arXiv:1108.1316v2 [hep-ex] 8 Dec 2011
CERN-PH-EP-2011-121
Search for a heavy gauge boson decaying to a charged lepton and a neutrino in
1 fb
−1of pp collisions at
√
s
= 7 TeV using the ATLAS detector
The ATLAS Collaboration
Abstract
The ATLAS detector at the LHC is used to search for heavy charged gauge bosons (W′), decaying to a charged lepton (electron or muon) and a neutrino. Results are presented based on the analysis of pp collisions at a center-of-mass energy of 7 TeV corresponding to an integrated luminosity of 1.04 fb−1. No excess above Standard Model expectations is observed. A W′ with Sequential Standard Model couplings is excluded at the 95% confidence level for masses up to 2.15 TeV.
1. Introduction
The high-energy collisions at the CERN Large Hadron Collider provide new opportunities to search for physics beyond the Standard Model (SM) of strong and electroweak interactions. One extension common to many models is the existence of additional heavy gauge bosons [1], the charged ones commonly denoted W′. Such particles are most easily searched for in their decay to a charged lepton (electron or muon) and a neutrino.
This letter describes such a search performed using 7 TeV pp collision data collected with the ATLAS detec-tor during 2011 and corresponding to a total integrated luminosity of 1.04 fb−1. No W′ signal is observed, and the data are used to extend current limits [2, 3, 4] on σB (cross section times branching fraction) as a function of W′ mass. The significant improvement over the previous ATLAS result [4] comes mostly from the increase in avail-able integrated luminosity, but also reflects optimization of the event selection and increased acceptance in the muon channel. A lower limit on the mass of a W′ boson in the Sequential Standard Model (SSM), i.e. the extended gauge model of Ref. [5] with W′ coupling to W Z set to zero, is also reported. In this model, the W′ has the same cou-plings to fermions as the SM W boson and thus a width which increases linearly with the W′ mass.
The analysis presented here identifies candidates in the electron and muon channels and sets separate limits for W′→ eν and W′→ µν. In addition, combined limits are evaluated, assuming the same branching fraction for both channels. The kinematic variable used to identify the W′ is the transverse mass
mT= q
2pTETmiss(1 − cos ϕlν), (1)
which displays a Jacobian peak that falls sharply above the resonance mass. Here pT is the lepton transverse mo-mentum, Emiss
T is the magnitude of the missing transverse momentum (missing ET), and ϕlν is the angle between
the pT and missing ET vectors. Throughout this letter, transverse refers to the plane perpendicular to the collid-ing beams, longitudinal means parallel to the beams, θ and ϕ are the polar and azimuthal angles with respect to the longitudinal direction, and pseudorapidity is defined as η = − ln(tan(θ/2)).
The main background to the W′ → ℓν signal comes from the high-mTtail of SM W boson decay to the same final state. Other backgrounds are Z bosons decaying into two leptons where one lepton is not reconstructed, W or Z decaying to τ -leptons where a τ subsequently decays to an electron or muon, and diboson production. These are col-lectively referred to as the electroweak (EW) background. In addition, there is a background contribution from t¯t pro-duction which is most important for the lowest W′masses considered here, where it constitutes about 10% of the background after event selection. Other strong-interaction background sources, where a light or heavy hadron decays semileptonically or a jet is misidentified as an electron, are estimated to be at most 10% of the total background in the electron channel and a negligible fraction in the muon channel, again after final selection. These are called QCD background in the following.
2. Data
The ATLAS detector [6] has three major components: the inner tracking detector, the calorimeter and the muon spectrometer. Charged particle tracks and vertices are re-constructed with silicon pixel and silicon strip detectors covering |η| < 2.5 and transition radiation detectors cov-ering |η| < 2.0, all immersed in a homogeneous 2 T mag-netic field provided by a superconducting solenoid. This tracking detector is surrounded by a finely-segmented, her-metic calorimeter system that covers |η| < 4.9 and pro-vides three-dimensional reconstruction of particle showers. It uses liquid argon for the inner, electromagnetic com-partment followed by a hadronic comcom-partment based on
scintillating tiles in the central region (|η| < 1.7) and addi-tional liquid argon for higher |η|. Outside the calorimeter, there is a muon spectrometer with air-core toroids provid-ing a magnetic field, whose integral averages about 3 Tm. The deflection of the muons in the magnetic field is mea-sured with three layers of precision drift-tube chambers for |η| < 2.0 and one layer of cathode-strip chambers followed by two layers of drift-tube chambers for 2.0 < |η| < 2.7. Additional resistive-plate and thin-gap chambers provide muon triggering capability and measurement of the ϕ co-ordinate.
The data used in the electron channel are the events recorded with a trigger requiring the presence of an elec-tron with pT > 20 GeV. The efficiency of this trig-ger is 98%. For the muon channel, matching tracks in the muon spectrometer and inner detector with combined pT> 22 GeV are used to identify events. Events are also recorded if a muon with pT> 40 GeV is found in the muon spectrometer. The muon trigger efficiency is 80-90% in the regions of interest.
Each energy cluster reconstructed in the electromag-netic compartment of the calorimeter with ET> 25 GeV and |η| < 1.37 or 1.52 < |η| < 2.47 is considered as an electron candidate if it matches with an inner detector track. The electron direction is defined as that of the reconstructed track and its energy as that of the clus-ter, with a small (less than 2%) η-dependent energy scale correction. The resolution of the energy measurement is 2% for ET≈ 50 GeV and approaches 1% in the high-ET range relevant to this analysis. To discriminate against hadronic jets, requirements are imposed on the lateral shower shapes in the first two layers of the electromag-netic part of the calorimeter and the fraction of energy leaking into the hadronic compartment. A hit in the first pixel layer is required to reduce background from photon conversions in the inner detector material. These require-ments give about 90% identification efficiency for electrons with ET> 25 GeV and a 2 × 10−4 probability to falsely identify jets as electrons before isolation requirements are imposed [7].
Muon tracks can be reconstructed independently in both the inner detector and muon spectrometer, and the muons used in this study are required to have matching tracks in both systems. The muons are required to have pT > 25 GeV, where the momentum of the muon is ob-tained by combining the inner detector and muon spec-trometer measurements. To ensure precise measurement of the momentum, muons are required to have hits in all three muon layers and are restricted to those η-ranges where the muon spectrometer alignment is best under-stood: approximately |η| < 1.0 and 1.3 < |η| < 2.0. The average momentum resolution is currently about 15% at pT = 1 TeV. About 80% of the muons in these η-ranges are reconstructed, with most of the loss coming from re-gions with limited detector coverage.
The missing ET in the electron channel is obtained from a vector sum over calorimeter cells associated with
topological clusters and using local hadronic calibration [8]: EmissT = EmissTcalo= −
X topo
EcellT . (2)
The topological clusters reduce contributions from elec-tronic noise. The ETof cells associated with the electron is corrected so their sum equals the electron ET. Muons only deposit a small fraction of their energy in the calorimeter, and so, in the muon channel, the missing ETis obtained from
EmissT = EmissTcalo− p µ
T+ E
µ,loss
T . (3)
The second term in this vector sum subtracts the muon transverse momentum and the last corrects for the trans-verse component of the energy deposited in the calorimeter by the muon, which is included in both of the first two terms. The energy loss is estimated by integrating the amount of material traversed and applying a calibrated conversion from path length to energy for each material type.
This analysis makes use of all the √s = 7 TeV data collected in March-June 2011 that satisfy data quality re-quirements which guarantee the relevant detector systems were operating properly. The integrated luminosity for the data used in this study is 1.04 fb−1 in both the elec-tron and muon decay channels. The uncertainty on this estimate is 3.7%.
3. Simulation
Except for the QCD background, which is estimated from data, expected signal and background levels are eval-uated with simulated samples and normalized using calcu-lated cross sections and the integrated luminosity of the data.
The W′ signal and the W/Z boson backgrounds are generated with Pythia 6.421 [9] using MRST LO* [10] parton distribution functions (PDFs). The t¯t background is generated with MC@NLO 3.41 [11]. For all samples, final-state photon radiation is handled by Photos [12]. ATLAS full detector simulation [13] based on Geant4 [14] is used to propagate the particles and account for the re-sponse of the detector.
The Pythia signal model for W′ has V − A SM cou-plings but does not include interference between W and W′. Decays to channels other than eν and µν, including τ ν, ud, sc and tb are included in the calculation of the W′ widths but are not explicitly included as signal or back-ground. At high mass (mW′ > 1 TeV), the branching
fraction to any of the lepton decay channels is 8.2%. The W → ℓν events are reweighted to have the NNLO (next-to-next-to-leading-order QCD) mass dependence of ZWPROD [15] with MSTW2008 PDFs [16] and following the Gµ scheme [17]. Higher-order electroweak corrections (in addition to the photon radiation included in the simu-lation) are calculated using Horace [17, 18]. In the high-mass region of interest, the electroweak corrections reduce
Table 1: Calculated values of σB for W′ →ℓν and the leading backgrounds. The value for t¯t → ℓX includes all final states with at least one lepton (e, µ or τ ). The others are exclusive and are used for both ℓ = e and ℓ = µ. All calculations are NNLO except t¯t which is approximate-NNLO. Mass Process [GeV] σB [pb] W′→ ℓν 500 17.25 600 8.27 750 3.20 1000 0.837 1250 0.261 1500 0.0887 1750 0.0325 2000 0.0126 2250 0.00526 2500 0.00234 W → ℓν 10460 Z/γ∗ → ℓℓ 989 (mZ/γ∗> 60 GeV) t¯t → ℓX 89.4
the cross sections by 11% at mℓν = 1 TeV and by 18% at mℓν = 2 TeV.
The W → ℓν and Z → ℓℓ cross sections are cal-culated at NNLO using FEWZ [19, 20] with the same PDFs, scheme and electroweak corrections used in the ZWPROD event reweighting. The W′ → ℓν cross sec-tions are calculated in the same way, except the elec-troweak corrections beyond final-state radiation are not included because the calculation for the SM W cannot be applied directly. The t¯t cross section is calculated at approximate-NNLO [21, 22, 23] assuming a top-quark mass of 172.5 GeV. The signal and most important back-ground values for σB are listed in Table 1.
Cross-section uncertainties for W′ → ℓν and the W/Z [7] and t¯t [24] backgrounds are estimated from the MSTW2008 PDF error sets, the difference between MSTW2008 and CTEQ6.6 [25] PDF sets, and variation of renormalization and factorization scales by a factor of two. The estimates from the three sources are combined in quadrature. Most of the net uncertainty comes from the error sets and the MSTW-CTEQ difference, in roughly equal proportion. The uncertainty on the cross section for the W → ℓν background varies from 5% at mℓν = 500 GeV to 19% at mℓν = 2500 GeV.
4. Event selection
Events are required to have their primary vertex recon-structed from at least three tracks with pT> 0.4 GeV and longitudinal distance less than 200 mm from the center of the collision region. Due to the high luminosity, there were typically five additional interactions per event and
the primary vertex is defined to be the one with the high-est summed track p2
T. Spurious tails in missing ETarising from calorimeter noise and other detector problems are suppressed by checking the quality of each reconstructed jet and discarding events where any jet has a shape indi-cating such problems, following Ref. [26]. Events are re-quired to have exactly one candidate electron or one candi-date muon satisfying the requirements described above. In addition, the inner detector track associated with the elec-tron or muon is required to be compatible with originating from the primary vertex, specifically to have transverse distance of closest approach |d0| < 1 mm and longitudinal distance at this point |z0| < 5 mm.
To suppress the QCD background, the lepton is re-quired to be isolated. In the electron channel, the isola-tion energy is measured with the calorimeter in a cone ∆R < 0.4 (∆R ≡ p(∆η)2+ (∆ϕ)2) around the elec-tron track, and the requirement is P ET< 9 GeV, where the sum includes all calorimeter energy clusters in the cone excluding the core energy deposited by the electron. The sum is corrected to account for additional interac-tions and leakage of the electron energy outside this core. In the muon channel, the isolation energy is measured us-ing inner detector tracks with ptrk
T > 1 GeV in a cone ∆R < 0.3 around the muon track. The isolation require-ment is Pptrk
T < 0.05 pT, where the muon track is ex-cluded from the sum. The scaling of the threshold with the muon pTreduces efficiency losses due to radiation from the muon at high pT.
Finally, missing ET requirements are imposed to fur-ther suppress the QCD background. In both channels, a fixed threshold is applied: Emiss
T > 25 GeV. In the elec-tron channel, where hadronic jets may be misidentified as electrons, a threshold proportional to the electron ET is also applied: Emiss
T > 0.6 ET.
In the electron channel, the QCD background is esti-mated from data using the ABCD technique [27] with the isolation energy and missing ET serving as discriminants. Consistent results are obtained using the “inverted isola-tion” technique described in Ref. [4]. In the higher mass bins (mT> 700 GeV) where no events remain in the esti-mate, the QCD background level is set to zero and assigned an uncertainty equal to 10% of the total background level, a conservative upper limit based on the QCD contribution to the electron mT distribution.
The QCD background for the muon channel is evalu-ated using a non-isolevalu-ated data sample following the same procedure used for the 2010 analysis [4]. With the higher statistics now available, it is clear this background is less than 1% of the total background, so it is neglected in the following.
The same reconstruction and event selection are ap-plied to both data and simulated samples. Figure 1 shows the pT, missing ET, and mTspectra for each channel after event selection for the data, for the expected background, and for three examples of W′ signals at different masses. The agreement between the data and expected background
Table 2: Expected numbers of events in 1.04 fb−1from the various background sources in each decay channel for mT> 891 GeV, the region used to search for a W′with a mass of 1500 GeV. The W → ℓν and Z → ℓℓ entries include the expected contributions from the τ -lepton. No muon events are found in the t¯t sample above this mT threshold. The uncertainties are statistical.
eν µν W → ℓν 1.59 ± 0.13 1.36 ± 0.13 Z → ℓℓ 0.00010 ± 0.00004 0.095 ± 0.005 diboson 0.08 ± 0.08 0.11 ± 0.08 t¯t 0.08 ± 0.08 0 QCD 0 +0.17−0 0.01 +0.02−0.01 Total 1.75 +0.24−0.18 1.57 ± 0.15
is good. Table 2 shows as an example how different sources contribute to the background for mT > 891 GeV, the re-gion used to search for a W′ with a mass of 1500 GeV. The W → ℓν background dominates. The Z → ℓℓ back-ground is much larger in the muon channel because most of the energy of the undetected muon is not captured in the calorimeter.
5. Statistical analysis
A Bayesian analysis is performed to determine if there is significant evidence for existence of a W′ → ℓν signal above the SM background and to set limits on that process. For each candidate mass and decay channel, events are counted above an mT threshold, mT > mTmin, with the threshold chosen to maximize sensitivity. The expected number of events in each channel is
Nexp= εsigLintσB + Nbg, (4)
where Lint is the integrated luminosity of the data sample and εsig is the event selection efficiency, i.e. the fraction of events that pass event selection criteria and have mT above threshold. Nbg is the expected number of back-ground events. Using Poisson statistics, the likelihood to observe Nobs events is
L(Nobs|σB) =
(LintεsigσB + Nbg)Nobse−(LintεsigσB+Nbg) Nobs!
.(5) Uncertainties are handled by introducing Gaussian nui-sance parameters θi, each with a probability density func-tion (pdf) gi(θi), and integrating the product of the Pois-son likelihood with the pdfs. The integrated likelihood is LB(Nobs|σB) = Z L(Nobs|σB) Y gi(θi)dθi. (6)
The nuisance parameters are taken to be the explicit de-pendencies: Lint, εsig and Nbg, with the latter evaluated at the central value of Lint. Correlations between the nui-sance parameters are neglected. This is justified by the
small effect that the nuisance parameters themselves have on the limits, as demonstrated below.
The measurements in the two decay channels are com-bined assuming the same branching fraction for each. Equa-tion (6) remains valid with the Poisson likelihood replaced by the product of the Poisson likelihoods for the two chan-nels. The electron and muon integrated luminosity mea-surements are fully correlated. The selection efficiencies are uncorrelated and the background levels are partly cor-related, including only the full correlation between the cross section uncertainties in the two channels. The ef-fect of this correlation is small: if it is not included, the observed σB limits for the lowest mass points improve by 2% and those for the high-mass points are unchanged.
Bayes theorem gives the posterior probability that the W′→ ℓν has signal strength σB:
Ppost(σB|Nobs) = N LB(Nobs|σB) Pprior(σB) (7) where Pprior(σB) is the assumed prior probability, here chosen to be one (i.e. flat in σB) for σB > 0. The con-stant factor N normalizes the total probability to one. The posterior probability is evaluated for each mass and each decay channel and their combination, and then used to assess discovery significance and set a limit on σB. 6. Parameter estimation and systematics
The inputs for the evaluation of LB (and hence Ppost) are Lint, εsig, Nbg, Nobs and the uncertainties on the first three. Except for Lintand its uncertainty, these inputs are all listed in Table 3. The uncertainties on εsigand Nbg ac-count for simulation statistics and all relevant experimen-tal and theoretical effects except for the uncertainty on the integrated luminosity. The latter is included separately to allow for the correlation between signal and background. The table also lists the predicted numbers of signal events, Nsig, with their uncertainties accounting for the uncertain-ties in both εsig and the cross-section calculation.
The maximum value for the signal selection efficiency is at mW′ = 1500 GeV. For lower masses, the efficiency falls
because the relative mTthreshold, mTmin/mW′, increases
to reduce the background level. For higher masses, the efficiency falls because a large fraction of the cross section goes to off-shell production with mℓν≪ mW′.
The fraction of fully simulated signal events that pass the event selection and are above the mT threshold pro-vides the initial estimate of εsig for each mass. Small corrections are made to account for the difference in ac-ceptance at NNLO (obtained from FEWZ) and that in the LO simulation. These vary from a 7% increase for mW′ = 500 GeV to a 10% decrease for mW′ = 2500 GeV.
Contributions from W′→ τν with the τ-lepton decaying leptonically have been neglected and would increase the W′ event selection efficiencies by 3-4% for the highest masses. The background level is estimated for each mass by summing the EW and t¯t event counts from simulation,
[GeV] e T p 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν e → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ [GeV] µ T p 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν µ → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ [GeV] miss T E 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν e → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ [GeV] miss T E 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν µ → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ [GeV] T m 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν e → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ [GeV] T m 2 10 103 Events -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Data 2011 W’(500) W’(1000) W’(2000) W Z ttbar Diboson QCD ATLAS ν µ → W’ = 7 TeV s -1 L dt = 1.04 fb ∫
Figure 1: Spectra of pT(top), missing ET(center) and mT(bottom) for the electron (left) and muon (right) channels after event selection. The points represent data and the filled histograms show the stacked backgrounds. Open histograms are W′ →ℓν signals added to the background with masses in GeV indicated in parentheses in the legend. The QCD backgrounds estimated from data are also shown. The signal and other background samples are normalized using the integrated luminosity of the data and the NNLO (approximate-NNLO for t¯t) cross sections listed in Table 1.
Table 3: Inputs for the W′→eν and W′→µν σB limit calculations. The first three columns are the W′ mass, mT threshold and decay channel. The next two are the signal selection efficiency, εsig, and the prediction for the number of signal events, Nsig, obtained with this efficiency. The last two columns are the expected number of background events, Nbg, and the number of events observed in data, Nobs. The uncertainties on Nsig and Nbg include contributions from the uncertainties on the cross sections but not from that on the integrated luminosity.
mW′ mTmin
[GeV] [GeV] εsig Nsig Nbg Nobs
500 398 eν 0.388 ± 0.019 6930 ± 620 101.9 ± 10.8 121 µν 0.252 ± 0.015 4500 ± 430 63.7 ± 6.5 91 600 447 eν 0.456 ± 0.022 3910 ± 330 62.1 ± 7.1 69 µν 0.286 ± 0.016 2450 ± 220 41.8 ± 4.7 57 750 562 eν 0.429 ± 0.020 1420 ± 110 20.7 ± 3.7 20 µν 0.293 ± 0.017 970 ± 79 14.3 ± 1.4 20 1000 708 eν 0.482 ± 0.022 417 ± 35 6.13 ± 0.92 4 µν 0.326 ± 0.019 282 ± 26 4.98 ± 0.54 4 1250 794 eν 0.527 ± 0.024 143 ± 14 3.09 ± 0.49 3 µν 0.367 ± 0.021 99 ± 10 2.87 ± 0.34 3 1500 891 eν 0.541 ± 0.026 49.6 ± 6.0 1.75 ± 0.32 2 µν 0.374 ± 0.024 34.4 ± 4.4 1.57 ± 0.23 2 1750 1000 eν 0.515 ± 0.024 17.3 ± 2.4 0.89 ± 0.20 1 µν 0.338 ± 0.020 11.4 ± 1.7 0.82 ± 0.14 1 2000 1122 eν 0.472 ± 0.023 6.16 ± 0.99 0.48 ± 0.10 1 µν 0.323 ± 0.021 4.21 ± 0.70 0.44 ± 0.09 1 2250 1122 eν 0.415 ± 0.019 2.84 ± 0.50 0.48 ± 0.10 1 µν 0.288 ± 0.018 1.97 ± 0.36 0.44 ± 0.09 1 2500 1122 eν 0.333 ± 0.018 0.81 ± 0.16 0.48 ± 0.10 1 µν 0.221 ± 0.017 0.53 ± 0.11 0.44 ± 0.09 1
and adding the small QCD contribution in the electron channel.
The experimental systematic uncertainties include effi-ciencies for the electron or muon trigger, reconstruction and selection. Lepton momentum and missing ET re-sponse, characterized by scale and resolution, are also in-cluded. Most of these performance metrics are measured at relatively low pT and their values are extrapolated to the high-pT regime relevant to this analysis. The uncer-tainties in these extrapolations are included but are too small to significantly affect the results. The uncertainty on the QCD background estimate also contributes to the background level uncertainties for the electron channel. In some cases, e.g. the missing ETscale and the muon QCD background, the experimental systematic uncertainties are significantly reduced from the previous study [4] because the additional available data allow more precise determi-nation. In other cases they are similar or even larger, but have little effect on the final results.
Table 4 summarizes the uncertainties on the event se-lection efficiencies and background levels for the W′→ ℓν signal with mW′ = 1500 GeV using mT> 891 GeV. 7. Results
None of the observations for any mass in either channel or their combination has a significance above three-sigma, so there is no evidence for the observation of W′ → ℓν. Table 5 and Fig. 2 present the 95% CL (confidence level) observed limits on σB for both W′ → ℓν decay channels and their combination. The figure also shows the expected limits and the theoretical σB for an SSM W′. The inter-section between the central theoretical prediction and the observed limits provides the 95% CL lower limit on the mass. Table 6 presents the expected and observed W′ mass limits for the electron and muon decay channels and for the combination of the two channels. The observed combined mass limit is 2.15 TeV.
The above results are obtained using a prior proba-bility flat in σB. If this prior is replaced by one flat in coupling strength, the σB limits improve by 20-28% for mW′ ≥ 1000 GeV and by smaller amounts at the lower
masses. The reference prior [28, 29], which minimizes the information supplied by the prior, gives intermediate re-sults. Limits evaluated with CLs[30] for the electron and muon channels and including all uncertainties are nearly identical to the corresponding values in Table 5.
Prior to this letter, the best limits for 500 < mW′ <
800 GeV were established by CDF [2] in W′ → eν with p¯p collisions at√s = 1.96 TeV using an integrated lumi-nosity of 5.3 fb−1. At higher masses, the best limits were set by CMS [3] and ATLAS [4], each combining electron and muon channels and using pp collisions at√s = 7 TeV with 36 pb−1 of data acquired in 2010. The CDF and CMS limits were obtained with a Bayesian approach, and the earlier ATLAS results were established with CLs. Fig-ure 3 compares the limits obtained here with those earlier
[GeV] W’ m 500 1000 1500 2000 2500 B [pb] σ -3 10 -2 10 -1 10 1 NNLO theory Observed limit Expected limit σ 1 ± Expected σ 2 ± Expected = 7 TeV, s = 7 TeV, Ldt = 1.04 fb
∫
-1 s ν e → W’ ATLAS [GeV] W’ m 500 1000 1500 2000 2500 B [pb] σ -3 10 -2 10 -1 10 1 NNLO theory Observed limit Expected limit σ 1 ± Expected σ 2 ± Expected = 7 TeV, s = 7 TeV, Ldt = 1.04 fb∫
-1 s ν µ → W’ ATLAS [GeV] W’ m 500 1000 1500 2000 2500 B [pb] σ -3 10 -2 10 -1 10 1 NNLO theory Observed limit Expected limit σ 1 ± Expected σ 2 ± Expected = 7 TeV, s = 7 TeV, Ldt = 1.04 fb∫
-1 s ν l → W’ ATLASFigure 2: Expected and observed limits on σB for W′→eν (top), W′→µν (center), and the combination (bottom) assuming the same branching fraction for both channels. The NNLO calculated cross section and its uncertainty are also shown.
Table 4: Relative uncertainties on the event selection efficiency and background level for a W′ with a mass of 1500 GeV. The efficiency uncertainties include contributions from trigger, reconstruction and event selection. The cross section uncertainty for εsigis that assigned to the acceptance correction described in the text. The last row gives the total uncertainties.
εsig Nbg
Source eν µν eν µν
Efficiency 3% 4% 3% 4%
Energy/momentum resolution - 2% 3% 1%
Energy/momentum scale 1% 1% 5% 3%
QCD background - - 10% 1%
Monte Carlo statistics 3% 3% 9% 10%
Cross section (shape/level) 3% 3% 10% 10%
All 5% 6% 18% 15% [GeV] W’ m 500 1000 1500 2000 2500 SSM σ / limit σ -2 10 -1 10 1 10 ATLAS (2011) ν l → W’ = 7 TeV s -1 L dt = 1.04 fb ∫ CDF ATLAS 2010 CMS 2010
Figure 3: Normalized cross section limits (σlimit/σSSM) for W′→ℓν as a function of mass for this measurement and from CDF [2], CMS [3] and the previous ATLAS search [4]. The cross section calcu-lations assume the W′has the same couplings as the standard model W boson. The region above each curve is excluded at the 95% CL.
measurements. The comparison is made using the ratio of the limit to the calculated value of σB, a quantity that is proportional to the square of the coupling strength. The NNLO cross sections in Table 1 are used for both the AT-LAS and CMS points. The limits presented here provide significant improvement for masses above 600 GeV. 8. Conclusions
The ATLAS detector has been used to search for new heavy charged gauge bosons decaying to a lepton plus missing ET. The search is performed in pp collisions at √
s = 7 TeV using 1.04 fb−1 of integrated luminosity. No excess above SM expectations is observed. Bayesian lim-its on σB are shown in Figs. 2 and 3. These are the best published limits for mW′ > 600 GeV. A W′ with SSM
couplings is excluded for masses up to 2.15 TeV at the 95% CL.
Acknowledgments
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China;
COLCIENCIAS, Colombia; MSMT CR, MPO CR
and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; ARTEMIS, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNAS, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America.
The crucial computing support from all WLCG part-ners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.
Table 5: Upper limits on σB for W′→ℓν. The first two columns are the mass and decay channel and the following columns are the 95% CL limits with headers indicating the nuisance parameters for which uncertainties are included: S for the event selection efficiency (εsig), B for the background level (Nbg), and L for the integrated luminosity (Lint). Columns labeled SBL include all uncertainties and are used to evaluate mass limits. Results are given for the electron and muon channels and both combined.
mW′ 95% CL limit on σB [fb] [GeV] none S SB SBL 500 eν 97 98 117 121 µν 171 174 186 191 both 109 110 127 130 600 eν 49 49 59 61 µν 99 100 108 110 both 55 55 64 65 750 eν 23.0 23.1 28.1 28.5 µν 49.2 49.8 50.9 51.7 both 23.7 23.8 27.8 28.1 1000 eν 10.1 10.2 10.5 10.6 µν 16.1 16.3 16.5 16.7 both 7.3 7.3 7.6 7.7 1250 eν 9.8 9.9 10.0 10.1 µν 14.4 14.5 14.6 14.7 both 7.3 7.3 7.4 7.5 1500 eν 8.8 8.9 9.0 9.0 µν 13.0 13.2 13.2 13.3 both 6.6 6.6 6.7 6.7 1750 eν 7.8 7.9 7.9 7.9 µν 12.0 12.1 12.1 12.2 both 5.6 5.6 5.7 5.7 2000 eν 8.9 9.0 9.0 9.1 µν 13.2 13.3 13.3 13.4 both 6.6 6.7 6.7 6.7 2250 eν 10.2 10.2 10.3 10.3 µν 14.8 14.9 14.9 15.0 both 7.5 7.5 7.6 7.6 2500 eν 12.7 12.8 12.8 12.9 µν 19.2 19.5 19.6 19.7 both 9.5 9.6 9.6 9.6
Table 6: Lower limits at 95% CL on the SSM W′ mass. The first column is the decay channel (eν, µν or both combined) and the following columns give the expected (Exp.) and observed (Obs.) mass limits. mW′ [TeV] Exp. Obs. eν 2.17 2.08 µν 2.08 1.98 both 2.23 2.15 References
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A. Aloisio102a,102b, R. Alon171, A. Alonso79, M.G. Alviggi102a,102b, K. Amako66, P. Amaral29, C. Amelung22, V.V. Ammosov128, A. Amorim124a,b, G. Amor´os167, N. Amram153, C. Anastopoulos29, L.S. Ancu16, N. Andari115, T. Andeen34, C.F. Anders20, G. Anders58a, K.J. Anderson30, A. Andreazza89a,89b, V. Andrei58a, M-L. Andrieux55, X.S. Anduaga70, A. Angerami34, F. Anghinolfi29, N. Anjos124a, A. Annovi47, A. Antonaki8, M. Antonelli47,
A. Antonov96, J. Antos144b, F. Anulli132a, S. Aoun83, L. Aperio Bella4, R. Apolle118,c, G. Arabidze88, I. Aracena143, Y. Arai66, A.T.H. Arce44, J.P. Archambault28, S. Arfaoui29,d, J-F. Arguin14, E. Arik18a,∗, M. Arik18a,
A.J. Armbruster87, O. Arnaez81, C. Arnault115, A. Artamonov95, G. Artoni132a,132b, D. Arutinov20, S. Asai155, R. Asfandiyarov172, S. Ask27, B. ˚Asman146a,146b, L. Asquith5, K. Assamagan24, A. Astbury169, A. Astvatsatourov52, G. Atoian175, B. Aubert4, E. Auge115, K. Augsten127, M. Aurousseau145a, N. Austin73, G. Avolio163, R. Avramidou9, D. Axen168, C. Ay54, G. Azuelos93,e, Y. Azuma155, M.A. Baak29, G. Baccaglioni89a, C. Bacci134a,134b, A.M. Bach14, H. Bachacou136, K. Bachas29, G. Bachy29, M. Backes49, M. Backhaus20, E. Badescu25a, P. Bagnaia132a,132b,
S. Bahinipati2, Y. Bai32a, D.C. Bailey158, T. Bain158, J.T. Baines129, O.K. Baker175, M.D. Baker24, S. Baker77, E. Banas38, P. Banerjee93, Sw. Banerjee172, D. Banfi29, A. Bangert137, V. Bansal169, H.S. Bansil17, L. Barak171, S.P. Baranov94, A. Barashkou65, A. Barbaro Galtieri14, T. Barber27, E.L. Barberio86, D. Barberis50a,50b, M. Barbero20, D.Y. Bardin65, T. Barillari99, M. Barisonzi174, T. Barklow143, N. Barlow27, B.M. Barnett129, R.M. Barnett14, A. Baroncelli134a, G. Barone49, A.J. Barr118, F. Barreiro80, J. Barreiro Guimar˜aes da Costa57, P. Barrillon115, R. Bartoldus143, A.E. Barton71, D. Bartsch20, V. Bartsch149, R.L. Bates53, L. Batkova144a,
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M. Cristinziani20, G. Crosetti36a,36b, R. Crupi72a,72b, S. Cr´ep´e-Renaudin55, C.-M. Cuciuc25a, C. Cuenca Almenar175, T. Cuhadar Donszelmann139, M. Curatolo47, C.J. Curtis17, P. Cwetanski61, H. Czirr141, Z. Czyczula117, S. D’Auria53, M. D’Onofrio73, A. D’Orazio132a,132b, P.V.M. Da Silva23a, C. Da Via82, W. Dabrowski37, T. Dai87, C. Dallapiccola84, M. Dam35, M. Dameri50a,50b, D.S. Damiani137, H.O. Danielsson29, D. Dannheim99, V. Dao49, G. Darbo50a,
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W. Fernando109, S. Ferrag53, J. Ferrando53, V. Ferrara41, A. Ferrari166, P. Ferrari105, R. Ferrari119a, A. Ferrer167, M.L. Ferrer47, D. Ferrere49, C. Ferretti87, A. Ferretto Parodi50a,50b, M. Fiascaris30, F. Fiedler81, A. Filipˇciˇc74, A. Filippas9, F. Filthaut104, M. Fincke-Keeler169, M.C.N. Fiolhais124a,i, L. Fiorini167, A. Firan39, G. Fischer41, P. Fischer20, M.J. Fisher109, S.M. Fisher129, M. Flechl48, I. Fleck141, J. Fleckner81, P. Fleischmann173,
S. Fleischmann174, T. Flick174, L.R. Flores Castillo172, M.J. Flowerdew99, M. Fokitis9, T. Fonseca Martin16,
D.A. Forbush138, A. Formica136, A. Forti82, D. Fortin159a, J.M. Foster82, D. Fournier115, A. Foussat29, A.J. Fowler44, K. Fowler137, H. Fox71, P. Francavilla122a,122b, S. Franchino119a,119b, D. Francis29, T. Frank171, M. Franklin57, S. Franz29, M. Fraternali119a,119b, S. Fratina120, S.T. French27, F. Friedrich43, R. Froeschl29, D. Froidevaux29, J.A. Frost27, C. Fukunaga156, E. Fullana Torregrosa29, J. Fuster167, C. Gabaldon29, O. Gabizon171, T. Gadfort24, S. Gadomski49, G. Gagliardi50a,50b, P. Gagnon61, C. Galea98, E.J. Gallas118, M.V. Gallas29, V. Gallo16, B.J. Gallop129, P. Gallus125, E. Galyaev40, K.K. Gan109, Y.S. Gao143,f, V.A. Gapienko128, A. Gaponenko14, F. Garberson175,
M. Garcia-Sciveres14, C. Garc´ıa167, J.E. Garc´ıa Navarro49, R.W. Gardner30, N. Garelli29, H. Garitaonandia105, V. Garonne29, J. Garvey17, C. Gatti47, G. Gaudio119a, O. Gaumer49, B. Gaur141, L. Gauthier136, I.L. Gavrilenko94, C. Gay168, G. Gaycken20, J-C. Gayde29, E.N. Gazis9, P. Ge32d, C.N.P. Gee129, D.A.A. Geerts105, Ch. Geich-Gimbel20, K. Gellerstedt146a,146b, C. Gemme50a, A. Gemmell53, M.H. Genest98, S. Gentile132a,132b, M. George54, S. George76, P. Gerlach174, A. Gershon153, C. Geweniger58a, H. Ghazlane135b, P. Ghez4, N. Ghodbane33, B. Giacobbe19a, S. Giagu132a,132b, V. Giakoumopoulou8, V. Giangiobbe122a,122b, F. Gianotti29, B. Gibbard24, A. Gibson158, S.M. Gibson29, L.M. Gilbert118, M. Gilchriese14, V. Gilewsky91, D. Gillberg28, A.R. Gillman129, D.M. Gingrich2,e, J. Ginzburg153, N. Giokaris8, M.P. Giordani164c, R. Giordano102a,102b, F.M. Giorgi15, P. Giovannini99, P.F. Giraud136, D. Giugni89a, M. Giunta93, P. Giusti19a, B.K. Gjelsten117, L.K. Gladilin97, C. Glasman80, J. Glatzer48, A. Glazov41, K.W. Glitza174, G.L. Glonti65, J. Godfrey142, J. Godlewski29, M. Goebel41, T. G¨opfert43, C. Goeringer81,
C. G¨ossling42, T. G¨ottfert99, S. Goldfarb87, T. Golling175, S.N. Golovnia128, A. Gomes124a,b, L.S. Gomez Fajardo41, R. Gon¸calo76, J. Goncalves Pinto Firmino Da Costa41, L. Gonella20, A. Gonidec29, S. Gonzalez172, S. Gonz´alez de la Hoz167, M.L. Gonzalez Silva26, S. Gonzalez-Sevilla49, J.J. Goodson148, L. Goossens29, P.A. Gorbounov95,
H.A. Gordon24, I. Gorelov103, G. Gorfine174, B. Gorini29, E. Gorini72a,72b, A. Goriˇsek74, E. Gornicki38, S.A. Gorokhov128, V.N. Goryachev128, B. Gosdzik41, M. Gosselink105, M.I. Gostkin65, I. Gough Eschrich163, M. Gouighri135a, D. Goujdami135c, M.P. Goulette49, A.G. Goussiou138, C. Goy4, I. Grabowska-Bold163,g, V. Grabski176, P. Grafstr¨om29, C. Grah174, K-J. Grahn41, F. Grancagnolo72a, S. Grancagnolo15, V. Grassi148, V. Gratchev121, N. Grau34, H.M. Gray29, J.A. Gray148, E. Graziani134a, O.G. Grebenyuk121, D. Greenfield129,
T. Greenshaw73, Z.D. Greenwood24,m, K. Gregersen35, I.M. Gregor41, P. Grenier143, J. Griffiths138, N. Grigalashvili65, A.A. Grillo137, S. Grinstein11, Y.V. Grishkevich97, J.-F. Grivaz115, J. Grognuz29, M. Groh99, E. Gross171,
J. Grosse-Knetter54, J. Groth-Jensen171, K. Grybel141, V.J. Guarino5, D. Guest175, C. Guicheney33, A. Guida72a,72b, T. Guillemin4, S. Guindon54, H. Guler85,n, J. Gunther125, B. Guo158, J. Guo34, A. Gupta30, Y. Gusakov65,
V.N. Gushchin128, A. Gutierrez93, P. Gutierrez111, N. Guttman153, O. Gutzwiller172, C. Guyot136, C. Gwenlan118, C.B. Gwilliam73, A. Haas143, S. Haas29, C. Haber14, R. Hackenburg24, H.K. Hadavand39, D.R. Hadley17, P. Haefner99, F. Hahn29, S. Haider29, Z. Hajduk38, H. Hakobyan176, J. Haller54, K. Hamacher174, P. Hamal113, A. Hamilton49, S. Hamilton161, H. Han32a, L. Han32b, K. Hanagaki116, M. Hance120, C. Handel81, P. Hanke58a, J.R. Hansen35, J.B. Hansen35, J.D. Hansen35, P.H. Hansen35, P. Hansson143, K. Hara160, G.A. Hare137, T. Harenberg174, S. Harkusha90, D. Harper87, R.D. Harrington21, O.M. Harris138, K. Harrison17, J. Hartert48, F. Hartjes105, T. Haruyama66, A. Harvey56, S. Hasegawa101, Y. Hasegawa140, S. Hassani136, M. Hatch29, D. Hauff99, S. Haug16, M. Hauschild29, R. Hauser88, M. Havranek20, B.M. Hawes118, C.M. Hawkes17, R.J. Hawkings29, D. Hawkins163, T. Hayakawa67, D Hayden76, H.S. Hayward73, S.J. Haywood129, E. Hazen21, M. He32d, S.J. Head17, V. Hedberg79, L. Heelan7, S. Heim88, B. Heinemann14, S. Heisterkamp35, L. Helary4, M. Heller115, S. Hellman146a,146b, D. Hellmich20, C. Helsens11, R.C.W. Henderson71, M. Henke58a, A. Henrichs54, A.M. Henriques Correia29, S. Henrot-Versille115, F. Henry-Couannier83, C. Hensel54, T. Henß174, C.M. Hernandez7, Y. Hern´andez Jim´enez167, R. Herrberg15, A.D. Hershenhorn152, G. Herten48, R. Hertenberger98, L. Hervas29, N.P. Hessey105, A. Hidvegi146a,
E. Hig´on-Rodriguez167, D. Hill5,∗, J.C. Hill27, N. Hill5, K.H. Hiller41, S. Hillert20, S.J. Hillier17, I. Hinchliffe14,
E. Hines120, M. Hirose116, F. Hirsch42, D. Hirschbuehl174, J. Hobbs148, N. Hod153, M.C. Hodgkinson139, P. Hodgson139, A. Hoecker29, M.R. Hoeferkamp103, J. Hoffman39, D. Hoffmann83, M. Hohlfeld81, M. Holder141, S.O. Holmgren146a, T. Holy127, J.L. Holzbauer88, Y. Homma67, T.M. Hong120, L. Hooft van Huysduynen108, T. Horazdovsky127,
C. Horn143, S. Horner48, K. Horton118, J-Y. Hostachy55, S. Hou151, M.A. Houlden73, A. Hoummada135a, J. Howarth82, D.F. Howell118, I. Hristova15, J. Hrivnac115, I. Hruska125, T. Hryn’ova4, P.J. Hsu175, S.-C. Hsu14, G.S. Huang111, Z. Hubacek127, F. Hubaut83, F. Huegging20, T.B. Huffman118, E.W. Hughes34, G. Hughes71, R.E. Hughes-Jones82, M. Huhtinen29, P. Hurst57, M. Hurwitz14, U. Husemann41, N. Huseynov65,o, J. Huston88, J. Huth57, G. Iacobucci49, G. Iakovidis9, M. Ibbotson82, I. Ibragimov141, R. Ichimiya67, L. Iconomidou-Fayard115, J. Idarraga115, M. Idzik37, P. Iengo102a,102b, O. Igonkina105, Y. Ikegami66, M. Ikeno66, Y. Ilchenko39, D. Iliadis154, D. Imbault78, M. Imhaeuser174, M. Imori155, T. Ince20, J. Inigo-Golfin29, P. Ioannou8, M. Iodice134a, G. Ionescu4, A. Irles Quiles167, K. Ishii66,
![Figure 3: Normalized cross section limits (σ limit /σ SSM ) for W ′ → ℓν as a function of mass for this measurement and from CDF [2], CMS [3] and the previous ATLAS search [4]](https://thumb-eu.123doks.com/thumbv2/123doknet/14041307.459009/8.892.85.426.334.652/figure-normalized-section-limits-function-measurement-previous-atlas.webp)
