining the (ℓ 3rd , E miss T ) system to have the pole mass of the W. This constraint results in a quadratic equation with two solutions for the longitudinal momentum of the neutrino. If the solutions are real, the one with the smaller absolute value is used. If the solutions are complex, the real part is used. To enhance the signal sensitivity, the rapidity difference must satisfy ∆y(W, Z) < 1.5 and requirements are placed on the azimuthal angle difference ∆φ(ℓ 3rd , E miss T ). Exclusive high-mass and low-mass regions are defined with ∆φ(ℓ 3rd , E miss T ) < 1.5 for boosted W bosons and ∆φ(ℓ 3rd , E miss T ) > 1.5 for W bosons at low p T , respectively. The main background sources in the ℓνℓ ′ ℓ ′ channel are SM WZ and ZZ processes with leptonic decays of the W and Z bosons, and are estimated from simulation. Other background sources are W/Z+jets, top quark and multijet production, where one or several jets are mis-reconstructed as leptons. To estimate these backgrounds the mis-reconstruction rate of jets as leptons is determined with data-driven methods, and applied to control data samples with leptons and one or more jets.
The ℓℓqq analysis channel is described in detail in Ref. [21]. The ℓℓqq channel requires exactly two leptons, having the same flavour and with p T > 25 GeV. Muon pairs are required to have opposite charge. At least one lepton is required to be matched to a lepton reconstructed by a trigger algorithm. The invariant mass of the lepton pair must be within 25 GeV of the Z mass. Three regions (merged, high-p T resolved and low-p T resolved) are defined to optimize the selection for different mass ranges. The merged region requirements are p T (ℓℓ) > 400 GeV and a groomed large-R jet described in Section 4 with p T (J) > 400 GeV and satisfying the boson-tagging criteria. The high-p T resolved region is defined by p T (ℓℓ) > 250 GeV, p T ( j j) > 250 GeV, and the low-p T resolved region requires p T (ℓℓ) > 100 GeV, p T ( j j) > 100 GeV. The invariant mass requirement on the jet system is 70 GeV < m j j/J < 110 GeV. The three regions are made exclusive by applying the above selections in sequence, starting with the merged region, and progressing with the high-p T and then the low-p T resolved regions. The main background sources in the ℓℓqq channel are Z+jets, followed by top-quark pair and non-resonant vector-boson pair production. Background estimates are based on simulation. Additionally, for the main background source, Z+jets, the shape of the invariant mass distribution is modelled with simulation, while the normalization and a linear shape correction are determined from data in a control region, defined as the side-bands of the qq invariant mass distribution outside the signal region.
The ℓνqq analysis channel is described in detail in Ref. [22]. In the ℓνqq channel exactly one lepton with p T > 25 GeV and matched to a lepton reconstructed by the trigger is required. The missing transverse momentum in the event is required to be E miss T > 30 GeV. Similar to the ℓℓqq channel the event selection contains three different mass regions of the signal, referred to as merged, high-p T resolved and low-p T resolved regions. In the merged region where the hadronic decay products merge into a single jet, a groomed large-R jet with p T > 400 GeV and 65 GeV < m J < 105 GeV is required. The leptonically decaying W candidate is reconstructed using the same W mass constraint technique used in the ℓνℓ ′ ℓ ′ channel. The leptonically decaying W → ℓν must have p T (ℓν) > 400 GeV, where p T (ℓν) is reconstructed from the sum of the charged-lepton momentum vector and the E miss T vector. To suppress the background from top-quark production, events with an identified b-jet separated by ∆R > 0.8 from the large-R jet are rejected. Additionally, in the electron channel the leading large-R jet and E miss T are required to be separated by ∆φ(E miss T , J) > 1 to reject multi-jet background. If the event does not satisfy the criteria of the merged region, the resolved region selection criteria are applied. In the high-p T resolved region, two small-R jets with p T > 80 GeV are required to form the hadronically decaying W/Z candidate with a transverse momentum of p T ( j j) > 300 GeV and an invariant mass of 65 GeV < m j j < 105 GeV. The leptonically decaying W → ℓν must have p T (ℓν) > 300 GeV. The event is rejected if a b-jet is identified in addition to the two leading jets. In the electron channel the leading small-R jet and E miss T are required to be separated by ∆φ(E miss T , j) > 1. If the event does not pass the selection requirements of the high-p T resolved region the selection of the low-p T resolved region is used, where p T ( j j) > 100 GeV and p T (ℓν) > 100 GeV are applied. The dominant background in the ℓνqq channel is W/Z+jets production, followed by top quark production, and multijet and diboson processes. The shape of the invariant mass distribution for the W/Z+jets background is modelled by simulation, while the normalization is determined from data in a control region, defined as the side-bands of the qq invariant mass distribution outside the signal region. The p T (W) distribution of the W+jets simulation is corrected using data to improve the modelling. The sub-dominant background processes are estimated using simulation only (diboson), or simulation and data-driven techniques (multijet, top quark).
The JJ analysis channel is described in detail in Ref. [23]. For the combined G * search the analysis is extended, combining the WW and ZZ selections into a single inclusive analysis of both decay modes. The analysis of the fully hadronic decay mode selects events that pass a large-R jet trigger 4 with a nominal threshold of 360 GeV in transverse momentum and have at least two large-R jets within |η| < 2.0, a rapidity difference between the two jets of |∆y 12 | < 1.2, and an invariant mass of the two jets of m(JJ) > 1.05 TeV. Events that contain one or more leptons with p T > 20 GeV or missing transverse momentum in excess of 350 GeV are vetoed. The large-R jets must satisfy the boson-tagging criteria described in Section 4. Furthermore, the dijet p T asymmetry defined as A = (p T1 − p T2 )/(p T1 + p T2 ) must be less then 0.15 to avoid mis-measured jets. In the search for the EGM W ′ decaying to WZ, events are selected by requiring one W boson candidate and one Z boson candidate in each event by applying the selections described in Section 4. In the search for the bulk G * decaying to WW and ZZ, events are selected by requiring two W boson or two Z boson candidates by applying the selections described in Section 4. Due to the overlapping jet mass windows applied to select W and Z candidates, the selection for the EGM W ′ and the bulk G * are not exclusive and about 20% of the inclusive event sample is shared. In the fully hadronic channel the dominant background is dijet production. The dijet background is estimated by a parametric fit with a smoothly falling function to the observed dijet mass spectrum in the data. Only diboson resonances with mass values > 1.3 TeV are considered as signal for this analysis channel.
The selections described above have a combined acceptance times efficiency of up to 17% for G * → WW, up to 11% for G * → ZZ, and up to 17% for W ′ → WZ. The acceptance times efficiency includes the W and Z branching ratios. Figs. 1(a) and 1(b) summarize the acceptance times efficiency for the different analyses as a function of the W ′ mass and of the G * mass, considering only decays of the resonance into VV, where V denotes a W or a Z boson.    Table 4: Summary of the event classification requirements in the different search channels. The classifications are mutually exclusive, applying the requirements in sequence beginning with the high-p T merged, followed by the high-p T resolved and finally with the low-p T resolved classification.
Channel High-p T merged High-p T resolved (high mass) Low-p T resolved (low mass)

Statistical procedure
The combination of the individual channels proceeds with a simultaneous analysis of the invariant mass distributions of the diboson candidates in the different channels. For each hypothesis being tested, only the channels sensitive to that hypothesis are included in the combination. The signal strength, µ, defined as a scale factor on the cross section times branching ratio predicted by the signal hypothesis, is the parameter of interest. The analysis follows the Frequentist approach with a test statistic based on the profile-likelihood ratio [72]. The test statistic extracts information on the signal strength from a binned maximum-likelihood fit of the signal-plus-background model to the data. The effect of a systematic uncertainty k on the likelihood is modelled with a nuisance parameter, θ k , constrained with a corresponding probability density function f (θ k ), as explained in the publications corresponding to the individual channels [19,[21][22][23]. In this manner, correlated effects across the different channels are modelled by the use of a common nuisance parameter and its corresponding probability density function. The likelihood model, L, is given by: where the index c represents the analysis channel, and i represents the bin in the invariant mass distribution, n obs , the observed number of events, n sig the number of expected signal events, and n bkg the expected number of background events.
The compatibility between the observations of different channels with a common signal strength of a particular resonance model and mass is quantified using a profile-likelihood-ratio test. The corresponding profile-likelihood ratio is where µ is the common signal strength,μ A andμ B are the unconditional maximum likelihood (ML) estimators of the independent signal strengths in the channels being compared,θ are the unconditional ML estimators for the nuisance parameters, andθ(µ) are the conditional ML estimators of θ for a given value of µ. The compatibility between the observations is tested by the probability of observing λ(μ), whereμ is the ML estimator for the common signal strength for the model in question. If the two channels being compared have a common signal strength, i.e. µ = µ A = µ B , then in the asymptotic limit −2 log(λ(μ)) is expected to be χ 2 distributed with one degree of freedom.
The significance of observed excesses over the background-only prediction is quantified using the local pvalue (p 0 ), defined as the probability of the background-only model to produce a signal-like fluctuation at least as large as observed in the data. Upper limits on µ for W ′ in the EGM and G * in the bulk RS model at the simulated resonance masses are evaluated at the 95% CL following the CL s prescription [73]. Lower mass limits at the 95% CL for new diboson resonances in these models are obtained by finding the maximum resonance mass where the 95% CL upper limit on µ is less or equal to 1. This mass is found by interpolating between the limits on µ at the simulated signal masses. The interpolation assumes monotonic and smooth behaviour of the efficiencies for the signal and background processes, and that the impact of the variation of signal mass distributions between adjacent test masses is negligible.
In the combined analysis to search for W ′ resonances, all four individual channels are used. For the charge-neutral bulk G * , only the ℓνqq, ℓℓqq, and the JJ channels contribute to the combination, and in the case of the fully hadronic channel, a merged signal region resulting from the union of the WW and ZZ signal regions is used in the analysis. The background to this merged signal region is estimated using the same technique as for the individual signal regions. Table 5 summarises the channels and signal regions combined in the analysis for the EGM W ′ and bulk G * .

Systematic uncertainties
The sources of systematic uncertainty along with their effects on the expected signal and background yields for each of the individual channels used in this combination are described in detail in their corresponding publications [19, 21-23]. Although the results from the different search channels in this combination are statistically independent, commonalities between the different search channels, such as the objects used, the signal and background simulation, and the integrated luminosity estimation, introduce correlated effects in the signal and background expectations. Whenever an effect due to an uncertainty in the triggering, identification, or reconstruction of leptons is considered for a channel, it is treated as fully correlated with the effects due to this uncertainty in other channels.
In the same manner, the effects of each uncertainty related to the small-R jet energy scale and resolution are treated as fully correlated in all channels using small-R jets or E miss T . For the search channels using large-R jets, uncertainties in the large-R jet energy scale, energy resolution, mass scale, mass resolution, or in the modelling of the boson-tagging discriminant √ y are taken as fully correlated. Uncertainties in the data-driven background estimates are treated as uncorrelated. The effects of uncertainty in the initialand final-state radiation (ISR and FSR) modelling and in the PDFs are each treated as fully correlated across all search channels.
The effect of a single source of systematic uncertainty on the combined limit can be ranked by the loss in sensitivity caused by its inclusion. To quantify the loss of sensitivity at a given mass point the value computed with all systematic uncertainties included is compared to the value obtained excluding the single systematic uncertainty. In the low mass region at 0.5 TeV the leading uncertainty is the modelling of the SM diboson background in the dominant ℓνℓ ′ ℓ ′ channel with an impact of 35% sensitivity degradation in the combined limit for EGM W ′ . The leading source of uncertainty in case of the G * limit is the modelling of the Z+jets background in the ℓνqqchannel with a degradation of 25%. In the intermediate mass region up to 1.5 TeV the uncertainty on the normalisation of the W+jets background in the ℓνqq channel is dominating with 20% to 30% degradation of the EGM W ′ limit and 25% to 55% degradation of the G * limit depending on the mass point, while in the high mass region up to 2 TeV the shape uncertainty on the W+jets background dominates with a degradation of around 25% for the EGM W ′ limit and 35% for the G * limit. Figure 2 shows the p 0 -value obtained in the search for the EGM W ′ and G * as a function of the resonance mass for the ℓνℓ ′ ℓ ′ , ℓℓqq, ℓνqq and JJ channels combined and for the individual channels. For the full combination the largest deviation from the background-only expectation is found in the EGM W ′ search at around 2.0 TeV with a p 0 -value corresponding to 2.5 standard deviations (σ). This is smaller than the p 0 -value of 3.4 σ observed in the JJ channel alone because the ℓνℓ ′ ℓ ′ , ℓℓqq, and ℓνqq channels are more consistent with the background-only hypothesis.

Results
The compatibility of the individual channels is quantified with the test described in Section 6. In the mass region around 2 TeV the JJ channel presents an excess while the other channels are in good agreement with the background-only expectation. For the EGM W ′ benchmark the compatibility of the combined ℓνℓ ′ ℓ ′ , ℓℓqq, and ℓνqq channels with the JJ channel is at the level of 2.9 σ. When accounting for the probability for any of the four channels to fluctuate the compatibility is found to be at the level of 2.6 σ.
In comparison the corresponding test for the bulk G * interpretation shows better compatibility.   Figure 2: The p 0 -value for the individual and combined channels for (a) the EGM W ′ search in the ℓνℓ ′ ℓ ′ , ℓℓqq, ℓνqq and JJ channels and (b) the bulk G * search in the ℓℓqq, ℓνqq and JJ channels. Figure 3 shows the combined upper limit on the EGM W ′ production cross section times its branching ratio to WZ at the 95% CL in the mass range from 300 GeV to 2.5 TeV. In Fig. 3(a) the observed and expected limits of the individual and combined channels are shown. In Fig. 3(b) the observed and expected combined limits are compared with the theoretical EGM W ′ prediction. The resulting combined lower limit on the EGM W ′ mass using a LO cross-section calculation is observed to be 1.81 TeV, with an expected limit of 1.81 TeV. The most stringent observed mass limit from an individual channel is 1.59 TeV at NNLO in the ℓνqq analysis. [GeV] W' m 500 1000 1500 2000 2500 1000 1500 2000 2500  Figure 3: The 95% CL limits on (a) the EGM W ′ using the ℓνℓ ′ ℓ ′ , ℓℓqq, ℓνqq, and JJ channels and their combination, and (b) the combined 95% CL limit with the green (yellow) bands representing the 1 σ (2 σ) intervals of the expected limit including statistical and systematic uncertainties.
In Fig. 4 the observed and expected upper limits at the 95% CL on the bulk G * production cross section times its branching ratio to WW and ZZ are shown in the mass range from 200 GeV to 2.5 TeV. In Fig. 4(b) the observed and expected limits of the individual and combined channels are shown and compared with the theoretical bulk G * prediction for k/M Pl = 1. The combined, lower mass limit for the bulk G * , assuming k/M Pl = 1, is 810 GeV, with an expected limit of 790 GeV. The most stringent lower mass limit from the individual ℓℓqq, ℓνqq and JJ channels is 760 GeV from the ℓνqq channel.  Figure 4: The 95% CL limits on (a) the bulk G * using the ℓℓqq, ℓνqq, and JJ channels and their combination, and (b) the combined 95% CL limit with the green (yellow) bands representing the 1 σ (2 σ) intervals of the expected limit including statistical and systematic uncertainties.

Conclusion
A combination of individual searches in all-leptonic, semileptonic, and all-hadronic final states to search for new heavy bosons decaying to WW, WZ and ZZ is presented. The searches use 20.3 fb −1 of 8 TeV pp collision data collected by the ATLAS detector at the LHC. Within the combined result, no significant excess over the background-only expectation in the invariant mass distribution of the diboson candidates is observed. Upper limits on the production cross section times branching ratio to dibosons at the 95% CL are evaluated within the context of an extended gauge model with a heavy W ′ boson and a bulk Randall-Sundrum model with a heavy spin-2 graviton. The combination significantly improves both the cross-section limits and the mass limits for EGM W ′ and bulk G * production over the most stringent limits of the individual analyses. The observed lower limit on the EGM W ′ mass is found to be 1.81 TeV and for the bulk G * mass, assuming k/M Pl = 1, the observed limit is 810 GeV.   The ATLAS Collaboration