Limits on the production of the standard model Higgs boson in pp collisions at √ s = 7 TeV with the ATLAS detector

A search for the Standard Model Higgs boson at the Large Hadron Collider (LHC) running at a centre-of-mass energy of 7 TeV is reported, based on a total integrated luminosity of up to 40 pb − 1 collected by the ATLAS detector in 2010. Several Higgs boson decay channels: H → γ γ , H → ZZ ( ∗ ) → (cid:4)(cid:4)(cid:4)(cid:4) , H → ZZ → (cid:4)(cid:4)νν , H → ZZ → (cid:4)(cid:4)qq , H → WW ( ∗ ) → (cid:4)ν(cid:4)ν and H → WW → (cid:4)νqq ( (cid:4) is e, μ ) are combined in a mass range from 110 GeV to 600 GeV. The highest sensitivity is achieved in the mass range between 160 GeV and 170 GeV, where the expected 95% CL exclusion sensitivity is at Higgs boson production cross sections 2.3 times the Standard Model prediction. Upper limits on the cross section for its production are determined. Models with a fourth generation of heavy leptons and quarks with Standard Model-like couplings to the Higgs boson are also investigated and are excluded at 95% CL for a Higgs boson mass in the range from 140 GeV to 185 GeV.


Introduction
The search for the Standard Model Higgs boson [1][2][3] is one of the key aims of the Large Hadron Collider (LHC) at CERN. Prior to the LHC, the best direct information is a lower limit of 114.4 GeV, set using the combined results of the four LEP experiments [4], and an excluded band of 158 GeV to 173 GeV from the combined Tevatron experiments [5,6]. First results from the ATLAS experiment are available in various Standard Model Higgs boson search channels [7][8][9][10][11]. There are also results from the CMS collaboration [12] in the H → WW ( * ) → ν ν 1 channel which have a sensitivity similar to the equivalent search reported here. These results are based on proton-proton collision data collected in 2010 at a centre-of-mass energy of √ s = 7 TeV. This paper combines the results from the different Higgs boson searches to obtain the overall sensitivity to a Standard Model Higgs boson with the 2010 ATLAS dataset.
All analyses use the most detailed calculations available for the cross sections, as discussed in Sect. 3. The searches in individual Higgs boson decay channels H → γ γ , H → WW ( * ) and H → ZZ ( * ) are outlined in Sects. 4, 5, and 6, respectively. The statistical interpretation uses the profilelikelihood ratio [13] as test-statistic. Thirty-one Higgs boson masses, in steps of 10 GeV from 110 GeV to 200 GeV (plus 115 GeV in addition) and 20 GeV from 200 GeV to 600 GeV, are tested. Exclusion limits are obtained using the power constrained CL sb limit [14], as discussed in Sect. 7. To allow for comparisons with the exclusion limits obtained by other experiments, the results are also determined using the CL s method [15]. The limits are presented in terms of σ/σ SM , the multiple of the expected Standard Model cross section at the Higgs boson mass considered. Results are also presented in terms of the corresponding ratio where the cross section in the denominator includes the effects of a fourth generation of heavy leptons and quarks with Standard Model-like couplings to the Higgs boson. Section 8 describes the treatment of the major sources of systematic uncertainty in the combined likelihood. The limits for individual channels and the combined results are detailed in Sect. 9 and the conclusions are drawn in Sect. 10.

The ATLAS detector
The ATLAS experiment [16] is a multipurpose particle physics apparatus with forward-backward symmetric cylindrical geometry covering |η| < 2.5 for tracks and |η < 4.5 for jets. 2 The inner tracking detector (ID) consists of a sili-con pixel detector, a silicon microstrip detector (SCT), and a transition radiation tracker (TRT). The ID is surrounded by a thin superconducting solenoid providing a 2 T magnetic field, and by high-granularity liquid-argon (LAr) sampling electromagnetic calorimeters. An iron-scintillator tile calorimeter provides hadronic coverage in the central rapidity range. The end-cap and forward regions are instrumented with LAr calorimetry for both electromagnetic and hadronic measurements. The muon spectrometer (MS) surrounds the calorimeters and consists of three large superconducting toroids, each with eight coils, a system of precision tracking chambers, and detectors for triggering.
The data used in this analysis were recorded in 2010 at the LHC at a centre-of-mass energy of 7 TeV. Application of beam, detector, and data-quality requirements results in a total integrated luminosity of 35 to 40 pb −1 depending on the search channel, with an estimated uncertainty of ±3.4% [17]. The events were triggered either by a single lepton or a pair of photon candidates with transverse momentum (p T ) thresholds which were significantly below the analysis offline requirements. The trigger introduces very little inefficiency except in one channel, H → WW → νqq, where there are efficiency losses in the muon channel of about 16%.
Electron and photon candidates are reconstructed from energy clusters recorded in the liquid-argon electromagnetic calorimeter. The clusters must have shower profiles consistent with those expected from an electromagnetic shower. Electron candidates are matched to tracks reconstructed in the inner detector, while photon candidates require either no track or an identified conversion candidate. Muon candidates are reconstructed by matching tracks found in the inner detector with either tracks or hit segments in the muon spectrometer. Details of the quality criteria required on each of these objects differ amongst the analyses discussed here. There are in addition isolation criteria which again depend upon the specific backgrounds relevant to each analysis.
Jets are reconstructed from topological clusters [18] in the calorimeter using an anti-k t algorithm [19] with a radius parameter R = 0.4. They are calibrated [18,20] from the electromagnetic scale to the hadronic energy scale using p T and η dependent correction factors based on Monte Carlo simulation and validated on data. They are required to have a p T greater than 25 GeV unless otherwise stated. B tagging is performed using a secondary vertex algorithm based upon the decay length significance. A selection requirement is set to describe a jet as 'b-tagged' which has a 50% efficiency for true b-jets. The missing transverse energy is reconstructed z-axis coinciding with the axis of 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). from topological energy clusters in the ATLAS calorimeters, with corrections for measured muons.

Search for the standard model Higgs boson
At the LHC, the most important Standard Model Higgs boson production processes are the following four: gluon fusion (gg → H ), which couples to the Higgs boson via a heavy-quark triangular loop; fusion of vector bosons radiated off quarks (qq → qqH ); associated production with a vector boson (qq → WH/ZH); associated production with a top-quark pair (qq/gg → ttH ). The current calculations of the production cross sections have been gathered and summarised in Ref. [21].
Higher-order corrections have been calculated up to nextto-next-to-leading order (NNLO) in QCD for the gluon fusion [22][23][24][25][26][27], vector boson fusion [28] and associated WH/ZH production processes [29], and to next-to-leading order (NLO) for the associated production with a tt pair [30,31]. In addition, QCD soft-gluon resummations up to nextto-next-to-leading log (NNLL) are available for the gluon fusion process [ The total signal production cross section in pp collisions at √ s = 7 TeV, multiplied by the branching ratio for the final states considered in this paper, is summarised in Fig. 1 as a function of the Higgs boson mass. Sources of uncertainties on these cross sections include missing higher-order corrections, imprecise knowledge of the parton distribution functions (PDFs) and the uncertainty on the strong force coupling constant, α s . These uncertainties are treated according to the recommendations given in Refs. [21,[42][43][44][45] and are ±(15-20)% for the gluon fusion process, ±(3-9)% for the vector boson fusion process and ±5% for the associated WH/ZH production process. Fig. 1 The cross section multiplied by decay branching ratios for Standard Model Higgs boson production in pp collisions at a 7 TeV centre-of-mass energy as a function of mass [21]. All production modes are summed, and only final states considered in this paper are shown. Two bands are shown for each curve; the inner represents the QCD scale uncertainty and the outer also includes the α s and PDF uncertainty

Higgs boson search in fourth generation models
Models with a fourth generation of heavy leptons and quarks with Standard Model-like couplings to the Higgs boson enhance its production cross section in gluon fusion by a factor of 4 to 10 compared to the predicted rate with three generations [46][47][48][49]

Search for H → γ γ
The search for the Higgs boson in the γ γ decay mode is described below; further details can be found in Ref. [7]. The event selection requires the presence of at least two identified photons [63], including converted photons, isolated from any other activity in the calorimeter. The leading and the sub-leading photons are required to have transverse momenta above 40 GeV and 25 GeV, respectively. The directions of the photons are measured using the position determined in the first sampling of the electromagnetic calorimeter and that of the reconstructed primary vertex. The diphoton invariant mass spectrum is used to search for a peak above the background contributions.
The main background processes in the H → γ γ search arise from the production of two isolated prompt photons (γ γ ) and from fake photons in photon-jet (γj ) and di-jet (jj ) events. Fake photons can originate from jets in which a leading π 0 or η meson from the quark or gluon fragmentation is reconstructed as a single isolated photon. Each of these background contributions has been estimated from sideband control samples in the data. The backgroud from Drell-Yan events, Z/γ * → ee, where the electrons are mistakenly identified as photons, is estimated from studies of the Z boson mass peak and extrapolated to the signal region. The total number of estimated background events is constrained to be the observed number. The di-photon invariant mass distribution for the events passing the full selection is shown in Fig. 2. The full-width at half maximum of a signal with m h = 120 GeV would be 4.2 GeV.
The expected signal yield, summing all production processes, and estimated background composition for a total integrated luminosity of 38 pb −1 are summarised in Table 1. A total of 99 events passing all selection criteria are observed in data in the di-photon mass range from 100 GeV to 150 GeV. The background in this region is modelled by fitting an exponential function to the data. The signal peak is modelled by a Gaussian core portion and a power-law low-end tail [64]. Tails in the signal resolution are modelled Fig. 2 Distribution of the di-photon invariant mass for the 99 events from data passing all event selection criteria in the H → γ γ search and for the Monte Carlo prediction. The overall uncertainty on the expected total yield is illustrated by the yellow band. The uncertainty due to the reducible background is also shown (dark yellow band). The predictions for the main components of the background (di-photon, photon-jet, jet-jet and Drell-Yan) are also illustrated Table 1 The number of expected and observed events in the H → γ γ search in the di-photon mass range from 100 GeV to 150 GeV for an integrated luminosity of 38 pb −1 . Also shown is the composition of the background expected from Monte Carlo simulation and the division of the observed data as discussed in the text as well as the expected number of H → γ γ signal events for a Higgs boson mass of m H = 120 GeV. Total uncertainties are shown in the middle column while in the rightmost column the statistical and systematic uncertainties, respectively, are given by a wide Gaussian component of small amplitude. No significant excess of events over the continuous background is found for any Higgs boson mass. The systematic uncertainty on the total signal acceptance is ±15%, where the dominant contributions come from photon identification (±11%) and photon isolation efficiencies (±10%).

Search for H → WW
The search for the Higgs boson in the decay channel H → WW benefits from the large branching ratio of the Higgs boson to decay into a pair of W bosons for masses above m H 110 GeV, the sizable W boson decay rates to leptons and the powerful identification of leptons with the ATLAS detector. It offers the greatest sensitivity of any search channel when the Higgs boson mass is close to twice the W boson mass, m H ∼ 165 GeV. Two different decay modes of the W bosons are considered: the H → WW ( * ) → ν ν channel is pursued for Higgs boson masses in the range from 120 GeV to 200 GeV, and the H → WW → νqq decay mode is used for Higgs boson masses in the range from 220 GeV to 600 GeV. The analyses are described below and further details can be found in Refs. [8,9].
The H → WW ( * ) → ν ν analysis is performed using a dataset corresponding to an integrated luminosity of 35 pb −1 . Events are selected requiring exactly two isolated leptons with opposite charge. The leading lepton is required to have p T > 20 GeV and the sub-leading lepton is required to have p T > 15 GeV. Events are classified into three channels depending on the lepton flavours: eμ, ee or μμ. If the two leptons are of the same flavour, their invariant mass (m ) is required to be above 15 GeV to suppress background from Υ production. To increase the sensitivity, the selections are then allowed to depend on the Higgs boson mass hypothesis. For all lepton combinations in the low (high) mass Higgs boson search, m is required to be below 50 (65) GeV for Higgs boson masses m H ≤ 170 GeV (m H > 170 GeV) which suppress backgrounds from top-quark production and Z boson production. The missing transverse energy in the event is required to be E miss where E T = (P T ) 2 + m 2 , |P miss T | = E miss T and P T is the transverse momentum of the dilepton system. The transverse mass is required to be 0.75 · m H < m T < m H for the event to be considered in a given m H range. Events are also treated separately depending on whether they have zero jets (0-jet channel) or one jet (1-jet channel) reconstructed with |η| < 4.5 due to the differences in background composition and expected signal-to-background ratio. To suppress background from top-quark production, events in the 1-jet channel are rejected if the jet is identified as coming from a bquark. Events with two or more jets have been analysed as a separate channel. However, due to the marginal contribution to the overall sensitivity given the current total integrated luminosity and the additional systematic uncertainties, this channel is not included in this combination.
The expected background contributions from WW, topquark and W + jets production are normalised using dedicated control regions in data as described in the next sections. Other smaller backgrounds are normalised according to their theoretical cross sections. The background from Z/γ * + jets production is normalised to the theoretical cross section with a correction factor determined from data.

The WW background
The di-boson WW continuum can be distinguished from the Higgs boson signal through the kinematic selections. A control region is defined by changing the cut on m to require over 80 GeV (but not within 10 GeV of the Z boson mass if the leptons are of the same flavour) and removing the selections on m T and Δφ . The expected ratio of the background contribution in the control region and in the signal region is taken from Monte Carlo simulation. The three main sources of systematic uncertainty affecting this ratio are the theoretical uncertainty on the extrapolation, the jet energy scale uncertainty and the limited statistics in the simulated sample. Uncertainties due to these effects of ±6% in the 0-jet channel and ±17% in the 1-jet channel have been determined.

The tt and single top-quark backgrounds
Top-quarks, whether from strong interaction tt production or weak interaction single top-quark production, are a copious source of final states with one or two W bosons accompanied by one or more jets. Due to kinematic selection one or more of these jets may fail identification, thereby leading to a final state similar to that from the H → WW signal.
The background from top-quark production in the 0-jet channel is estimated by first removing the jet veto. This gives a sample dominated by top-quarks, and the expected contamination from other processes in the control region is subtracted from the observed event yield. Then the probability that top events pass the jet veto is derived from the measured probability of not reconstructing a jet in data, using a sample of top candidates with two leptons, one b-jet and no other jet. The dominant systematic uncertainties originate from the limited statistics in data and the jet energy scale. A total uncertainty of ±60% has been determined for the top-quark background estimate in the 0-jet channel.
The top-quark background in the 1-jet channel is normalised using a control region where the veto on jets coming from b-quarks is reversed and the Δφ , m and m T selections are removed. An extrapolation factor from the control region to the signal region is estimated from Monte Carlo simulation. The dominant systematic uncertainties on the top-quark background estimate in the 1-jet channel are ±23% from the theoretical uncertainties on the extrapolation factor and ±22% from the uncertainty on the b-tagging efficiency.

The W + jets background
The production of W bosons accompanied by jets can mimic the H → WW signal if one of the jets is mis-identified as an isolated lepton. The W + jets background is normalised using a control region defined by relaxing the identification and isolation criteria for one of the two leptons. The contribution to the signal region is estimated by multiplying the rate measured in the control region by the probability for fake leptons which pass the relaxed identification and isolation criteria to also pass the original lepton selection criteria. This misidentification probability is measured in a multi-jet data sample. The major sources of systematic uncertainty for the W + jets background estimate come from the bias introduced by the jet trigger threshold used to select the multi-jet events and the residual difference in kinematics and flavour composition of the jets in multi-jet events and in events from W + jets production. The total uncertainty on the estimated W + jets background is ±50%.

The Z/γ * + jets background
The largest cross section for producing two isolated, highp T leptons comes from the Z/γ * → process. The background from Z/γ * + jets is significantly reduced by the upper bound on m and the requirement of high E miss T in the signal region. To correct for potential mis-modelling of the distribution of E miss T at high values, a correction factor is derived from the observed difference between the fraction of events passing the E miss T > 30 GeV selection in data and Monte Carlo simulation for events with m within 10 GeV of the Z boson mass [41]. As the discrepancy between data and Monte Carlo tends to be larger in events with jets, the correction factor is larger in the 1-jet channel than in the 0-jet channel. The flavours of the two leptons in the event also impact the magnitude of the correction factor, since any discrepancies between data and simulation have different sources. In the 1-jet channel, the correction factors are found to be 1.2 ± 0.4 ± 0.1 3 in the ee analysis and 2.4 ± 0.5 ± 0.2 in the μμ analysis. Under the assumption that the same correction factors apply to events below the upper bound on m , the expected Z/γ * + jets background is obtained from the Monte Carlo simulation normalised to the product of the theoretical cross section and the correction factors.

Results for the H → WW ( * ) → ν ν search
The expected and observed numbers of events in the H → WW analysis for a Higgs boson mass of 170 GeV are shown in Table 2. Three events in total are observed in the 0-jet tt and single top 0.26 ± 0.07 ± 0.11 0.10 ± 0.02 ± 0.04 0.15 ± 0.04 ± 0.07 Observed 0 0 1 channel for the combined ee, eμ and μμ final states, compared to an expected number of events from background sources only of 1.70 ± 0.12 ± 0.17. More events are expected in the μμ channel compared to the ee channel due to different lepton identification efficiencies for electrons and muons. In the 1-jet channel, one event is observed in the data compared to a total number of expected events from background sources of 1.26 ± 0.13 ± 0.23. The observed m T distributions in data after all selections except the transverse mass cut for the combined eμ, ee and μμ channels are compared to the expected distributions from simulated events in Fig. 3.

Search for H → WW → νqq
The H → WW → νqq analysis uses a dataset corresponding to an integrated luminosity of 35 pb −1 . Events are selected requiring exactly one lepton with p T > 30 GeV. The missing transverse energy in the event is required to be E miss T > 30 GeV. Events with fewer than two jets are rejected. 4 Events with ≥ 4 jets are treated as a separate search channel, which is however not included in the current combination. The pair of jets with invariant mass closest to the W boson mass is considered to be coming from the W boson and the measured mass must be between 71 GeV and 4 In this channel the jet p T threshold is raised from 25 GeV to 30 GeV. 91 GeV. The event is rejected if any of the jets in the event is identified as coming from a b-quark. The invariant mass of the Higgs boson candidate, m νqq , is reconstructed with a W boson mass constraint on the lepton-neutrino system giving rise to a quadratic equation. If there are two solutions the one corresponding to the lower longitudinal momentum is taken; if complex the real part is used.
The dominant source of background events in the H → WW → νqq search comes from W + jets production. The contribution from QCD events is estimated by fitting the observed E miss T distribution as the sum of templates taken from simulation. Table 3 shows the expected numbers of signal and background events in the signal region, as well as the observation. In the channel with only two and no additional jets, 450 events are observed in the data passing all selection criteria compared to an expected yield from background sources of 450 ± 41 events. In the channel with one extra jet 263 events are observed, compared to an expected number of background events of 224 ± 15.
The distributions of the invariant mass for the Higgs boson candidates in data are compared to the expected distributions from simulated events in Fig. 4. The m νqq background spectrum is modelled with a falling exponential function. The impact of the functional form has been investigated by replacing the single exponential with a double exponential, by histograms taken from simulation, and by a mixture of both methods without significant change in the results. It should be noted that the limit extraction is made using the exponential fit, not by comparison with the simulated background.
search, the excellent energy and momentum resolutions of the ATLAS detector for electrons and muons lead to a narrow expected four-lepton invariant mass peak on top of a continuous background. The dominant background component is the irreducible ZZ ( * ) → process. In the low Higgs boson mass region, where one of the Z bosons is off-shell and decays into a pair of low transverse momentum leptons, the reducible backgrounds from Z + jets production and tt production are also important. For Higgs boson masses above m H 200 GeV both Z bosons are on-shell. In this region the decay modes H → ZZ → qq and H → ZZ → νν, which have substantially larger branching ratios but also larger backgrounds compared to the H → ZZ ( * ) → decay, provide additional sensitivity. The analyses of the H → ZZ → qq and H → ZZ → νν channels require that both Z bosons are on-shell, which limits the contribution from the reducible backgrounds from Z + jets production and tt production. In this paper the H → ZZ → qq and H → ZZ → νν search channels have been used for Higgs boson masses in the range 200 GeV ≤ m H ≤ 600 GeV, a range extending beyond the sensitivities of LEP and Tevatron experiments [4,6]. Further details of the three analyses can be found in Refs. [10, 11].

Search for H → ZZ ( * ) →
Candidate events are selected requiring two same-flavour and opposite-charge pairs of leptons. Muons with p T > 7 GeV and electrons with p T > 15 GeV are considered, while at least two out of the four leptons must satisfy p T > 20 GeV. All leptons are required to be well separated from each other, isolated from other activity in the tracking detectors and the calorimeters and have low track impact parameters with respect to the primary vertex. At least one of the lepton pairs is required to have an invariant mass within 15 GeV (within 12 GeV if the combined four-lepton mass is high) of the Z boson mass. The requirement on the invariant mass of the second lepton pair varies as a function of the Higgs boson candidate mass, m . The effective Higgs boson candidate mass resolution σ (m H ), including the intrinsic width at the Higgs boson mass hypothesis being tested, is used to define an allowed range for the reconstructed Higgs boson candidate mass. The latter is required to be within ±5σ (m H ) of the tested Higgs boson mass for the event to be considered.
The magnitude of the ZZ ( * ) background is normalised to the measured Z boson cross section multiplied by the expected ratio of the cross sections σ ZZ /σ Z from theoretical calculations [67]. This estimate is independent of the luminosity uncertainty, and the cross section ratio is less affected by theoretical uncertainties than the σ ZZ cross section alone. The total uncertainty on the ZZ ( * ) background estimate is ±15%. The reducible Z + jets background arises predominantly from Z boson production in association with a pair of heavy flavour quarks which decay semi-leptonically. This background is normalised using dedicated control regions in data where the lepton identification requirements are relaxed for the second pair of leptons. The final uncertainty on the Z + jets background is ±20%. The tt background is estimated from Monte Carlo simulation and normalised to its theoretical cross section. A total uncertainty of ±25% is estimated for the tt background contribution.
After the application of all selection criteria, no candidate events remain in data for the H → ZZ ( * ) → search at any Higgs boson mass. This is consistent with the small background and signal yields expected with the integrated luminosity of 40 pb −1 used in this analysis. The results are shown in Table 4  Events are selected requiring exactly two same-flavour leptons with an invariant mass 76 GeV < m < 106 GeV and at least two jets. To reduce background from top production the missing transverse energy is required to be E miss T < 50 GeV. The two jets in the event with the highest individual p T are required to have an invariant mass, m jj , in the range 70 GeV < m jj < 105 GeV. Additional background rejection is obtained for high mass by using the fact that the final state jets and leptons are boosted in the directions of the two Z bosons. For Higgs boson searches at m H ≥ 360 GeV, the two jets are required to have p T > 50 GeV. Furthermore, the azimuthal angles between the two jets, Δφ jj , and between the two leptons, Δφ , must both be less than π/2. The Higgs boson candidate mass is constructed from the invariant mass of the two leptons and the two jets in the event, m jj . The two jets are constrained to have an invariant mass equal to the Z boson mass to improve the Higgs boson candidate mass resolution.

Background estimates for the H → ZZ → qq search
The dominant background in the H → ZZ → qq search channel is expected to come from Z + jets production. Other significant sources are tt production, multi-jet production and ZZ/WZ production. All backgrounds, except for the multi-jet background, are estimated from Monte Carlo simulation. For the Z + jets and the tt backgrounds the predictions from simulation are compared against data in control samples which are dominated by these backgrounds. The Z + jets control region is defined by modifying the m jj selection to instead require 40 GeV < m jj < 70 GeV or 105 GeV < m jj < 150 GeV. The tt control region is defined by reversing the E miss T selection and modifying the m selection to require 60 GeV < m < 76 GeV or 106 GeV < m < 150 GeV. Both the Z + jets and the tt background estimates from Monte Carlo simulation are found to be in good agreement with data in the control samples. The contribution from W + jets is very small and assumed to be adequately modelled. The multi-jet background in the electron channel is derived from a sample where the electron identification requirements are relaxed. In the muon channel, the multi-jet background is taken from Monte Carlo after verifying the accuracy of the simulation using a data sample where the two muons in the event are required to have the same charge.

Results for the H → ZZ → qq search
The H → ZZ → qq analysis is performed for Higgs boson masses between 200 GeV and 600 GeV in steps of 20 GeV. Table 5 summarises the numbers of estimated background events and observed events in data for the selections below and above m H = 360 GeV. The numbers of expected signal events for two representative Higgs boson masses are also shown. For the low mass search, 216 events are observed in data passing all selection criteria compared to an expected number of events from background sources only of 226 ± 4 ± 28 events. The corresponding numbers for the high mass searches are 11 events observed in data compared to an expected yield of 9.9 ± 0.9 ± 1.5 events from background sources only. The distribution of the reconstructed Higgs boson candidate mass m jj for the events passing all of the selection criteria is shown in Fig. 6.

Search for H → ZZ → νν
The H → ZZ → νν final state is characterised by two charged leptons and large E miss T . Events are selected by requiring exactly two leptons of the same flavour with an invariant mass 76 GeV < m < 106 GeV. Events are rejected if any jet is identified as coming from a b-quark. The selection has been optimised separately for searches at low (m H < 280 GeV) and high (m H ≥ 280 GeV) values of the Higgs boson mass. Events are required to have E miss T > 66 (82) GeV and Δφ < 2.64 (2.25) radians for  GeV is also shown, multiplied by a factor of 20 for illustrative purposes. The contribution labelled "Other" is mostly from top events but includes also QCD multijet production the low (high) mass region. For the low mass region Δφ > 1 radian is also required. The Higgs boson candidate transverse mass is obtained from the invariant mass of the two leptons and the missing transverse energy.

Background estimates for the H → ZZ → νν search
A major background in the H → ZZ → νν search channel comes from di-boson production and is estimated from Monte Carlo simulation. Background contributions from tt and W + jets production are also obtained from Monte Carlo simulation, and the estimated yields are verified by comparing with the number of observed events in dedicated control samples in the data. Both the tt and the W + jets con-trol regions are defined by modifying the m selection to instead require 60 GeV < m < 76 GeV or 106 GeV < m < 150 GeV. The tt control region also requires that the events pass E miss T > 20 GeV and that at least one jet is identified as coming from a b-quark. The W + jets control region instead requires E miss T > 36 GeV and that no jets in the events are identified as coming from a b-quark. The observed event yields in the control regions for tt and W + jets production are in good agreement with the predictions from the Monte Carlo simulation. The background from Z + jets production is estimated from Monte Carlo simulation after comparison studies of the E miss T distribution between Monte Carlo and data. The multi-jet background in the electron channel is derived from a sample where the electron identification requirements are relaxed. In the muon channel, the multi-jet background is estimated from a simulated sample of semi-leptonically decaying b-and c-quarks and found to be negligible after the application of the m selection. This was verified in data using leptons with identical charges.

Results for the H → ZZ → νν search
The H → ZZ → νν analysis is performed for Higgs boson masses between 200 GeV and 600 GeV in steps of 20 GeV. Table 6 summarises the numbers of events observed in the data, the estimated numbers of background events and the expected numbers of signal events for two selected m H values. For the low mass selections, five events are observed in data compared to an expected number of events from background sources only of 5.8 ± 0.5 ± 1.3. The corresponding results for the high mass selections are five events observed in data compared to an expected yield of 3.5 ± 0.4 ± 0.8 events from background sources only. In addition to the H → ZZ → νν decays, several other Higgs boson channels give a non-negligible contribution to  Fig. 7.   Fig. 7 Distribution of missing transverse energy in the H → ZZ → νν search in the electron channel before vetoing events with low E miss T . The expected yield for a Higgs boson with m H = 400 GeV is also shown. The distribution in the muon channel is similar with four events seen which have E miss T above 80 GeV

Combination method
The limit-setting procedure uses the power-constrained profile likelihood method known as the Power Constrained Limit, PCL [13, 14, 68]. This method is preferred to the more familiar CL s [15] technique because the constraint is more transparently defined and it has reduced overcoverage resulting in a more precise meaning of the quoted confidence level. The resulting PCL median limits have been found to be around 20% tighter than those obtained with the CL s method in several Higgs searches. The application of the PCL method to each of the individual Higgs boson search channels is described in Refs. [7][8][9][10][11]. A similar procedure is used here. The individual analyses are combined by maximising the product of the likelihood functions for each channel and computing a likelihood ratio. A single signal normalisation parameter μ is used for all analyses, where μ is the ratio of the hypothesised cross section to the expected Standard Model cross section.
Each channel has sources of systematic uncertainty, some of which are common with other channels. Table 7 lists the common sources of systematic uncertainties, which are taken to be 100% correlated with other channels. Let the search channels be labelled by l (l = H → γ γ , H → WW, . . . ), the background contribution, j , to channel l by j l and the systematic uncertainties by i (i = luminosity, jet energy scale, . . . ). The relative magnitude of the effect on the Higgs boson signal yield in channel l due to systematic uncertainty i is then denoted by s li , and on background contribution j l , b jli . The li 's are constants; an individual s li can be zero if the channel in question is not affected by this source of systematic uncertainty. A common systematic uncertainty, i, which is shared between channels l and l implies that s li and s l i are both different from zero. If a systematic source i is shared between the signal in channel l and background contribution j l then both s li and b jli are non-zero. For each source of systematic uncertainty i there is a corresponding nuisance parameter δ i and an associated auxiliary measurement m i on a control sample (e.g. sidebands in a mass spectrum) that is used to constrain the parameter. The δ i and m i are scaled so that δ i = 0 corresponds to the nominal expectation and δ i = ±1 corresponds to the ±1σ variations of the source. When constructing ensembles for statistical evaluation, each m i is sampled according to G(m i |δ i , 1), the standard normal distribution. Using this notation, the total number of expected events in the signal region for channel l is given by: for luminosity L, Standard Model cross sections σ l (including efficiencies and acceptances), and expected backgrounds b jl . Background estimates b jl may come either from Monte Carlo simulations or from control regions in which the expected number of events,n jl , is proportional to the expected background, via b jl = α jlnjl . Given the number of observed events in the signal region N obs l , the likelihood function can be written as: where n jl are the observed numbers of background events in the control regions and Pois(x|y) is the Poisson probability of observing x events given an expectation y. The combined likelihood is given by the product of the individual likelihoods for each channel: where l is implicitly an index over the individual histogram bins within the channels that used a binned distribution of a discriminating variable.
The profile likelihood ratiõ is computed by maximising the likelihood function twice: in the numerator μ, the ratio of the hypothesised cross section to the expected Standard Model cross section, is restricted to a particular value and in the denominator μ is allowed to float. The set of all nuisance parameters δ i andn jl is denoted θ . The maximum likelihood estimates of μ and θ are denotedμ andθ , whileθ(μ) denotes the conditional maximum likelihood estimate of all nuisance parameters with μ fixed. In this analysis the range of μ is restricted to the physically meaningful regime, i.e. it is not allowed to be negative. The test statisticq μ is defined to bẽ Monte Carlo pseudo-experiments are generated to construct the probability density function f (q μ |μ,θ(μ)) under an assumed signal strength μ, giving a p-value To find the upper limit on μ at 95% confidence level, μ up , μ is varied to find p μ up = 5%. Similarly, background-only Monte Carlo pseudo-experiments are used to find the median μ med along with the ±1σ and +2σ bands expected in the absence of a signal. The procedure so far can be referred to as a CL sb limit. To protect against excluding the (signal) null hypothesis in cases of downward fluctuations of the background, the observed limit is not allowed to fluctuate below the −1σ expected limit. This is equivalent to restricting the interval to cases in which the statistical power of the test of μ against the alternative μ = 0 is at least 16%. This is referred to as a Power Constrained Limit. If the observed limit fluctuates below the 16% power, the quoted limit is μ med − 1σ .

Systematic uncertainties in the combination
The systematic uncertainty related to the luminosity is ±3.4% and is fully correlated among all channels. It affects background estimates that are normalised to their theoretical cross sections; for most channels this is only true for backgrounds that are known to be small. In the H → ZZ → νν and H → ZZ → qq channels major backgrounds are normalised to their theoretical cross sections, but in the latter case this is only done after comparing with control regions. Sources of systematic uncertainty related to the event reconstruction are correlated between all the Higgs boson search channels. The uncertainty on the efficiency to reconstruct electrons varies between 2.5% (central high-p T elec-trons) and 16% (p T near 15 GeV, the lowest value used here) but it is assumed to be completely correlated. For muons the efficiency uncertainty ranges between 0.4% and 2%. The jet systematic errors are typically larger for the channels where jets are explicitly required. They are dominated by the jet energy scale as the resolution effects tend to partially cancel and the E miss T uncertainties are largely by-products of the uncertainties already discussed.
The effect on the signal yield in each channel of the major sources of systematic uncertainty is summarised in Table 7. Uncertainties are treated as either uncorrelated or 100% correlated among channels. The largest uncorrelated errors are photon isolation in H → γ γ and jet rates in H → WW ( * ) → ν ν; the latter is in principle correlated with the H → WW → νqq channel but these channels are never used in the same mass region. Most backgrounds have been estimated by means of independent control samples; these estimates are assumed to be uncorrelated between the channels.
Systematic uncertainties on the signal shape are accounted for in the H → γ γ , H → ZZ → qq and H → ZZ → νν channels by considering three possible distributions and interpolating between them. Small signal shape systematic uncertainties in the H → ZZ ( * ) → and H → WW → νqq channels are neglected. For m H ≥ 200 GeV the correlations in the shape systematics are taken into account and are treated as correlated with the signal normalisation uncertainties.
The width of the Higgs boson signal at high mass is taken from the PYTHIA Monte Carlo [53]. This underestimates the width and the accepted cross section is conservatively scaled down by the ratio of the widths given in Ref. [69], which reached a maximum of 8% at 600 GeV, in all plots showing a ratio to the Standard Model.
The systematic uncertainty coming from the total theoretical Higgs boson cross section is not included in the combination and is shown separately in the figures as an uncertainty on the predicted cross section.

Combination
Each Higgs boson search channel is only sensitive for a range of Higgs boson masses. The ranges in which the various channels have been analysed are detailed in Table 8.  In the H → γ γ , H → ZZ → νν and H → ZZ → qq channels, the final result is extracted from a fit of signal plus background contributions to the observed Higgs boson candidate mass distributions. In all other channels, limits are extracted from a comparison of the numbers of observed events in one or more signal regions to the numbers of estimated background events.
The individual channels are shown in Fig. 8 in terms of the observed and the expected upper limits on σ/σ SM at the 95% confidence level. The step with which the limit is extracted, 5-10 GeV, does not match the H → γ γ resolution which has a full-width at half maximum of 4.4 GeV. However, it was established in Ref.
[7] that no important fluctuations are missed.
The search channels are grouped by the primary Higgs boson decay mode searched for, γ γ , WW or ZZ, and the limit on each mode is extracted in terms of the cross section for the process intended. Some channels have a contribution from signal modes other then the intended one. This is only significant for the H → ZZ → νν search, as discussed in Sect. 6.3, and implies that the ZZ limit assumes the Standard Model ratio between H to ZZ and H to WW decays. In addition, the WW search requires zero or one jet and is essentially designed for a spin-zero object produced largely via gluon fusion. The upper limits at 95% confidence level observed and expected in the absence of a signal are compared with the cross section expected for a Standard Model Higgs boson in Fig. 9.   Fig. 9 The expected and observed 95% PCL limits on the total cross section of a particle produced like the Standard Model Higgs boson and decaying with the width predicted by PYTHIA[53] to pairs of bosons: γ γ , WW or ZZ. The limits are calculated at the masses marked with symbols. The lines between the points are to guide the eye. The coloured bands show the cross section predictions and their uncertainties, with the inner region highlighting the contribution of QCD scale uncertainties Fig. 10 The expected and observed upper limits on the total cross section divided by the expected Standard Model Higgs boson cross section. This is a 95% PCL limit. The green and yellow bands indicate the range in which the limit is expected to lie in the absence of a signal. The fine dotted line marks the results obtained using CL sb , and the application of the power constraint gives the solid line. The limits are calculated at the masses marked with symbols and the lines between the points are to guide the eye Table 9 The signal cross sections, in multiples of the Standard Model cross section, that are excluded, and expected to be excluded, at 95% CL. The expected variation at ±1σ is also given for the PCL limits. The bold numbers show the limit which should be used; for mass of 500 and 520 GeV the power constraint is applied. The likelihood ratio of signal plus background to background is also shown, as is the p-value (modified to go between 0 and 1) for μ = 0, which can be used to estimate the discovery significance  The point set at 500 GeV is at the limit allowed by the power constraint. The limits are calculated at the masses marked with symbols. The lines between the points are to guide the eye The combination of all channels is tested and the p μ=0 in these fits varies between 7% and 89%, which does not suggest the presence of a signal. The combination of all channels is shown in Fig. 10 in terms of the observed and the expected upper limit at the 95% confidence level. The statistical accuracy of the toy Monte Carlo used to extract the limits is about 5% on the observed limits and 7% on the expected ones, with somewhat larger variation on the edges of the one and two σ bands.
The excluded signal strength as a function of m H is summarised in Table 9, using the PCL method. The results are also calculated using the CL s method for comparison pur-poses: the extracted limits from both procedures are shown in Fig. 11. Also given is the profile likelihood ratio of a Standard Model Higgs boson to background only and the consistency of the data with the background-only hypothesis, p μ=0 .
The results have been interpreted in terms of the heavy mass fourth generation model introduced in Sect. 3. This involves rescaling the gluon fusion component of the production cross section and the Higgs boson decay branching ratios. The limits are shown in Fig. 12. This model is excluded for Higgs boson masses between 140 GeV and 185 GeV, while the region in which exclusion might be expected is between 136 GeV and 208 GeV.
The excluded cross section ratios are summarised in Table 10.

Conclusions
The ATLAS search for the Standard Model Higgs boson in the mass range from 110 GeV to 600 GeV in 35 to 40 pb −1 of data recorded in 2010 has been presented. With this luminosity there is not sufficient sensitivity to exclude the Standard Model Higgs boson, nor is there any evidence of an excess of events over the predicted background rates. However, these results give the most stringent constraints to date for Higgs boson masses above 250 GeV and are close to the Tevatron limits [6] at intermediate masses.
An extension of the Standard Model, assuming the Higgs mechanism and adding a fourth generation of heavy quarks and leptons, is excluded for Higgs boson masses between 140 and 185 GeV.