Combined Standard Model Higgs boson searches … CMS PAS HIG-11-023 Combined Standard Model Higgs...

ATLAS-CONF-2011-157

CMS PAS HIG-11-023

Combined Standard Model Higgs boson searcheswith up to 2.3 fb−1 of pp collision data

at√

s = 7 TeV at the LHC

The ATLAS and CMS Collaborations

November 14, 2011

Abstract

A combination of searches for the Standard Model (SM) Higgs boson by the ATLASand CMS experiments at the LHC is presented. The dataset used corresponds to anintegrated luminosity per experiment ranging from 1.0 to 2.3 fb−1 of pp collisions ata centre-of-mass energy of 7 TeV. The combination includes searches using the fol-lowing Higgs boson decay signatures: H → γγ, H → bb, H → ττ , H → WW (`ν`ν)and H → ZZ(4`, 2`2ν, 2`2q, 2`2τ). The SM Higgs boson masses tested in thesesearches range from 110 to 600 GeV/c2. The expected exclusion region in the ab-sence of a signal is 124-520 GeV/c2. The observed data are compatible with thebackground-only hypothesis and the SM Higgs boson is excluded at 95% confidencelevel (C.L.) or higher in the mass range 141-476 GeV/c2. The region from 146to 443 GeV/c2 is excluded at 99% C.L., with the exception of three small regionsbetween 220 and 320 GeV/c2.

Contents

1 Introduction 3

2 Signal and background cross sections and simulations 32.1 Higgs cross sections and decay branching ratios . . . . . . . . . . . . . . . 32.2 Background cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Monte Carlo generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Search channels 73.1 Search channels used by the ATLAS experiment . . . . . . . . . . . . . . . 73.2 Search channels used by the CMS experiment . . . . . . . . . . . . . . . . 9

4 Uncertainties correlated between ATLAS and CMS 14

5 Combination procedure 175.1 Exclusion limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175.2 Quantifying an excess of events . . . . . . . . . . . . . . . . . . . . . . . . 18

6 Combined results 19

7 Conclusions 28

A Detector systematic uncertainties 29

B Additional plots 32

2

1 Introduction

The discovery of the mechanism for electroweak symmetry breaking is one of the key goalsof the physics programme at the Large Hadron Collider (LHC). In the Standard Model(SM), this is achieved by invoking what is known as the Higgs mechanism, leading to theprediction of the Higgs boson [1–6]. The Higgs boson mass, mH , is an unknown parameterin the SM, although weakly coupled to other observables. The direct experimental searchesfor this elusive particle have yielded negative results and limits1 on its mass have beenplaced by experiments at LEP, mH > 114.4 GeV/c2 [7], and the Tevatron, excludedin the 156-177 GeV/c2 range [8]. The ATLAS [9] and CMS [10] Collaborations havereported results on Higgs boson searches in Refs. [11,12]. Fits of the electroweak precisionmeasurements, not taking into account the direct search results, constrain indirectly, at95% C.L., the SM Higgs boson mass to be relatively light, mH < 161 GeV/c2 [13].

The results of the combination of the SM Higgs boson searches performed by the AT-LAS and CMS experiments as mentioned above are presented in this note. In addition,the combination includes the recent updates of the H → ττ search by the CMS experi-ment [14] and the H → ZZ → 2`2ν search by the ATLAS experiment [15]. The presentedcombination uses pp collision data at a centre-of-mass energy of 7 TeV with an integratedluminosity of up to 2.3 fb−1. The LHC instantaneous luminosity during the 2011 runningperiod has been rapidly increasing. The bulk of the data on which the current analysesare based was taken with a peak luminosity ∼ 2× 1033 cm−2s−1 and proton bunches col-liding every 50 ns. The average number of interactions per bunch crossing in this datasetis about six.

The structure of this note is as follows. In Section 2, the theoretical cross sections andbranching ratios together with the Monte Carlo (MC) generators used are summarised.Then, in Section 3, a brief overview of analyses entering the overall combination is given.In Section 4, a summary of systematic errors correlated between the ATLAS and CMSanalyses is presented. Discussion of the uncertainties specific to ATLAS or CMS can befound in Appendix A. An overview of the statistical procedure used in the combinationis reported in Section 5. The main results are presented in Section 6.

2 Signal and background cross sections and simula-

tions

2.1 Higgs cross sections and decay branching ratios

The SM Higgs boson production cross sections and decay branching ratios are compiledin the LHC Higgs Cross Section Group report [16]. For this combination, the parameterset given in Ref. [17] was used.

At the LHC, the most important SM Higgs boson production processes are: gluon fu-sion (gg → H), which annihilates to the Higgs boson through a triangular loop dominatedby heavy quarks; vector-boson fusion (qq′ → qq′H), where vector bosons are radiatedfrom quarks and couple to produce a Higgs boson; vector-boson associated production

1All limits quoted in this note are at 95% confidence level (C.L.) unless explicitly stated otherwise.

3

)2Higgs boson mass (GeV/c

100 200 300 400 500

BR

(pb)

× σ

-410

-310

-210

-110

1

10

LH

C H

IGG

S X

S W

G 2

01

1

= 7TeVs

µl = e,

τν,µν,eν = νq = udscb

bbν± l→WH

bb-l+ l→ZH

-τ+τ

γγ

qqν± l→WW

ν-lν

+ l→WW

qq-l+ l→ZZ

νν-l+ l→ZZ

-l+l

-l+ l→ZZ

Figure 1: The SM Higgs boson production cross sections multiplied by decay branchingratios in pp collisions at

√s = 7TeV as a function of Higgs boson mass. All final states

analysed in this note are shown, where all production modes are summed in the channelsof H → ττ , γγ or WW/ZZ(→ 4 fermions). In the H → bb channel, only the vector-bosonassociated production is considered.

(qq → WH/ZH), where the Higgs boson is radiated from a gauge boson; top-quark pairassociated production (qq/gg → ttH), where the Higgs boson is radiated from a topquark.

The Higgs boson production cross sections are calculated with varying precision inthe perturbative expansion. For the gluon-fusion process through a heavy-quark loop(gg → H), the QCD radiative corrections at next-to-leading order (NLO) were performedeither in the large-mt limit [18, 19], or by maintaining the full top- and bottom-quarkmass dependence [20]. These increase the leading-order (LO) cross section by about 80-100%. The next-to-next-to-leading-order (NNLO) QCD correction for the gluon-fusionprocess [21–23] was calculated in the large-mt limit, which leads to an additional 25%increase in the cross section. In addition, QCD soft-gluon resummations up to next-to-next-to-leading log (NNLL) improve the NNLO calculation [24]. The NLO electroweak(EW) corrections are applied [25, 26] assuming factorisation with the QCD corrections.In recent calculations [27–29], accurate theoretical predictions are performed with exacttop- and bottom-loop corrections up to NLO, and with the large-mt approximation ofthe higher-order corrections. The gg → H cross section used in this analysis is thecombination of the NNLO QCD [27] and the NNLL QCD [28] predictions (both with exacttop/bottom-loop corrections up to NLO) together with NLO EW corrections from [26] asdescribed in Section 13 of Ref. [16].

The vector-boson fusion (VBF) process involves quark and anti-quark initial states

4

(qq′ → qq′H) for electroweak Higgs boson production at LO, with full NLO EW andQCD corrections [30, 31] and NLO QCD MC [32]. The EW and QCD corrections areboth important, being of the order of 5-10%. Approximate NNLO QCD correctionshave been presented using the structure-function approach [33] and the scale uncertaintyreduces to 1-2%. The Higgs boson WH and ZH production modes (qq → WH/ZH),referred to as Higgs-strahlung, have been calculated at NLO [34] and later at NNLO [35].QCD corrections are calculated via the Drell-Yan process [36]. The NLO EW radiativecorrections [37] are applied assuming the full QCD and EW factorisation. The full NLOQCD corrections to the tt associated Higgs boson production (qq/gg → ttH) have beencalculated [38–41], resulting in a moderate increase in the total cross section by at most20% compared to LO.

The Higgs boson decay branching ratios take into account the recently calculatedhigher-order QCD and EW corrections in each Higgs boson decay mode. The Higgsboson decay width and branching ratios are calculated with hdecay [42]. For most four-fermion final states the predictions by prophecy4f [43, 44] which include the completeNLO QCD+EW corrections with all interference and leading two-loop heavy Higgs bosoncorrections to the four-fermion width are used. The total SM Higgs boson signal produc-tion cross sections multiplied by the branching ratios for the final states analysed in thispaper are shown in Fig. 1.

The choice of factorisation and renormalisation scales is process-dependent and is spec-ified for each Higgs boson production process in Ref. [16]. The QCD scale uncertaintiesare +12

−7 % for the gluon-fusion process, ±1% for the vector-boson fusion process, ±1% forthe associated WH/ZH production process and +4

−10% for the associated ttH productionprocess. The theoretical and parametric uncertainties for the Higgs boson decay branch-ing ratios [45] are small compared to the production cross section uncertainties, and aregenerally neglected in the current study.

Parton Distribution Functions (PDFs) are crucial for the prediction of Higgs bosonproduction processes, hence PDFs and their uncertainties are of particular significance.At present these PDFs are obtained from fits to data from Deep-Inelastic Scattering,Drell-Yan processes, and jet production from a wide variety of different experiments. Anumber of groups have produced publicly available PDFs using different datasets andanalysis frameworks. The PDF4LHC working group’s [46] interim recommendation [47]was implemented to obtain the current combined predictions and uncertainties basedon several global PDF sets. For NLO calculations, CTEQ6.6 [48], MSTW2008 [49] andNNPDF2.0 [50] are used as the default sets. Others, e.g. HERAPDF1.0 [51], ABKM [52]and GJR [53] were also used to cross check the results. For NNLO, the MSTW2008 resultis the default set.

In addition to experimental uncertainties on PDFs determined in the global fits, the-oretical uncertainties due to the QCD coupling constant αs and heavy-quark masses (mc

and mb), and the uncertainties related to the truncation of the perturbative expansionmay enter. The uncertainty on αs has been explored systematically by the PDF workinggroups. The total PDF+αs uncertainty is evaluated by adding the variations in the PDFsdue to the uncertainty in αs in quadrature with the fixed-αs PDF uncertainty. For theNLO calculation, the envelope provided by the central values and PDF+αs errors fromthe MSTW2008, CTEQ6.6 and NNPDF2.0 PDFs is defined. For the NNLO calculation,

5

the MSTW2008 uncertainty at NNLO was multiplied by the factor obtained from theenvelope at NLO. The PDF+αs uncertainty amounts to ±8% for gg-dominant Higgs bo-son production processes (gg → H, qq/gg → ttH) and ±4% for qq-dominant processes(qq′ → qq′H, qq → WH/ZH).

The current searches for a heavy Higgs boson assume on-shell (stable) Higgs bosonproduction. The Higgs boson is then decayed via an ad hoc Breit-Wigner (either fixed-width or running-width scheme) implemented in the MC simulations. Recent studiesshow that the effects due to off-shell Higgs boson production and decay, and due tothe interference with the SM backgrounds, may become sizable for Higgs boson massesmH > 300 GeV/c2 [54–56]. The Higgs boson mass line shape is expected to be altered aswell. Following the recommendation by the LHC Higgs Cross Section working group [57],

an additional theoretical uncertainty of (150%)×(

mH

TeV/c2

)3

on the total cross section has

been included. This amounts to about ±10 (30)% uncertainty for mH = 400 (600) GeV/c2

and should effectively cover the possible uncertainties in both the Higgs boson event yieldand the line shape in different theoretical schemes.

2.2 Background cross sections

Most of the backgrounds in the signal regions are derived from measurements in controlregions (“data-driven” methods). The extrapolation to the signal region relies on MCsimulations and the related theoretical uncertainty is usually estimated by comparingdifferent MC generators and by varying the QCD scale. Whenever possible, not onlythe normalisation but also the parametrisation of the background shape is taken fromthe control region. The corresponding uncertainty is usually dominated by the limitedstatistics in the data sample.

There are backgrounds for which theoretical predictions are relied upon. The mainexamples are the di-boson backgrounds where data control regions can not be used due tothe limited size of the data sample available. See Section 3 for details of the backgroundestimations in each signal channel.

The following programs are used to determine the background cross sections: mcfm [58]for vector-boson pair production and several other processes at NLO, fewz [59, 60] forW and Z boson production at NNLO and hathor [61] for the approximate NNLO QCDcalculation of top-pair production. The theoretical uncertainty is estimated by varyingthe QCD scale and PDF following the prescription of Refs. [16,47].

2.3 Monte Carlo generators

For the Higgs boson signal and SM background simulation, a wide variety of event genera-tors are used in the analyses contributing to this combination: pythia [62], herwig [63],(jimmy [64] simulates the underlying events in herwig) and sherpa [65] are used forgeneral purpose and parton-shower MC simulations. Recent progress in MC calcula-tions enables the simulation of many processes at NLO accuracy via mc@nlo [66, 67]and powheg [68–72]. Reweighting of the Higgs pT spectrum is carried out using theNLO+NNLL distribution computed by the hqt program [73]. Matrix element generatorsare also widely used via alpgen [74], madgraph [75] and acermc [76]. The gg2ww [77]

6

and gg2zz [78] programs are used for gluon-induced di-boson pair production processes.photos [79] is used for QED radiative corrections in the final-state, and tauola [80]for the simulation of τ decays. Finally, the generated signal events are fed through thegeant4-based detector simulations [81].

3 Search channels

The basic information about the analyses used in the combination is given in Table 1.The total number of independent signal search sub-channels is 67; 47 sub-channels inthe low mass range (e.g. mH = 115 GeV/c2) and 30 in the high-mass range (e.g.mH = 400 GeV/c2) are combined. The middle mass range (e.g. mH = 180 GeV/c2)has contributions from only the H → WW → 2`2ν and H → ZZ → ```` channels(` = e, µ); here, only the 17 independent sub-channels are combined. In the next two sub-sections, the search analyses of the ATLAS and CMS experiments are briefly described.Only the main analysis features, such as the discriminating variables considered and es-timation methods for the main backgrounds, are summarised here. More details can befound in the references provided in the summary Table 1 and in the next two sub-sections.

3.1 Search channels used by the ATLAS experiment

• H → γγ [82]: This analysis is carried out for Higgs boson mass hypotheses between110 and 150 GeV/c2. Selected events are separated into five independent channels,with fully correlated systematics, based on the direction in which each photon wasemitted (hence with different detector resolution and signal-to-background ratios)and whether or not it is reconstructed as a photon conversion. The background isestimated from an unbinned fit of the di-photon invariant mass spectrum, which isthe sole discriminant used in the definition of the test statistic.

• H → ττ [83, 84]: This search is performed as a counting analysis for Higgs bosonmass hypotheses between 110 and 150 GeV/c2, in the H → ττ → `+`− + 4ν andH → ττ → `τhad3ν channels. These events are triggered by the presence of a lepton.They are required to have two high-pT leptons and a jet with transverse momentumthat exceeds 20 GeV/c2 in the fully leptonic τ -final state and one high-pT leptonin the semi-leptonic τ -final state. The resulting boost of the Higgs boson impliesa large missing transverse energy Emiss

T in the event, which, when combined withthe presence of high-pT jets in the VBF topology, allows for a good discriminationagainst background processes such as Z/γ∗→ ``, Z → ττ and QCD multi-jet events.The boost of the Higgs boson also increases the efficiency of the cut on the fractionsof undetected momentum in the collinear approximation [83, 84], which are in turnimportant to define the kinematic selection. In the case of H → ττ → `τhad3ν,events with an additional lepton are removed to suppress the Z/γ∗ → `+`− andtt background processes. The W → `ν background is suppressed by requiringthe transverse mass of the lepton and missing energy system to be smaller than30 GeV/c2.

7

The main background in this analysis is the Z/γ∗ → τ+τ− process. Its invariantmass shape is estimated using an embedding technique where muons from Z → µµevents are substituted by simulated τ decays. The top-quark pair production andall other backgrounds are taken from simulation, except for the QCD backgroundwith jets faking leptons which is estimated within an independent control sample.

• H → bb [85]: The WH (`νbb) and ZH (`+`−bb) analyses search for the Higgs bosonin the mass range between 110 and 130 GeV/c2. In the `νbb channel, the dominantbackgrounds arise from top-quark production and W+jets. The contribution fromthe multi-jet, top and W+jets backgrounds is determined by a simultaneous tem-plate fit to data control regions. The small contribution from other backgroundsis subtracted before fitting. The top and W+jets templates are determined fromMC simulation. The discriminant is the invariant mass distribution of the bb pairs.In the `+`−bb channel, the dominant background comes from Z+jets productionand is estimated using a data control region for normalisation and simulation fora shape template. Other sources of background are estimated by simulation. Thebackground coming from top production was also checked in the sidebands of thedi-lepton invariant mass distribution.

• H → WW (∗) → `ν`ν [86]: This search is performed as a counting analysis forHiggs boson mass hypotheses between 110 and 300 GeV/c2. The main backgroundcontributions are estimated from the data using control regions. Nine bins of thesecontrol regions are explicitly included in the analysis in addition to signal regions.The analysis is separated into 0- and 1-jet channels (the two or more jets channelis not included in this combination). To suppress the background from top-quarkproduction in the 1-jet channel, events are rejected if the jet is tagged as originatingfrom a b-quark (b-tagged) [87].

The systematic uncertainty on the WW background estimate is mainly due to thelow number of events in data control regions and to the uncertainty on the extrap-olation from theoretical scale variations and jet energy scale uncertainties. Thereare significant uncertainties considered on the top-quark background in both the0-jet and 1-jet channels (the latter is mostly due to the uncertainty on the b-taggingefficiency). The other backgrounds such as W+jets, Z/γ∗+jets, albeit significantlysmaller, are also measured in data control samples. The small WZ and ZZ back-grounds are taken from simulation. The transverse mass distributions are usedas discriminants. The event selection is optimised in three mass regions (below170 GeV/c2 between 170 and 220 GeV/c2, and above 200 GeV/c2) with differentsignal and background control regions. The τ polarisation is taken into account inthe simulation of the background processes (such as WW , tt and Z+jets produc-tion).

• H → ZZ(∗) → ```` [88]: This search is performed for Higgs boson mass hypothe-ses in the range from 110 to 600 GeV/c2, selecting three distinct final states: 4µ,2e2µ and 4e. The main background in this search is continuum ZZ(∗) production,and is estimated from simulation using MCFM [58] for the normalisation. Thereducible Z+jets background is estimated from data control regions, while the top-

8

quark background is estimated from the simulation, with verification from the data.The final discriminating variable is the 4-lepton invariant mass. All detector andluminosity-related systematic uncertainties are taken to be fully correlated betweensignal and background.

• H → ZZ → ``νν [15, 89]: This analysis is carried out for the 200 to 600 GeV/c2

range of Higgs boson mass hypotheses, and divided into a high (≥ 280 GeV/c2) anda low mass region. This search is orthogonal to the H → WW (∗) → `ν`ν searchby design. The main background to this search at high transverse mass valuesis di-boson production, ZZ, WWand WZ, and the corresponding normalisationuncertainty is taken from theory. Normalisation uncertainties for Z+jets, W+jets,top and QCD multi-jet production are estimated from data. The final discriminatingvariable is the transverse mass of the di-lepton plus missing momentum system,where the missing momentum is assumed to originate from a Z boson decay.

• H → ZZ → ``qq [90]: This analysis is performed for Higgs boson mass hypothe-ses in the 200 to 600 GeV/c2 range, divided into two regions: below and above300 GeV/c2. The final state is separated into two categories: the tagged analysiswhere the two jets are b-tagged and the untagged analysis where at most one of thejets is b-tagged. The dominant background in this analysis is Z+jets production,which is normalised from a control region defined by the sidebands of the di-jetmass distribution. The other backgrounds are estimated from the simulation, andverified with data control samples for the top-quark background. The di-lepton anddi-jet invariant mass is used as the final discriminant and its shape is estimatedusing simulation for both the signal and the backgrounds.

3.2 Search channels used by the CMS experiment

• H → γγ [91]: This analysis is carried out for Higgs boson mass hypotheses between110 and 150 GeV/c2. A narrow peak is searched for in the di-photon invariant massdistribution, dominated by experimental resolution on a large falling backgroundspectrum. The data are split into eight categories based on the three binary per-mutations of whether or not: (1) the transverse momentum of the di-photon systempγγ

T > 40 GeV/c; (2) both photon candidates are in the barrel detector; (3) bothphotons pass a cut selecting predominantly non-converted photons. The analysisis performed in an unbinned fashion. The background is estimated from the fitsto the observed di-photon invariant mass spectra; hence, the main uncertainties onthe background predictions are statistical. Corrections to the photon efficiencies,energy scales, and energy resolutions are inferred from studying Z → ee events andusing MC simulation to account for differences in the detector response to electronsand photons.

• H → ττ [14]: This analysis is carried out for Higgs boson mass hypotheses between110 and 140 GeV/c2. An excess of events is searched for in the visible mass mvis

ττ

distributions of e + τhad, µ + τhad and e + µ final states, each of which is furthersubdivided into two: with two VBF-like jets or not. The visible mass is built

9

from the measured momenta of the electrons, muons, and hadronically decayingτ ’s and does not attempt to recover the momentum carried away by neutrinos. Atopological cut based on the transverse momentum vectors of the two leptons and themissing transverse energy Emiss

T is applied to exploit the fact that the boosted visibleτ -decay products and neutrinos tend to be collinear. The six mass distributionsare binned and the entire shape is used in the statistical analysis. The dominantirreducible background in this analysis is Z → ττ production. The other threemain backgrounds are electroweak (W (`ν)+jets, Z(``)+jets), tt, and QCD, in whichone or both leptons are fakes. The Z → ττ shape is taken from MC, while itsnormalisation is constrained by Z → `` measurements and by the fit of the mvis massshape distribution. The W (`ν)+jets and QCD backgrounds are estimated using twocontrol samples: one with the topological cut inverted and another with same-signdi-lepton events. The normalisations for the Z(``)+jets (important for the eτ -channel), tt and di-boson backgrounds are taken from corresponding control sampleswithout τ -leptons and scaling them by the probabilities for electrons, muons, andjets to fake τ -leptons as measured directly from data.

• H → bb [92]: CMS searches for the associated production of the Higgs bosonwith W or Z bosons with the Higgs boson decaying to bb pairs. The analysis iscarried out for Higgs boson mass hypotheses between 110 and 135 GeV/c2. Thefollowing five final states are included: W (µν)H(bb), W (eν)H(bb), Z(µµ)H(bb),Z(ee)H(bb) and Z(νν)H(bb). CMS requires two b-tagged jets with di-jet transversemomentum pT > 100 GeV/c for the Z(``)H(bb) channel and > 150 GeV/c for theothers. One requires the missing transverse energy Emiss

T > 80 GeV for W (`ν) finalstates and > 150 GeV for Z(νν). The analysis is based on a cutting and countingapproach, where the cut is on a multivariate analysis (MVA) discriminant. The mainbackgrounds (Z+jets, W+jets, tt, QCD) are derived using data-driven techniques,by inverting some of the event selection requirements (e.g. b-tagging and m``). Theelectroweak di-boson W +Z(bb) and Z +Z(bb) backgrounds are evaluated from MCpredictions.

• H → WW (∗) → `ν`ν [93]: This search is performed for Higgs boson mass hy-potheses between 110 and 600 GeV/c2. Events with two oppositely charged leptonsand large missing energy arising from neutrinos in W -decays are searched for. Tosuppress the tt background, events with b-tagged jets and additional soft muons arerejected. To suppress the Z+jets background, events with same-flavour di-leptonsforming an invariant mass consistent with mZ are discarded. Events are classifiedby the presence of 0, 1, or 2 jets with pT > 30 GeV/c and |η| < 5.0. The 0- and1-jet bin categories are further split into same-flavour and different-flavour leptongroups, making a total of four categories. A simple cutting and counting approach isused for events in each of the five categories. After all selection cuts are applied themain backgrounds are the W+W− continuum, tt, Drell-Yan, and W+jets. The mainbackgrounds are evaluated using data-driven techniques (except for the W+W− con-tinuum in the high-mass range for the Higgs boson). The WZ/ZZ backgrounds,negligible in this analysis, are taken from simulation.

• H → ZZ(∗) → ```` [94]: This search is carried out for Higgs boson mass hypotheses

10

in the 110 to 600 GeV/c2 range using an unbinned approach. The analysis is per-formed in three sub-channels: 4e, 4µ, 2e2µ. The dominant irreducible backgroundis electroweak pp → ZZ(∗) production. The mass shape for this background and itsnormalisation are known at NLO and further corrected to include the contributionof gg → ZZ(∗) → ````, calculated at leading order. To reduce systematic uncertain-ties associated with luminosity and lepton reconstruction/identification efficiencies,the ZZ(∗) background is estimated by scaling the observed numbers of Z events inthe 2e- and 2µ-channels by the ratio of the ZZ(∗) and Z production cross sections.The reducible backgrounds Z+jets (including heavy flavour jets) and tt are evalu-ated from the data, relying on the inversion of the isolation and impact parametercuts—their contribution is estimated to be negligible.

• H → ZZ → 2`2τ [95]: The range of Higgs boson masses probed in this search isbetween 180 and 600 GeV/c2. The analysis is based on selecting the following eightfinal states: Z(``) + τhadτhad, Z(``) + eτhad, Z(``) + µτhad, Z(``) + eµ, where theZ(``) stands for ee and µµ pairs forming a di-lepton invariant mass m`` consistentwith the Z boson mass, while the other pair of leptons should have an invariantvisible mass 40 < mvis

ττ < 80 GeV/c2. The presence of the Higgs boson is expected tomanifest itself as a relatively broad peak over the continuum four-lepton visible massdistribution composed of reducible and irreducible backgrounds. The irreducibleZZ background is evaluated using simulation and theoretical cross sections (NLOZZ and gg → ZZ). The reducible backgrounds from Z+jets, WZ+jets, tt andQCD multi-jet production are not negligible in this search and are estimated alltogether using a data-driven method by counting events with relaxed τ identificationrequirements and scaling the observed event rates by the probability of a looselydefined τ to pass the tight selection criteria. This loose-to-tight probability is alsoassessed directly from data using QCD multi-jet events.

• H → ZZ → ``νν [96]: The analysis in this channel is carried out in the 250 to600 GeV/c2 range of Higgs boson mass hypotheses. This search is performed usinga cut-and-count approach and two sub-channels: 2e2ν, 2µ2ν. The two leptons arerequired to form an invariant mass within ±15 GeV/c2 of mZ . Cuts on the missingtransverse energy Emiss

T , the transverse mass mT and the azimuthal opening anglebetween the transverse missing energy and the jet ∆φ(Emiss

T , Jet), are applied tosuppress a huge reducible background of Z+jets. The transverse missing energy, mT ,and ∆φ(Emiss

T , Jet) cuts depend on the Higgs boson mass being searched for. To helpsuppress the tt and single-top backgrounds, events with b-tagged jets are vetoed.The ZZ and WZ backgrounds are taken from simulation. The WZ backgroundcross section is calculated at NLO. The Z+jets background has a very large crosssection which is suppressed by the analysis cuts with an efficiency O(10−5). Toestimate the remaining rate of Z+jets events, one relies on a data-driven techniquetaking advantage of the fact that the Z(``)+jets and γ+jets processes are veryclosely related, while the latter has a much higher observable event yield. The non-resonant backgrounds, i.e. those without any Z-boson (mostly tt and WW ), arealso derived from data, taking advantage of non-resonant backgrounds giving e±µ∓

events in addition to e+e− and µ+µ− final states.

11

• H → ZZ → ``qq [97]: This search is carried out for Higgs boson masses in the225 to 600 GeV/c2 range. The Higgs boson search in the channel H → ZZ → 2`qqproceeds by searching for a peak in the invariant mass of the di-lepton plus di-jetsystem m2`2q. The width of the peak is affected by the jet energy resolution andis improved by constraining the di-jet invariant mass mjj to the Z boson mass.Events are categorised in exclusive channels according to the lepton flavour (ee andµµ) and the number of b-tagged jets (zero, one, or two b-tagged jets). Furtherbackground rejection is achieved by exploiting the different angular distribution ofthe Higgs boson signal with respect to background and applying a quark-jet/gluon-jet discriminator in the category with no b-tagged jets. To help suppress the ttbackground in the category with two b-tagged jets a cut on the missing transverseenergy significance is also used. The statistical analysis is based on the m2`2q massdistributions using an unbinned maximum likelihood fit. The background shapeand normalisation are determined from data using the m2`2q distribution in thesidebands obtained by inverting the mjj requirement. The signal shape is describedby a relativistic Breit-Wigner convolved with a Crystal-Ball function determinedfrom simulation. The signal reconstruction efficiency and the resolution functionsare parametrised as functions of the hypothetical Higgs boson mass.

12

Tab

le1:

Sum

mar

yin

form

atio

non

the

anal

yse

sin

cluded

inth

eco

mbin

atio

n(`

=e,

µ).

Cha

nnel

Exp

erim

ent

mH

rang

eLum

iN

umbe

rof

Typ

eR

efer

ence

(GeV

/c2)

(fb−

1)

sub-

chan

nels

ofan

alys

is

H→

γγ

AT

LA

S11

0–15

01.

15

mas

ssh

ape

(unb

inne

d)[8

2]C

MS

110–

150

1.7

8m

ass

shap

e(u

nbin

ned)

[91]

H→

ττ

AT

LA

S11

0–15

01.

15

mas

ssh

ape

(bin

ned)

[83,

84]

CM

S11

0–14

01.

66

mas

ssh

ape

(bin

ned)

[14]

H→

bbA

TLA

S11

0–13

01.

02

mas

ssh

ape

(bin

ned)

[85]

CM

S11

0–13

51.

15

cutt

ing

and

coun

ting

[92]

H→

WW→

`ν`ν

AT

LA

S11

0–30

01.

76

cutt

ing

and

coun

ting

[86]

CM

S11

0–60

01.

54

cutt

ing

and

coun

ting

[93]

H→

ZZ→

````

AT

LA

S11

0–60

02.

0-2.

33

mas

ssh

ape

(bin

ned)

[88]

CM

S11

0–60

01.

73

mas

ssh

ape

(unb

inne

d)[9

4]

H→

ZZ→

2`2τ

CM

S18

0–60

01.

18

mas

ssh

ape

(unb

inne

d)[9

5]

H→

ZZ→

2`2ν

AT

LA

S20

0–60

02.

02

mT

shap

e(b

inne

d)[1

5,89

]C

MS

250–

600

1.6

2cu

t&co

unt

[96]

H→

ZZ→

2`2q

AT

LA

S20

0-60

01.

02

mas

ssh

ape

(bin

ned)

[90]

CM

S22

5–60

01.

66

mas

ssh

ape

(unb

inne

d)[9

7]

13

4 Uncertainties correlated between ATLAS and CMS

The treatment of the systematic uncertainties is an essential part of the overall combina-tion of the search results. The details of the chosen methodology for treating systematicuncertainties, characterised by nuisance parameters, in the statistical analysis presentedcan be found in Ref. [98]. Below, the most relevant points are highlighted.

From mass point to mass point, the number of channels used in the combination varies,as does the total number of independent nuisance parameters. The number of nuisanceparameters is 268 in the mass range below 135 GeV/c2. In the high mass range above250 GeV/c2, it is reduced to 191.

All systematic uncertainties can be classified in two main categories: those expected tobe correlated between the ATLAS and CMS experiments and those specific to individualexperiments. In this section, uncertainties in the former category are summarised. Theuncertainties tracked independently within each experiment are discussed in Appendix A.The full list of uncertainties that are correlated between ATLAS and CMS are shown inTable 2. Quantities affected by these uncertainties are all positive-definite and their sys-tematic uncertainties are modelled with log-normal probability density functions (pdfs).

The top block in Table 2 defines nuisance parameters used for modelling systematicuncertainties associated with the uncertainties in partonic luminosities, or PDFs, and αs.Any physics process whose rate is derived using a theoretical cross section and detectorsimulation is assigned one of the three nuisance parameters based on whether its pre-dominant production at LO is initiated by gg, gq or qq pair interactions. Examples aregiven in the column labelled “Affected Processes”. The absolute scale of uncertainties forprocesses within one group are not necessarily the same, but they are taken to be 100%correlated.

The next block of systematic uncertainties are theoretical uncertainties associated withmissing higher-order corrections. These are typically assessed by varying QCD renormal-isation and factorisation scales up and down by some appropriate factor (usually 2 or 3)and, hence, are known as QCD scale uncertainties. Theoretical uncertainties for differentphysics processes are assumed to be independent of each other. The only exceptions are afew processes involving W and Z bosons (e.g., pp → WH and pp → ZH) for which “QCDscale” uncertainties are thought to be strongly correlated and, therefore, are assigned acommon nuisance parameter.

The PDF+αs uncertainties for different Higgs boson production mechanisms and dif-ferent Higgs boson masses are provided by the LHC Higgs Cross Section and PDF4LHCworking groups [16, 47]. PDF uncertainties for the SM processes, often within analysis-specific acceptances, are calculated separately by the ATLAS and CMS groups. The sameis applicable to the “QCD scale” uncertainties: those associated with the Higgs boson pro-duction come from the LHC Higgs Cross Section group, while those for SM backgroundprocesses are computed within experiments and have been checked for consistency. Uncer-tainties on branching ratios [45] are typically very small in comparison to the productioncross section uncertainties and are neglected in the majority of the analyses entering thecombination presented here.

Theoretical uncertainties on the acceptance of analysis cuts, due to both QCD scalesand PDFs, are typically small in comparison to those on the total cross sections and are

14

thus often neglected. The important exceptions are theoretical uncertainties associatedwith the exclusive production modes with 0, 1, and 2 jets, where such an approximation isnot valid. Such a split into exclusive n-jet states is encountered in the H → WW → `ν`νanalysis. The procedure adopted for an evaluation of uncertainties on the exclusive gg →H + n-jet states is described in detail in Ref. [98] and is endorsed by the LHC HiggsCross Section group. The acceptance uncertainties associated with the event selectionin the different jet multiplicity bins in the H → WW → `ν`ν search are rather small,but, nevertheless, are explicitly included in both the ATLAS and CMS statistical modelsand hence made correlated in this combination. There could be some common modellinguncertainties affecting the WW channel in ATLAS and CMS in the same way, such asDrell-Yan, Wγ with asymmetric γ conversion, etc (these are not considered in the presentcombination).

Splitting of the final states in the H → WW → `ν`ν search according to the numberof jets makes this analysis sensitive to underlying event (UE) and parton showering (PS)modelling. The two collaborations used the same event generators (POWHEG interfacedto PYTHIA) for signal simulation. Therefore, one expects that uncertainties associatedwith the UE and PS phenomenological models are strongly correlated between the twocollaborations. Therefore, the UE/PS uncertainties were 100% correlated between theH → WW → `ν`ν analyses of the two experiments.

The probability of a loosely defined lepton to fake a lepton passing the final highquality selection is assessed by ATLAS and CMS using virtually identical methods. Alarge component of the uncertainty in this method comes from differences between jetsassociated with W bosons and those produced in generic di-jet and γ-jet events. There-fore, the uncertainties on fake lepton rates may be strongly correlated between the twoexperiments. The uncertainties are taken to be 100% correlated to be conservative.

The ATLAS and CMS luminosity uncertainties of 3.7% (ATLAS) and 4.5% (CMS),respectively, have substantial uncorrelated contributions. However, for the sake of sim-plicity and at the cost of being conservative, they are assumed to be 100% correlated inthe current combination.

15

Tab

le2:

Syst

emat

icunce

rtai

nties

corr

elat

edbet

wee

nth

eAT

LA

San

dC

MS

anal

yse

sco

ntr

ibuti

ng

toth

ecu

rren

tco

mbin

atio

n.

Eac

hline

corr

espon

ds

toon

ein

dep

enden

tnuis

ance

par

amet

er.

Vst

ands

for

Wan

dZ

bos

ons.

Sour

ceA

ffect

edP

roce

sses

Typ

ical

unce

rtai

nty

PD

Fs+

αs

gg→

H,tt

H,gg→

VV

±8

%(c

ross

sect

ions

)V

BF

H,V

H,V

V@

NLO

±4

%H

ighe

r-or

der

tota

lin

clus

ive

gg→

H+

12%

−7%

unce

rtai

ntie

sin

clus

ive

“gg”→

H+≥

1je

ts±

20%

oncr

oss

incl

usiv

e“g

g”→

H+≥

2je

ts±

20%

(NLO

),±

70%

(LO

)se

ctio

nsV

BF

H±

1%

asso

ciat

edV

H±

1%

ttH

+4

%−

10

%

unce

rtai

ntie

ssp

ecifi

cto

high

mas

sH

iggs

boso

n,se

eSe

ctio

n2.

1±

30%

V±

1%

VV

upto

NLO

±5

%gg→

VV

±30

%tt

,in

cl.

sing

leto

ppr

oduc

tion

sfo

rsi

mpl

icity

±6

%ac

cept

ance

acce

ptan

cefo

rH→

WW→

`ν`ν

even

ts±

2%ph

enom

enol

ogy

mod

ellin

gof

unde

rlyi

ngev

ent

and

part

onsh

ower

ing

±10

%fa

kele

pton

prob

abili

ty(W

+je

ts→

``fake)

±40

%lu

min

osit

ies

AT

LA

San

dC

MS

unce

rtai

ntie

son

thei

rlu

min

osity

mea

sure

men

ts±

3.7

%,±

4.5

%

16

5 Combination procedure

The primary software package used for producing the combined ATLAS and CMS results isRooStats [99]. The combination procedure used in this note follows closely that describedin the LHC Higgs Combination Group report [98]. Below, only a short summary is given.

5.1 Exclusion limits

The primary technique for deriving exclusion limits is based on the so-called CLs pre-scription [100–102], which is used with the profile likelihood test statistic qµ [103]:

qµ = −2 lnL(data|µ, θµ)

L(data|µ, θ), with a constraint 0 ≤ µ ≤ µ, (1)

where the parameter µ is the signal strength modifier, µ=σ/σSM , and θ represents thefull suite of nuisance parameters. The maximum likelihood estimates or best-fit-valuesof µ and θ are denoted µ and θ, while θµ denotes the conditional maximum likelihoodestimate of all nuisance parameters with µ fixed. In the evaluation of CLs the range of µis restricted to the physically meaningful regime, i.e. it is not allowed to be negative.

The likelihood is given by the product of the individual likelihoods for each channel

L(data |µ, θ) = Poisson ( Ni|µ · si(θ) + bi(θ) ) · p(θ | θ) . (2)

Here “data” is either the actual experimental observation or pseudo-data used to constructsampling distributions. The symbols Ni, si and bi represent the observed, expected signal,and expected background rates in bin i. Poisson (Ni |µ · si(θ) + bi(θ) ) stands for theoverall Poisson probability to observe Ni events given the expected event rate µ · si(θ) +bi(θ), with the understanding that some analyses are unbinned and use the extendedlikelihood formalism. The probabilities p(θ | θ) encode information about the systematicuncertainties.

Following a frequentist methodology, MC pseudo-experiments are generated includingpseudo-measurements of the nuisance parameters θ to construct the pdfs:

• fµ(qµ |µ, θobsµ ) under an assumed signal strength µ with a given background strength

and the corresponding best-fit nuisance parameters θobsµ , given the observed data;

• fb(qµ | 0, θobs0 ) for the background-only hypothesis (µ = 0) and the corresponding

best-fit nuisance parameters θobs0 , given the observed data.

The CLs value is calculated as the ratio of two probabilities:

CLs(µ) =P (qµ ≥ qobs

µ |µ, θobsµ )

P (qµ ≥ qobsµ | 0, θobs

0 ). (3)

If CLs < 0.05 for µ = 1, the SM Higgs boson with a nominal production rate is said tobe excluded at 95% C.L.

The main results obtained with the procedure described above are supplemented withlimits obtained with the asymptotic approximation following the prescription given in

17

Ref. [103]. This method has the advantage of reducing the computing time immensely.With increasing integrated luminosity, the asymptotic calculations are expected to becomeas accurate as CPU-intensive computations that generate pseudo-data. Such convergenceis ensured by the choice of the test statistic as given in Eq. (1).

The results obtained with the Bayesian approach are also given, based on the marginal-isation of nuisance parameters and assuming a flat prior for the signal strength parameterµ. This provides one more general check and, more importantly, allows us to validate thestability of the results obtained in the frameworks of different statistical paradigms.

5.2 Quantifying an excess of events

To quantify an excess of events, one uses the test statistic q0, defined as follows:

q0 = −2 lnL(data|0, θ0)

L(data|µ, θ), if µ ≥ 0, and q0 = 0 otherwise. (4)

This test statistic is known to have the proper χ2 distribution in the asymptoticlimit, which allows us to evaluate significances (Z) and p-values (p0) from the followingasymptotic formula:

Z =√

qobs0 , (5)

p0 = P (q0 ≥ qobs0 ) =

∫ ∞

Z

e−x2/2

√2π

dx =1

2

[1− erf

(Z/√

2)]

. (6)

Due to a significant look-elsewhere effect (LEE) inevitable in a search for a signal in avery broad mass range, the observed minimum local p-value pmin

0 (and the correspondingmaximum significance Zmax) may be misleading. The evaluation of this effect is a complexissue and more than one method was investigated with similar results; the approachdescribed here follows the prescription outlined in Ref. [98]. The global probability pglobal

0

to observe pmin0 , or lower, is estimated by counting the number of times the observed

q0(mH) crosses over (in one direction) some low threshold line2. Equivalently, instead ofusing q0(mH), one uses µ(mH), fitted freely without the constraint µ ≥ 0, and counts thenumber of up-crossings N0 at the level µ = 0. This gives the best statistical precision ofthe estimated global probability [104]:

pglobal0 ∼ pmin

0 + N0 e−12

Z2max . (7)

2This is a reasonable procedure when it is not practical to generate global pseudo-experiments underthe background-only hypothesis.

18

6 Combined results

The combined results of the SM Higgs boson searches performed by the ATLAS and CMSexperiments are presented in Figs. 2-18, and summarised in Tables 3-6.

Figure 2 shows the CLs value for the Standard Model Higgs boson hypothesis as afunction of the Higgs boson mass in the range 110-600 GeV/c2. The observed valuesare shown by a solid line. The dashed black line indicates the median expected for thebackground-only hypothesis, while the green (yellow) bands indicate the ranges expectedto contain 68% (95%) of the limit excursions from the median. The three red horizontallines show confidence levels of 90%, 95%, and 99% defined as (1− CLs).

The SM Higgs boson is excluded at 95% C.L. in the mass range 141-476 GeV/c2,which substantially extends the exclusion limits established by LEP and Tevatron. Theexpected exclusion in the absence of a signal is 124-520 GeV/c2, which extends to lowermasses than the observed limits. The difference is further discussed below in this section.

The combined 95% C.L. upper limits on the signal strength modifier µ as a functionof the Higgs boson mass are presented in Fig. 3. This plot shows the factor by whichthe SM Higgs boson cross section must be scaled to be excluded at 95% C.L. The filledpoints show the observed CLs limits calculated by generating pseudo-data as describedin Section 5. By construction, the exclusion range (µ ≤ 1) for the SM Higgs bosonis identical to that shown in Fig. 2 (CLs < 0.05). The plots in Figs. 2 and 3 exhibitthe same pattern of observed versus expected variations since these results are different“representations” of the same information. However, due to the strong dependency ofCLs on µ and the different scales used, the oscillations with µ ∼ 1 for Higgs boson massesaround 138 GeV/c2 and 245 GeV/c2 are magnified in Fig. 2 with respect to Fig. 3.

A detailed description of how the theoretical uncertainties are taken into account andtreated can be found in the combination procedural report [98]. To get an estimate ofthe impact of theoretical uncertainties on the obtained limits, the limits on the signalstrength modifier µ are evaluated with all theoretical and phenomenological uncertaintieson the signal and backgrounds (when not derived from data) turned off. The differencesin the limits on µ are approximately 3-6% in the entire Higgs boson mass range, exceptfor very large masses where it changes by as much as 20% at the highest tested massmH = 600 GeV/c2 as shown in Fig. 18. This is due to the large systematic uncertaintieson the Higgs boson cross section and mass line shape assigned for high mass Higgs bosons(see Section 2). In the absence of theoretical uncertainties, the expected exclusion limitswiden by 1 GeV/c2 at the low mass end and by 20 GeV/c2 at the high mass end.

The impacts of correlated jet energy scale and b-tagging uncertainties were alsochecked. This test is motivated by an observation that there are some commonalitiesin how these uncertainties are assessed in the two experiments. The level of correlationsis believed to be small and, hence, the default setting is that these uncertainties are notcorrelated. However, a test was done to see how the expected limits would change if thesetwo uncertainties were 100% correlated between the experiments. The differences in limitson µ were found to be very small, < 1% at high masses and < 4% below 250 GeV/c2.The consequences of such correlations for the reported excluded mass range are thereforenegligible.

At masses above 170 GeV/c2, there are modest upward and downward modulations

19

of the observed limits with respect to the expected ones. Modulations of this scale areconsistent with statistical fluctuations of the background. The excursion of the observedlimits on µ from the expected median value is larger in the mass range below 170 GeV/c2.

Figure 4 shows a scan of the observed combined local p-value p0 as given by Eq. (6)vs. Higgs boson mass mH , p0(mH). This scan characterises how unlikely the observedvalues of the test statistic qobs

0 approximately are, assuming the predicted backgroundand no signal. The ATLAS-only and CMS-only results are shown with symbols, whilethe ATLAS and CMS combination is given by a solid line without symbols 3. One cansee that the p-value curve dips downward over a broad range of low masses and alsohas a higher “frequency” component in its shape. This structure is mostly driven bythe broad excesses observed in the ATLAS and CMS WW analyses, with the narrowerfeatures corresponding to the 4` events and excursions in the γγ limits. Note that theH → WW → 2`2ν analyses have a very poor mass resolution and, therefore, any excessin this channel is bound to give a broad excursion. The H → ZZ → 4` mass peak isexpected to be very narrow with a large signal-to-background ratio. Therefore, the p-valuescan with the current dataset is expected to show sharp variations.

The minimum local p-value is pmin0 ∼0.001, which corresponds to a maximum local

significance of Zmax = 3.1. The global probability to obtain a minimum local p-value pmin0

as low as or lower than the observed one is further assessed below.A small p-value characterises the chance of an upward fluctuation of the estimated

background, but it does not tell whether such an excess would actually be consistent withthe expected signal or not. The dashed line in Fig. 4 shows the median expected p-valueat a given test mass mH , if a hypothesised SM Higgs boson of that mass had been presentin data. For instance, one observes a small p-value at mH ∼ 160 GeV/c2 with significanceof about 2σ, whereas a SM Higgs boson with that mass would be expected to produce amuch smaller p-value with a significance greater than 5σ. In other words, even thoughone sees an excess in this mass range, one can still exclude the SM Higgs boson with itsnominal properties. Note that the dashed curve as a whole should not be compared tothe observed p0(mH) curve.

The bottom panel in Fig. 4 shows the best-fit µ value (without the µ ≥ 0 constraint )that represents the factor by which the SM Higgs boson cross section has to be rescaled tomake the best match to the observed data. The µ scan over the entire search mass rangeallows one to approximately assess the scale of the look-elsewhere effect. The number ofup-crossings N0 of the µ(mH) curve with the level µ = 0 is six . Hence, following Eq. (7),the global p-value to observe an excess somewhere in the full mass range as high as seenin the actual data is pglobal

0 ∼0.001+6·e−3.12/2=0.05, which corresponds to an approximateglobal significance of Zglobal=1.6σ for the largest deviation of data with respect to theexpected background.

3It is worthwhile noting that the combined p-value is not a simple product of p-values obtained byeach experiment. The combination assesses the p-value assuming a common signal strength µ for allchannels and takes into account the correlation of systematic errors between the two experiments.

20

)2Higgs boson mass (GeV/c100 200 300 400 500 600

of S

M H

iggs

bos

on h

ypot

hesi

sS

CL

0.00

0.05

0.10 90%

95%

99%

/experiment-1 = 1.0-2.3 fbintL

= 7 TeVsATLAS + CMS Preliminary,

Observedσ 1±Expected σ 2±Expected

Figure 2: The CLs value for the Standard Model Higgs boson hypothesis as a functionof the Higgs boson mass in the range 110-600 GeV/c2. The observed values are shownby a solid line. The dashed black line indicates the median expected CLs value for thebackground-only hypothesis, while the green (yellow) band indicates the range that isexpected to contain 68% (95%) of all observed limit excursions from the median. The threered horizontal lines show confidence levels of 90%, 95%, and 99% defined as (1− CLs).

21


SM

σ/σ95

% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected


= 7 TeVsATLAS + CMS Preliminary, Observed

σ 1±Expected

σ 2±Expected



Figure 3: The combined 95% C.L. upper limits on the signal strength modifier µ = σ/σSM ,obtained with the CLs method, as a function of the SM Higgs boson mass in the range110-600 GeV/c2. The observed limits are shown by solid symbols. The dashed lineindicates the median expected µ95% value for the background-only hypothesis, while thegreen (yellow) band indicates the range expected to contain 68% (95%) of all observedlimit excursions from the median.

22

Loca

l p-v

alue

-710

-610

-510

-410

-310

-210

-110

1σ1σ2

σ3

σ4

σ5

CombinedExp. for SM Higgs bosonCMSATLAS

/experiment-1 = 1.0-2.3 fbintL = 7 TeVsATLAS + CMS Preliminary,

σsignificance = 1.6 LEE corrected max.


S

Mσ/σ

Bes

t fit

-1

0

1

2 from fitσ1±

Figure 4: (Top) Local p-values as a function of the Higgs boson mass. The p-valuecharacterises the probability of upward fluctuations in the background as high as or higherthan the excesses observed in data. The p-values that test the background-only hypothesisin the ATLAS-only and CMS-only data are shown with symbols. The p-values that testthe background-only hypothesis in the combination of the ATLAS and CMS searchesare shown as a solid line without symbols. The dashed line is the median expected p-value, assuming signal, for prospective SM Higgs boson masses, tested at that point.Including the look-elsewhere effect in the analysis implies that the statistical chance toobserve a local p-value as low as seen here (∼0.001) is about 0.05, which is equivalent toa significance of 1.6σ. (Bottom) The best-fit signal strength µ = σ/σSM as a function ofthe Higgs boson mass. The µ value indicates by what factor the SM Higgs boson crosssection would have to be scaled to best match the observed data. The light-blue bandshows the approximate ±1σ range.

23

Table 3: Results of combining ATLAS and CMS SM Higgs boson searches in the massrange 110-140 GeV/c2. The CLs values quantify the exclusion confidence levels for theSM Higgs boson, while the limits on µ define factors by which the SM Higgs boson crosssections must be scaled in order to be excluded at 95% C.L. The observed local p-valuescharacterise probabilities for the predicted background to fluctuate at least as high as theobserved excesses. Note that local p-values do not include the trials factor arising fromthe look-elsewhere effect. See the text for the discussion and estimate of the effect.

Higgs boson obs’d (exp’d) obs’d (exp’d) observed observed observedmass CLs value upper limits on µ upper limits on µ upper limits on µ local

(GeV/c2) for µ = 1 (CLs method) (asymptotic CLs) (Bayesian) p-value110 0.201 (0.274) 1.64 (1.82) 1.44 1.59 5.0 · 10−1

111 0.371 (0.269) 2.14 (1.80) 1.94 2.48 4.1 · 10−1

112 0.554 (0.252) 2.62 (1.71) 2.35 2.53 1.9 · 10−1

113 0.549 (0.222) 2.61 (1.63) 2.34 2.82 1.7 · 10−1

114 0.501 (0.195) 2.44 (1.66) 2.20 2.46 1.9 · 10−1

115 0.480 (0.192) 2.33 (1.55) 2.07 2.39 2.2 · 10−1

116 0.430 (0.170) 2.19 (1.48) 1.97 2.28 2.4 · 10−1

117 0.999 (0.166) 2.40 (1.35) 2.19 2.26 6.9 · 10−2

118 0.999 (0.131) 2.72 (1.28) 2.47 2.35 8.8 · 10−3

119 0.996 (0.112) 2.77 (1.24) 2.47 2.66 4.2 · 10−3

120 0.998 (0.100) 2.23 (1.19) 2.04 2.21 1.9 · 10−2

121 0.358 (0.080) 1.77 (1.13) 1.61 1.65 1.0 · 10−1

122 0.190 (0.070) 1.45 (1.08) 1.28 1.46 2.6 · 10−1

123 0.175 (0.056) 1.42 (1.03) 1.25 1.32 1.9 · 10−1

124 0.221 (0.044) 1.42 (0.95) 1.29 1.35 1.1 · 10−1

125 0.326 (0.029) 1.59 (0.88) 1.43 1.54 3.0 · 10−2

126 0.397 (0.021) 1.67 (0.82) 1.51 1.63 1.4 · 10−2

127 0.376 (0.015) 1.62 (0.75) 1.48 1.52 1.4 · 10−2

128 0.353 (0.012) 1.58 (0.75) 1.43 1.52 1.7 · 10−2

129 0.264 (0.008) 1.44 (0.67) 1.32 1.39 2.9 · 10−2

130 0.204 (0.007) 1.33 (0.68) 1.21 1.28 4.3 · 10−2

131 0.181 (0.002) 1.30 (0.59) 1.18 1.20 4.6 · 10−2

132 0.137 (0.003) 1.21 (0.57) 1.10 1.07 6.6 · 10−2

133 0.119 (0.001) 1.17 (0.56) 1.06 1.03 6.5 · 10−2

134 0.096 (0.002) 1.12 (0.52) 1.02 0.96 6.6 · 10−2

135 0.073 (0.000) 1.04 (0.49) 0.95 0.97 5.7 · 10−2

136 0.052 (0.001) 1.00 (0.46) 0.90 0.88 5.6 · 10−2

137 0.055 (0.000) 1.01 (0.44) 0.92 0.86 3.1 · 10−2

138 0.085 (0.000) 1.08 (0.44) 0.99 0.98 1.0 · 10−2

139 0.069 (0.000) 1.04 (0.41) 0.95 0.92 9.4 · 10−3

140 0.068 (0.000) 1.05 (0.41) 0.96 0.93 4.4 · 10−3

24

Table 4: Results of combining ATLAS and CMS SM Higgs boson searches in the massrange 141-198 GeV/c2. Definitions for the quantities shown are given in the caption ofTable 3 and in the text.

Higgs boson obs’d (exp’d) obs’d (exp’d) observed observed observedmass CLs value limits on µ limits on µ limits on µ local


142 0.036 (0.000) 0.94 (0.38) 0.87 0.84 5.7 · 10−3

143 0.033 (0.000) 0.93 (0.37) 0.86 0.83 2.7 · 10−3

144 0.032 (0.000) 0.93 (0.36) 0.87 0.83 1.1 · 10−3

145 0.016 (0.000) 0.85 (0.35) 0.79 0.78 1.1 · 10−3

146 0.008 (0.000) 0.78 (0.33) 0.73 0.73 3.0 · 10−3

147 0.008 (0.000) 0.78 (0.33) 0.73 0.72 5.6 · 10−3

148 0.005 (0.000) 0.76 (0.32) 0.71 0.68 1.1 · 10−2

149 0.004 (0.000) 0.72 (0.32) 0.67 0.65 2.0 · 10−2

150 0.002 (0.000) 0.69 (0.31) 0.66 0.65 2.4 · 10−2

152 0.002 (0.000) 0.69 (0.30) 0.65 0.62 2.5 · 10−2

154 0.001 (0.000) 0.59 (0.29) 0.53 0.51 6.4 · 10−2

156 0.000 (0.000) 0.44 (0.23) 0.40 0.38 6.6 · 10−2

158 0.000 (0.000) 0.47 (0.22) 0.42 0.39 2.8 · 10−2

160 0.000 (0.000) 0.44 (0.21) 0.41 0.39 2.3 · 10−2

162 0.000 (0.000) 0.43 (0.21) 0.39 0.38 2.6 · 10−2

164 0.000 (0.000) 0.44 (0.21) 0.40 0.39 2.4 · 10−2

166 0.000 (0.000) 0.38 (0.22) 0.35 0.32 7.6 · 10−2

168 0.000 (0.000) 0.42 (0.22) 0.39 0.39 4.3 · 10−2

170 0.000 (0.000) 0.49 (0.24) 0.44 0.40 4.4 · 10−2

172 0.000 (0.000) 0.44 (0.25) 0.39 0.37 1.1 · 10−1

174 0.000 (0.000) 0.42 (0.26) 0.37 0.36 1.5 · 10−1

176 0.000 (0.000) 0.32 (0.30) 0.28 0.27 5.0 · 10−1

178 0.000 (0.000) 0.32 (0.30) 0.28 0.27 5.0 · 10−1

180 0.000 (0.000) 0.32 (0.31) 0.29 0.29 5.0 · 10−1

182 0.000 (0.000) 0.31 (0.32) 0.28 0.28 5.0 · 10−1

184 0.000 (0.000) 0.30 (0.34) 0.27 0.26 5.0 · 10−1

186 0.000 (0.000) 0.39 (0.36) 0.35 0.33 5.0 · 10−1

188 0.000 (0.000) 0.42 (0.38) 0.37 0.36 5.0 · 10−1

190 0.000 (0.000) 0.43 (0.38) 0.39 0.38 5.0 · 10−1

192 0.000 (0.000) 0.45 (0.40) 0.40 0.39 5.0 · 10−1

194 0.001 (0.000) 0.52 (0.40) 0.46 0.45 3.6 · 10−1

196 0.001 (0.000) 0.55 (0.43) 0.50 0.49 3.7 · 10−1

198 0.001 (0.000) 0.58 (0.44) 0.52 0.53 3.1 · 10−1

25




202 0.002 (0.000) 0.59 (0.45) 0.53 0.51 3.3 · 10−1

204 0.002 (0.000) 0.54 (0.47) 0.54 0.49 4.3 · 10−1

206 0.002 (0.001) 0.53 (0.49) 0.50 0.48 5.0 · 10−1

208 0.001 (0.001) 0.52 (0.49) 0.49 0.46 5.0 · 10−1

210 0.001 (0.001) 0.47 (0.50) 0.45 0.43 5.0 · 10−1

212 0.001 (0.001) 0.47 (0.53) 0.43 0.43 5.0 · 10−1

214 0.000 (0.001) 0.46 (0.56) 0.42 0.43 5.0 · 10−1

216 0.001 (0.001) 0.50 (0.59) 0.45 0.45 5.0 · 10−1

218 0.001 (0.001) 0.52 (0.56) 0.48 0.47 4.9 · 10−1

220 0.005 (0.001) 0.63 (0.54) 0.61 0.60 4.3 · 10−1

222 0.011 (0.003) 0.73 (0.56) 0.63 0.63 4.0 · 10−1

224 0.005 (0.002) 0.65 (0.57) 0.59 0.60 4.6 · 10−1

226 0.002 (0.002) 0.51 (0.57) 0.46 0.48 5.0 · 10−1

228 0.002 (0.003) 0.50 (0.58) 0.47 0.47 4.9 · 10−1

230 0.001 (0.002) 0.55 (0.58) 0.51 0.53 5.0 · 10−1

232 0.004 (0.002) 0.62 (0.57) 0.60 0.61 4.9 · 10−1

234 0.010 (0.002) 0.73 (0.57) 0.70 0.70 3.5 · 10−1

236 0.014 (0.002) 0.77 (0.59) 0.75 0.73 2.6 · 10−1

238 0.023 (0.002) 0.86 (0.59) 0.81 0.79 1.6 · 10−1

240 0.025 (0.002) 0.88 (0.58) 0.81 0.80 1.4 · 10−1

242 0.039 (0.003) 0.95 (0.60) 0.86 0.86 1.3 · 10−1

244 0.031 (0.002) 0.93 (0.59) 0.82 0.82 1.4 · 10−1

246 0.021 (0.002) 0.88 (0.60) 0.79 0.79 2.0 · 10−1

248 0.016 (0.004) 0.80 (0.61) 0.71 0.71 3.0 · 10−1

250 0.009 (0.004) 0.69 (0.58) 0.64 0.65 3.7 · 10−1

252 0.007 (0.004) 0.66 (0.59) 0.60 0.64 4.9 · 10−1

254 0.003 (0.002) 0.61 (0.56) 0.57 0.59 4.2 · 10−1

256 0.003 (0.003) 0.57 (0.58) 0.53 0.57 5.0 · 10−1

258 0.008 (0.004) 0.65 (0.59) 0.58 0.59 4.0 · 10−1

260 0.004 (0.003) 0.62 (0.57) 0.56 0.59 5.0 · 10−1

262 0.003 (0.002) 0.62 (0.60) 0.57 0.59 5.0 · 10−1

264 0.007 (0.005) 0.63 (0.57) 0.61 0.61 5.0 · 10−1

266 0.007 (0.003) 0.65 (0.60) 0.61 0.63 5.0 · 10−1

268 0.004 (0.002) 0.65 (0.60) 0.59 0.61 5.0 · 10−1

270 0.003 (0.001) 0.65 (0.60) 0.60 0.60 4.9 · 10−1

26




274 0.003 (0.002) 0.60 (0.59) 0.57 0.57 5.0 · 10−1

276 0.005 (0.002) 0.65 (0.58) 0.59 0.60 4.9 · 10−1

278 0.002 (0.001) 0.58 (0.54) 0.53 0.55 5.0 · 10−1

280 0.004 (0.001) 0.64 (0.55) 0.56 0.60 5.0 · 10−1

282 0.006 (0.003) 0.63 (0.59) 0.55 0.57 5.0 · 10−1

284 0.005 (0.002) 0.64 (0.56) 0.59 0.60 5.0 · 10−1

286 0.007 (0.002) 0.66 (0.55) 0.56 0.64 4.7 · 10−1

288 0.006 (0.003) 0.67 (0.57) 0.61 0.61 5.0 · 10−1

290 0.010 (0.002) 0.74 (0.57) 0.60 0.69 3.8 · 10−1

295 0.012 (0.001) 0.74 (0.58) 0.69 0.70 3.4 · 10−1

300 0.002 (0.002) 0.54 (0.55) 0.50 0.55 5.0 · 10−1

305 0.001 (0.002) 0.52 (0.58) 0.47 0.51 5.0 · 10−1

310 0.000 (0.001) 0.46 (0.56) 0.41 0.45 5.0 · 10−1

315 0.000 (0.001) 0.42 (0.54) 0.38 0.40 5.0 · 10−1

320 0.000 (0.001) 0.40 (0.54) 0.35 0.36 5.0 · 10−1

325 0.000 (0.001) 0.36 (0.49) 0.31 0.33 5.0 · 10−1

330 0.000 (0.001) 0.33 (0.51) 0.29 0.30 5.0 · 10−1

335 0.000 (0.000) 0.32 (0.48) 0.27 0.28 5.0 · 10−1

340 0.000 (0.001) 0.28 (0.45) 0.24 0.26 5.0 · 10−1

345 0.000 (0.001) 0.27 (0.46) 0.23 0.25 5.0 · 10−1

350 0.000 (0.000) 0.25 (0.45) 0.23 0.25 5.0 · 10−1

360 0.000 (0.000) 0.28 (0.43) 0.25 0.27 5.0 · 10−1

370 0.000 (0.000) 0.29 (0.44) 0.26 0.28 5.0 · 10−1

380 0.000 (0.000) 0.26 (0.42) 0.24 0.27 5.0 · 10−1

390 0.000 (0.000) 0.29 (0.45) 0.27 0.30 5.0 · 10−1

400 0.001 (0.001) 0.33 (0.44) 0.30 0.33 5.0 · 10−1

420 0.002 (0.002) 0.47 (0.53) 0.40 0.47 5.0 · 10−1

440 0.008 (0.005) 0.60 (0.59) 0.52 0.60 5.0 · 10−1

460 0.024 (0.011) 0.83 (0.67) 0.69 0.77 4.7 · 10−1

480 0.054 (0.012) 1.04 (0.77) 0.87 0.97 3.0 · 10−1

500 0.115 (0.033) 1.25 (0.86) 1.05 1.14 3.4 · 10−1

520 0.190 (0.048) 1.54 (1.01) 1.30 1.40 1.6 · 10−1

540 0.271 (0.073) 1.83 (1.14) 1.55 1.64 1.1 · 10−1

560 0.388 (0.105) 2.28 (1.27) 1.93 2.06 6.7 · 10−2

580 0.490 (0.148) 2.80 (1.64) 2.31 2.40 5.3 · 10−2

600 0.525 (0.197) 3.04 (1.72) 2.58 2.64 6.2 · 10−2

27

7 Conclusions

The combination of ATLAS and CMS searches for the Standard Model Higgs boson inpp collisions at a centre-of-mass energy of 7 TeV at the LHC has been presented. Thedatasets used correspond to an integrated luminosity of 1.0-2.3 fb−1 per experiment. TheSM Higgs boson has been searched for in the mass range of 110-600 GeV/c2 and is excludedat 95% C.L. in the mass range 141-476 GeV/c2, while the median expected excluded massregion in the absence of a signal is 124-520 GeV/c2. The region from 146 to 443 GeV/c2

is also excluded at 99% C.L., with the exception of three small regions between 220 and320 GeV/c2. The largest excess observed, after the look-elsewhere effect correction in thesearch mass range from 110-600 GeV/c2, has an estimated significance of about 1.6σ andmakes the observed limits at low mass less restrictive than expected for the background-only hypothesis. The limits obtained from this combination of ATLAS and CMS resultssubstantially restrict the allowed mass range for the Standard Model Higgs boson.

28

A Detector systematic uncertainties

Both ATLAS and CMS track more than 100 nuisance parameters associated with instru-mental systematic uncertainties. These are generally taken to be uncorrelated betweenthe two experiments as discussed in Section 4.

All detector-related systematic uncertainties can be grouped according to whetherthey affect event yields (e.g. via uncertainties on trigger and reconstruction efficiencies),shapes of distributions (e.g. via uncertainties on momentum scales and resolutions),or both. They also can be classified according to their associations with reconstructedobjects and observables (e.g. electrons, muons, taus, photons, jets, missing transverseenergy, b-tags, etc.).

Brief summaries of the main instrumental uncertainties affecting the signal events aregiven in Tables 7 (ATLAS) and 8 (CMS). Each line in the tables represents a potential in-dependent source of systematic uncertainty. The relative uncertainties shown correspondto the overall effect (e.g. an event yield, invariant mass measurement) for ±1σ variationsof the source of systematic uncertainty. Note that each analysis column by itself corre-sponds to a combination of a number of sub-channels. Therefore, the quoted systematicuncertainties are for a sub-channel most affected by the given uncertainty source.

As can be seen in the tables, a single source of uncertainty typically affects morethan one statistically independent analysis. In these cases, the affected channels haveuncertainties that are 100% correlated but not necessarily of the same absolute scale.The first obvious reason is the differences in the number of objects used (e.g. a 1%muon reconstruction error would propagate into a 1% error on the event yield in theH → WW → eµνν channel and a 4% error in the H → ZZ(∗) → 4µ channel). Theother reason is the differences in identification criteria used (e.g. isolation cuts are oftentuned differently). In the latter case, such uncertainties are expected to be somewhatde-correlated. However, for the purposes of the combination, they are still assumed to be100% correlated between different analyses. Ignoring partial de-correlations simplifies thecombination at a price of somewhat more conservative results.

For the backgrounds estimated from simulation, uncertainties similar to those quotedin Tables 7 and 8 equally apply. However, using data-driven techniques for evaluation ofvarious backgrounds, in addition to reducing theoretical prediction uncertainties, oftenallows one to diminish the influence of instrumental reconstruction uncertainties.

To fully appreciate the interplay of all uncertainties in each of the analyses and howthey were assessed, one should refer to the corresponding references provided in Table 1.

29

Tab

le7:

The

mai

nAT

LA

Sin

stru

men

talsy

stem

atic

unce

rtai

nti

eson

sign

alin

the

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n.

Syst

emat

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cert

aint

ies

Hig

gsbo

son

deca

ych

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ls(m

ass

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eV/c

2)

sour

cety

peγγ

bbττ

WW

ZZ

`ν`ν

````

``νν

``qq

(120

)(1

20)

(120

)(1

50)

(200

)(4

00)

(400

)lu

min

osity

lum

i3.

7%re

cons

truc

tion

µ1%

1.1%

0.6%

1.2%

0.7%

0.5%

effici

enci

ese

1%3.

4%2%

1.9%

1.2%

1.1%

γ11

%τ h

ad

8.3%

b-ta

g16

%0.

7%4.

9%p

Tsc

ale

jets

/Em

iss

T2-

8%16

%6%

1.4%

1.3

%(e

vent

yiel

d)e

1%+

1.2

−0.1%

0.2%

0.1%

0.2%

0.3%

pT

reso

luti

onµ

2%1.

5%0.

1%1%

1.2%

e1%

0.1%

0.1%

0.2%

0.2%

γ jets

1%0.

2%2%

0.2%

2.2%

Em

iss

T2%

0.4%

0.6%

30

Tab

le8:

The

mai

nC

MS

inst

rum

enta

lsy

stem

atic

unce

rtai

nti

eson

sign

alin

the

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emat

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tain

ties

Hig

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ass

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eV/c

2)

sour

cety

peγγ

bbττ

WW

ZZ

`ν`ν

````

``ττ

``νν

``qq

(120

)(1

20)

(120

)(1

50)

(200

)(4

00)

(400

)(4

00)

lum

inos

ity

lum

i4.

5%tr

igge

rµ

2%2%

1%2%

1%effi

cien

cies

e2%

2%1%

1%1%

γ1%

Em

iss

T2%

reco

nstr

ucti

onµ

4%1%

3%3%

2%2%

1%effi

cien

cies

e4%

2%4%

3%6%

2%2%

γ1-

3%τ h

ad

6%10

%b-

tag

20%

20%

pT

scal

eµ

2%1%

1%2%

1%(e

vent

yiel

d)e

2%2%

2%5%

2%je

ts/E

mis

sT

2%4%

2-10

%2%

0.2%

pT

scal

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0.3%

(sha

pe)

e0.

3%γ

0.1-

0.3%

τ had

3%p

Tre

solu

tion

jets

/Em

iss

T10

%(e

vent

yiel

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ts/E

mis

sT

2%4%

2-10

%2%

0.2%

pT

reso

luti

onµ

10%

(sha

pe)

e10

%γ

20%

31

B Additional plots

Figures 5-9 show the ATLAS and CMS combination channel by channel using the asymp-totic approximation. Figure 10 compares limits obtained using the CLs methodology andthe Bayesian approach [98]. The filled points show the observed CLs limits calculated bygenerating pseudo-data as described in Section 5. By construction, the exclusion range(µ ≤ 1) for the SM Higgs boson is identical to that shown in Fig. 2 (CLs ≤ 0.05). Thesolid line without symbols in Fig. 10 shows the CLs limit calculated using the asymptoticapproximation and demonstrates that the asymptotic approximation provides an averageagreement of 10% with a maximum difference of 20% with the current dataset. Opensymbols in Fig. 10 are the limits obtained with the Bayesian approach [98]. Althoughthe two methodologies, CLs and Bayesian, need not give identical results, the observedself-consistency of limits obtained with these two methods at the 10-20% level affirmsthe robustness of the methods employed. Figures 11 and 12 are the same as Fig. 10 butrestricted to the low mass range up to 200 GeV/c2 and showing only the CLs results. Fig-ure 13 compares limits set by this combination with the previous constraints from LEPand the Tevatron. Figures 14-17 show the combined ATLAS and CMS results, brokendown into the different Higgs boson decay modes considered here. Figure 18 shows thecombined limits with and without the theoretical systematic uncertainties.

32


SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.0-1.1 fbint

bb, L→H


Figure 5: The 95% C.L. upper limits, in the H → bb decay channel, on the signal strengthmodifier µ = σ/σSM , obtained with the CLs method in the asymptotic approximation,as a function of the SM Higgs boson mass. The observed limits are shown by solidsymbols. The dashed line indicates the median expected µ95% value for the background-only hypothesis. The region above 130 GeV/c2 is covered by the CMS experiment only.

33

)2Higgs boson mass (GeV/c110 115 120 125 130 135 140 145 150

SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.0-1.7 fbint

, Lγγ →H


Figure 6: The 95% C.L. upper limits, in the H → γγ decay channel, on the signal strengthmodifier µ = σ/σSM , obtained with the CLs method in the asymptotic approximation,as a function of the SM Higgs boson mass. The observed limits are shown by solidsymbols. The dashed line indicates the median expected µ95% value for the background-only hypothesis.

34

)2Higgs boson mass (GeV/c110 115 120 125 130 135 140 145 150

SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

210Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.1-1.6 fbint

, Lττ →H


Figure 7: The 95% C.L. upper limits, in the H → ττ decay channel, on the signal strengthmodifier µ = σ/σSM , obtained with the CLs method in the asymptotic approximation,as a function of the SM Higgs boson mass. The observed limits are shown by solidsymbols. The dashed line indicates the median expected µ95% value for the background-only hypothesis. The region above 140 GeV/c2 is covered by the ATLAS experimentonly.

35


SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.5-1.7 fbint

WW, L→H


σ 1±Expected

σ 2±Expected

/exp.-1 = 1.5-1.7 fbint

WW, L→H


)2Higgs boson mass (GeV/c110 120 130 140 150 160 170 180 190 200

SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.5-1.7 fbint

WW, L→H


Figure 8: The 95% C.L. upper limits, in the H → WW → `ν`ν decay channel, on thesignal strength modifier µ = σ/σSM , obtained with the CLs method in the asymptoticapproximation, as a function of the SM Higgs boson mass. The observed limits areshown by solid symbols. The dashed line indicates the median expected µ95% value forthe background-only hypothesis. The region above 300 GeV/c2 is covered by the CMSexperiment only. The bottom plot is a zoom in the low mass region. The discontinuitiesare due to changes in the selection requirements used for different Higgs boson masshypotheses. 36


SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

210 Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.7-2.3 fbint

ZZ, L→H


σ 1±Expected

σ 2±Expected

/exp.-1 = 1.7-2.3 fbint

ZZ, L→H



SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

210 Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected

/exp.-1 = 1.7-2.3 fbint

ZZ, L→H


Figure 9: The 95% C.L. upper limits, in the H → ZZ(∗) decay channel, on the signalstrength modifier µ = σ/σSM , obtained with the CLs method in the asymptotic approxi-mation, as a function of the SM Higgs boson mass. The observed limits are shown by solidsymbols. The dashed line indicates the median expected µ95% value for the background-only hypothesis. The bottom plot is a zoom in the low mass region. Table 1 shows thesub-channels and the ranges covered by ATLAS and CMS for the H → ZZ(∗) decay mode.

37


SM

σ/σ95

% C

L lim

it on

-110

1

10

ObservedSCL

σ 1± Expected SCL

σ 2± Expected SCL

Bayesian Observed

Obs.S

Asymptotic CL

ObservedSCL

σ 1± Expected SCL

σ 2± Expected SCL

Bayesian Observed

Obs.S

Asymptotic CL


= 7 TeVsATLAS + CMS Preliminary, ObservedSCL

σ 1± Expected SCL

σ 2± Expected SCL

Bayesian Observed

Obs.S

Asymptotic CL



Figure 10: The combined 95% C.L. upper limits on the signal strength modifier µ =σ/σSM , as a function of the SM Higgs boson mass in the range 110-600 GeV/c2. Theobserved limits, obtained with the CLs method, are shown by solid symbols. The dashedline indicates the expected median 95% C.L. upper limit on µ for the background-onlyhypothesis, while the green (yellow) bands indicate the ranges expected to contain 68%(95%) of all observed limit excursions from the median. The solid red line without sym-bols shows the observed CLs limits calculated using the asymptotic approximation. Theobserved limits inferred from the Bayesian approach are shown with blue open circles.The differences observed in this plot are model specific and should not be taken to applyto other combinations. The bands and the median are shown for the CLs method.

38


SM

σ/σ95

% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

Observed

σ 1±Expected

σ 2±Expected



Figure 11: The combined 95% C.L. upper limits on the signal strength modifier µ =σ/σSM , obtained with the CLs method, as a function of the SM Higgs boson mass in therange 110-200 GeV/c2. The observed limits are shown by solid symbols. The dashed lineindicates the median expected µ95% value for the background-only hypothesis, while thegreen (yellow) band indicates the range expected to contain 68% (95%) of all observedlimit excursions from the median.

39


SM

σ/σ95

% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

Tevatron Observed

Tevatron Expected

Observed

σ 1±Expected

σ 2±Expected

Tevatron Observed

Tevatron Expected



Figure 12: The combined 95% C.L. upper limits on the signal strength modifier µ =σ/σSM , obtained with the CLs method, as a function of the SM Higgs boson mass in therange 110-200 GeV/c2. The observed limits are shown by solid symbols. The dashed lineindicates the median expected µ95% value for the background-only hypothesis, while thegreen (yellow) band indicates the range expected to contain 68% (95%) of all observedlimit excursions from the median. The current limits from the Tevatron, obtained withthe Bayesian method, are also shown.

40


SM

σ/σ95

% C

L lim

it on

-110

1

10

Observed

σ 1±Expected

σ 2±Expected

LEP excluded

Tevatron excluded

LHC excluded

Observed

σ 1±Expected

σ 2±Expected

LEP excluded

Tevatron excluded

LHC excluded



σ 1±Expected

σ 2±Expected

LEP excluded

Tevatron excluded

LHC excluded



Figure 13: The combined 95% C.L. upper limits on the signal strength modifier µ =σ/σSM , obtained with the CLs method, as a function of the SM Higgs boson mass in therange 110-600 GeV/c2. The observed limits are shown by solid symbols. The dashed lineindicates the median expected µ95% value for the background-only hypothesis, while thegreen (yellow) bands indicate the ranges expected to contain 68% (95%) of all observedlimit excursions from the median. The SM Higgs boson mass ranges excluded by LEP,by the Tevatron and by this combination are shown as hatched areas.

41


SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

210 Combined observedCombined expected

bb→H ττ →H γγ →H

WW→H ZZ→H

Combined observedCombined expected


WW→H ZZ→H


= 7 TeVsATLAS + CMS Preliminary, Combined observedCombined expected


WW→H ZZ→H



Figure 14: The 95% C.L. upper limits for each Higgs boson decay mode separately, andcombined, on the signal strength modifier µ = σ/σSM , obtained with the CLs method inthe asymptotic approximation, as a function of the SM Higgs boson mass in the range110-600 GeV/c2. The observed limits are shown by solid symbols. The dashed linesindicate the median expected µ95% value for the background-only hypothesis.

42


SM

σ/σA

sym

ptot

ic 9

5% C

L lim

it on

1

10

210Combined observedCombined expected


WW→H ZZ→H

Combined observedCombined expected


WW→H ZZ→H



Figure 15: The 95% C.L. upper limits for each Higgs boson decay mode separately, andcombined, on the signal strength modifier µ = σ/σSM , obtained with the CLs method inthe asymptotic approximation, as a function of the SM Higgs boson mass in the range110-200 GeV/c2. The observed limits are shown by solid symbols. The dashed linesindicate the median expected µ95% value for the background-only hypothesis.

43


SM

σ/σE

xpec

ted

95%

CL

limit

on

1

10

210Expected limits

Combined bb→H

ττ →H γγ →H

WW→H ZZ→H

Expected limits

Combined bb→H

ττ →H γγ →H

WW→H ZZ→H


= 7 TeVsATLAS + CMS Preliminary, Expected limits

Combined bb→H

ττ →H γγ →H

WW→H ZZ→H



Figure 16: The 95% C.L. upper limits for each Higgs boson decay mode separately, andcombined, on the signal strength modifier µ = σ/σSM , obtained with the CLs method inthe asymptotic approximation, as a function of the SM Higgs boson mass in the range 110-600 GeV/c2. Only the median expected µ95% value for the background-only hypothesis isshown.

44


SM

σ/σE

xpec

ted

95%

CL

limit

on

1

10

210Expected limits

Combined bb→H

ττ →H γγ →H

WW→H ZZ→H

Expected limitsCombined


WW→H ZZ→H



Figure 17: The 95% C.L. upper limits for each Higgs boson decay mode separately, andcombined, on the signal strength modifier µ = σ/σSM , obtained with the CLs method inthe asymptotic approximation, as a function of the SM Higgs boson mass in the range 110-200 GeV/c2. Only the median expected µ95% value for the background-only hypothesis isshown.

45


SM

σ/σ95

% C

L lim

it on

-110

1

10

210

ObservedExpected

σ 1 ±σ 2 ±

Observed w/o TH sysExpected w/o TH sys

/experiment-1 = 1.0-2.3 fbintL = 7 TeVsATLAS+CMS Preliminary,

Figure 18: The combined 95% C.L. upper limits on the signal strength modifier µ =σ/σSM , obtained with the CLs method, as a function of the SM Higgs boson mass in therange 110-600 GeV/c2. The observed limits are shown by solid symbols. The dashed lineindicates the median expected µ95% value for the background-only hypothesis, while thegreen (yellow) bands indicate the ranges expected to contain 68% (95%) of all observedlimit excursions from the median. The limits obtained without the theoretical systematicuncertainties are also shown for comparison.

46

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