Available on the CERN CDS information server CMS PAS HIG-12-008

CMS Physics Analysis Summary

Contact: cms-pag-conveners-higgs@cern.ch 2012/03/07

Combined results of searches for a Higgs boson in thecontext of the standard model and beyond-standard

models

The CMS Collaboration

Abstract

Combined results are reported from searches for a Higgs boson in proton-proton col-lisions at

√s = 7 TeV in five Higgs boson decay modes: γγ, bb, ττ, WW, and ZZ. The

explored Higgs boson mass range is 110–600 GeV. The analysed data correspond toan integrated luminosity of 4.6–4.8 fb−1. The expected excluded mass range in the ab-sence of the standard model Higgs boson is 114.5–543 GeV at 95% CL. The observedresults exclude the standard model Higgs boson in the mass range 127.5–600 GeV at95% CL, and in the mass range 129–525 GeV at 99% CL. An excess of events abovethe expected standard model background is observed at the low end of the exploredmass range making the observed limits weaker than expected in the absence of asignal. The largest excess, with a local significance of 2.8σ, is observed for a Higgsboson mass hypothesis of 125 GeV. The global significance of observing an excesswith a local significance ≥2.8σ anywhere in the search range 110–600 (110–145) GeVis estimated to be 0.8σ (2.1σ). More data are required to ascertain the origin of the ob-served excess. For an extension of the standard model including a fourth generationof fermions (SM4), the SM4 Higgs boson is excluded in the mass range 120–600 GeVat 95% CL. In the fermiophobic (FP) Higgs boson scenario, the FP Higgs boson isexcluded in the mass range 110–192 GeV at 95% CL.

1

1 IntroductionThe discovery of the mechanism for electroweak symmetry breaking is one of the goals of thephysics programme at the Large Hadron Collider (LHC). Here we report on the combinationof Higgs boson searches carried out in proton-proton collisions at

√s = 7 TeV using the Com-

pact Muon Solenoid (CMS) detector [1] at the LHC. The analysed data recorded in 2010-2011correspond to an integrated luminosity of 4.6–4.8 fb−1, depending on the search channel. Thefollowing three scenarios are considered: the standard model (SM) with the Higgs boson inthe mass range 110–600 GeV; an extension to include a fourth generation of fermions, i.e. afour-generation standard model (SM4), in the mass range 110–600 GeV; and a fermiophobic(FP) Higgs boson in the mass range 110–300 GeV. The SM Higgs boson result is an update ofthe previous combination [2] performed using the same dataset, which now includes a moresensitive H→ γγ analysis and three additional channels.

1.1 SM Higgs boson

In the standard model [3–5], the electroweak symmetry breaking is achieved by introducing acomplex scalar doublet, leading to the prediction of the Higgs boson (H) [6–11]. To date, exper-imental searches for this particle have yielded null results. Limits at 95% confidence level (CL)on its mass have been placed by experiments at LEP, mH > 114.4 GeV [12] and the Tevatron,mH /∈ (162–166) GeV [13], as well as by the LHC experiments ATLAS, mH /∈ (112.7–115.5), (131–237), (251–453) GeV [14], and CMS, mH /∈ (127–600) [2]. Precision electroweak measurements,not taking into account the results from direct searches, indirectly constrain the SM Higgs bo-son mass to be less than 158 GeV [15].

Early phenomenological work on Higgs boson production and decay can be found in Refs. [17–19]. The cross sections for the Higgs boson production mechanisms and the decay branchingfractions, together with their uncertainties, are taken from the LHC Higgs Cross Section Groupreport [16] and are derived from Refs. [20–65]. There are four main mechanisms for Higgsboson production in pp collisions. The gluon-gluon fusion mechanism has the largest crosssection, followed in turn by vector boson fusion (VBF), associated WH and ZH production,and production in association with top quarks, ttH. The relevant decay modes of the SM Higgs

[GeV] HM100 200 300 400 1000

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Figure 1: The standard model Higgs boson production cross sections (left) and decay branchingfractions (right). The plots are taken from Ref. [16].

2 1 Introduction

boson depend strongly on its mass mH. The results presented here are based on the followingfive decay modes: H → γγ, H → ττ, H → bb, H → WW, and H → ZZ. Figure 1 shows thedependence of the cross sections and branching fractions on the SM Higgs boson mass.

There are three types of independent theoretical uncertainties on Higgs boson production: un-certainties associated with (i) parton density functions (PDFs), (ii) incomplete perturbative cal-culations (also known as QCD scale uncertainties), and (iii) the treatment of the finite width ofthe Higgs boson. All these uncertainties are taken from Ref. [16].

1.2 SM4 Higgs boson

In an extension of the standard model including a fourth generation of fermions (the SM4model) [66], the additional heavy quarks in the quark loop associated with the gg→ H processgreatly enhance its production cross-section. Other production mechanisms are not affected.The Higgs boson decay branching fractions are also strongly affected by the presence of thevirtual heavy quarks. Figure 2 shows the ratio of the SM4 to SM gg → H cross section (left)and branching fractions (right) for the SM4 benchmark parameters recommended by the LHCHiggs cross section group in Ref. [67]: mD4 = mL4 = 600 GeV and mU4 − mD4 = (50 + 10 ·ln(mH/115)) GeV. Here mU4 and mD4 are the masses of the “up” and “down” quarks of the4th generation, and mL4 is the mass of the 4th generation charged lepton.

Following the LHC Higgs cross section group prescription, the theoretical uncertainties on theproduction and decay of the SM4 Higgs boson are kept the same as for the SM Higgs boson.

For the SM4 Higgs boson search, for each of the production-decay modes, a signal acceptanceas used in the SM interpretation is assumed.

Higgs boson mass, GeV

100 200 300 400 500 600

Rat

io

0

2

4

6

8

10

12

H)→(ggSM3σH)→(ggSM4σ

Higgs boson mass, GeV

100 200 300 400 500 600

Rat

io

-110

1

10ττ→ bb and H→H

100)× (γγ→H

ZZ→ WW and H→H

Figure 2: Scale factors for the SM4 Higgs boson gg→ H cross section (left) and decay branchingfractions (right). The plots are obtained using the numbers from Ref. [67]. The scale factorcurves for different decay modes are shown in the mass ranges as used in the correspondinganalyses.

1.3 Fermiophobic Higgs boson

If the Higgs boson responsible for the electroweak symmetry breaking does not couple tofermions, then the gg → H and ttH production modes disappear, while the VBF and VH

3

production cross sections remain unchanged. Direct decays H → ττ and H → bb become im-possible, while branching fractions for H→ γγ, H→ WW, and H→ ZZ become significantlyenhanced for the low mass Higgs boson, as shown in Fig 3. Such a Higgs boson is referred to asfermiophobic and appears in a variety of extensions to the SM (e.g. [68] and references therein).In this analysis, loop-induced decays to fermions are ignored.

Following the LHC Higgs cross section group prescription, the QCD scale uncertainties on theFP Higgs boson production are increased by 5% with respect to those of the SM Higgs boson.This 5% uncertainty, added linearly to the SM Higgs QCD scale uncertainties, is introducedto cover the effects of electroweak corrections, which have not yet been calculated. For thefermiophobic Higgs boson search, for each of the production-decay modes, a signal acceptanceas used in the SM interpretation is assumed.

Higgs boson mass, GeV

100 120 140 160 180 200 220 240 260 280 300

Rat

io

1

10

210γγ→H

ZZ→WW and H→H

Figure 3: Ratio of the branching fractions for a fermiophobic and the SM Higgs boson as afunction of mH. The plots are obtained using the numbers from Ref. [69]. The shown range forthe H → γγ curve is defined by the range of Higgs boson masses used in the analysis. TheH → WW and H → ZZ searches extend up to mH=300 GeV; the ratio of branching ratios formH=250–300 GeV is assumed to be equal to unity.

2 CMS DetectorThe CMS apparatus consists of a barrel assembly and two endcaps, comprising, in successivelayers outwards from the collision region, the silicon pixel and strip tracker, the lead tungstatecrystal electromagnetic calorimeter, the brass/scintillator hadron calorimeter, the supercon-ducting solenoid, and gas-ionization chambers embedded in the steel return yoke for the de-tection of muons.

3 Search channelsThe results presented in this note are obtained by combining searches in the individual Higgsboson decay channels as listed in Table 1. The table summarizes the main characteristics ofthese searches, namely: the mass range of the search, the integrated luminosity used, the num-ber of exclusive sub-channels, and the approximate instrumental mass resolution. The presence

4 3 Search channels

of a signal or an upward fluctuation of the background in one of the channels, at a certain valueof the Higgs boson mass, is expected to manifest itself as an excess extending around that valuefor a range corresponding to the mH resolution.

The H → γγ analysis [70] is focused on a search for a narrow peak in the diphoton massdistribution. Events are classified according to a multivariate analysis (MVA) discriminatorincorporating the kinematics of the di-photon system (excluding mγγ), a per-event estimate ofthe expected di-photon mass resolution, and a per-object photon-jet discriminator. This classi-fication is motivated by the fact that the signal-to-background-ratio and relative contributionof fakes from jets varies as a function of the photon kinematics, and the di-photon mass reso-lution depends on the location of the photons in the calorimeter, whether or not one or bothphotons convert in the detector volume traversed before the calorimeter, and the probabilitythat the correct primary vertex has been used to compute the di-photon mass. After a loose cuton this multivariate discriminant, the event sample is split into two mutually exclusive sets:(i) diphoton events with one forward and one backward jet, consistent with the VBF topol-ogy, and (ii) all remaining events. This division is motivated by the consideration that thereis a better signal-to-background-ratio in the first set compared to the second. The second set,containing over 99% of data, is further subdivided into four classes based on the multivariatediscriminant, in order of decreasing S/B. The background in the signal region is estimated froma fit to the observed diphoton mass distribution in data.

The search for a fermiophobic Higgs boson decaying to two photons [71] is performed in foursub-channels: VBF, H + µ, H + e, and “remainder”. The VBF sub-channel is defined by thepresence of two forward/backward jets in an event. The next two sub-channels identify Higgsboson production in association with W and Z bosons. Events failing the VBF and W/Z bo-son tags constitute the fourth sub-channel “remainder”, which is further sub-divided into fourclasses, based on whether or not both photons produce compact electromagnetic showers, andwhether or not both photons are in the central part of the CMS detector. This subdivision ismotivated by the fact that the photon energy resolution depends on whether or not a photonconverts in the detector volume in front of the electromagnetic calorimeter, and whether it ismeasured in the barrel or in the endcap section of the calorimeter. The diphoton mass mγγ

distributions are the final discriminants for the VBF, H + µ, H + e sub-channels. For the “re-mainder” sub-channel, the final discriminant is a 2D-distribution of diphoton mass mγγ andthe ratio of the diphoton transverse momentum and mass pγγ

T /mγγ. These 2D-distributionsare constructed separately for the four sub-classes of events. The background in the signalregion is estimated from fits to the observed final discriminant distributions in data.

The H → ττ search [72–74] is performed using the final-state signatures eµ, µµ, eτh, and µτh,where electrons and muons arise from leptonic τ-decays τ → `ν`ντ and τh denotes hadronic τ-decays τ → hadrons + ντ. Each of these four categories is further divided into three exclusivesub-categories according to the nature of the associated jets: (i) events with the VBF signature,(ii) events with just one jet with large transverse energy ET, and (iii) events with either no jetsor with one with a small ET. In each of these twelve categories we search for a broad excessin the reconstructed ττ mass distribution. The main irreducible background is from Z → ττproduction, whose ττ mass distribution is derived from data by using Z→ µµ events, in whichthe reconstructed muons are replaced with reconstructed particles from the decay of simulatedτ leptons of the same momenta. The reducible backgrounds (W + jets, multijet production,Z → ee) are also evaluated from control samples in data. In addition, a search for H → ττ isperformed for a Higgs boson produced in association with a W boson. Two final states, e±µ±τ∓hand µ±µ±τ∓h , are considered.

5

Tabl

e1:

Sum

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atio

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the

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yses

incl

uded

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isco

mbi

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arks

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hich

chan

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are

used

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est

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odel

(SM

),fo

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atio

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anda

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(SM

4),a

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ic(F

P)H

iggs

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Ana

lyse

sm

arke

das

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ange

dar

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actl

yth

esa

me

asin

the

prev

ious

com

bina

tion

ofSM

Hig

gsbo

son

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ches

[2].

Cha

nnel

mH

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min

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b-m

HC

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SMSM

4FP

Ref

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anne

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solu

tion

H→

γγ

110–

150

4.8

21–

2%up

date

dx

x[7

0]H→

γγ

(fer

mio

phob

ic)

110–

150

4.8

41–

3%ne

wx

[71]

H→

ττ→

eτh

/µ

τ h/

eµ+

X11

0–14

54.

69

20%

unch

ange

dx

x[7

2]H→

ττ→

µµ+

X11

0–14

04.

53

20%

new

xx

[73]

WH→

eµτ h

/µ

µτ h

+ν

’s10

0–14

04.

72

20%

new

xx

[74]

(W/

Z)H→

(`ν

/``

/ν

ν)(

bb)

110–

135

4.7

510

%un

chan

ged

xx

[75]

H→

WW∗→

2`2ν

110–

600

4.6

520

%un

chan

ged

xx

x[7

6]W

H→

W(W

W∗ )→

3`3ν

110–

200

4.6

120

%ne

wx

xx

[77]

H→

ZZ(∗)→

4`11

0–60

04.

73

1–2%

unch

ange

dx

xx

[78]

H→

ZZ→

2`2ν

250–

600

4.6

27%

unch

ange

dx

xx

[79]

H→

ZZ(∗)→

2`2q

{ 130–

164

200–

600

4.6

63% 3%

unch

ange

dx

xx

[80]

H→

ZZ→

2`2τ

190–

600

4.7

810

–15%

unch

ange

dx

xx

[81]

6 3 Search channels

The H → bb search [75] concentrates on Higgs boson production in association with W or Zbosons, in which the focus is on the following decay modes: W→ eν/µν and Z→ ee/µµ/νν.The Z→ νν decay is identified by requiring a large missing transverse energy Emiss

T . The valueEmiss

T is defined as the modulus of the vector ~EmissT computed as the negative of the vector sum

of the transverse momenta of all reconstructed objects in the volume of the detector (leptons,photons, and charged/neutral hadrons). The dijet system, with both jets tagged as b-quarkjets [82], is also required to have a large transverse momentum, which helps to reduce back-grounds and improves the dijet mass resolution. We use a multivariate analysis technique, inwhich a classifier is trained on simulated signal and background events for a number of Higgsboson masses, and the events above an MVA output threshold are counted as signal-like. Therates of the main backgrounds, consisting of W/Z + jets and top-quark events, are derivedfrom control samples in data. The WZ and ZZ backgrounds with a Z boson decaying to a pairof b-quarks, as well as the single-top background, are estimated from simulation.

The H → WW(∗) → 2`2ν analysis [76] searches for an excess of events with two leptons ofopposite charge, large Emiss

T , and up to two jets. Events are divided into five categories, withdifferent background compositions and signal-to-background ratios. For events with no jets,the main background stems from non-resonant WW production; for events with one jet, thedominant backgrounds are from WW and top-quark production. The events with no jets andone jet are split into same-flavour and different-flavour dilepton sub-channels, since the back-ground from Drell–Yan production is much larger for the same-flavour dilepton events. Thetwo-jet category is optimized to take advantage of the VBF production signature. The mainbackground in this channel is from top-quark production. To improve the separation of sig-nal from backgrounds, MVA classifiers are trained for a number of Higgs boson masses, anda search is made for an excess of events in the output distributions of the classifiers. All back-ground rates, except for very small contributions from WZ, ZZ, and Wγ, are evaluated fromdata.

The WH → WWW → 3`3ν analysis [77] searches for an excess of events with three leptons,electrons or muons, large missing transverse energy, and low hadronic activity. The domi-nant background is from WZ→ 3`ν production, which is largely reduced by requiring that allsame-flavour oppositely charged lepton pairs have a dilepton mass away from mZ. In addition,oppositely charged leptons are required not to be back-to-back. The background processes withjets misidentified as leptons, e.g. Z+jets and top, as well as the WZ→ 3`ν background are esti-mated from data. The small contribution from the ZZ → 4` process with one unreconstructedlepton is estimated using simulated samples.

In the H → ZZ(∗) → 4` channel [78], we search for a four-lepton mass peak over a smallcontinuum background. The 4e, 4µ, 2e2µ sub-channels are analyzed separately since thereare differences in the four-lepton mass resolutions and the background rates arising from jetsmisidentified as leptons. The dominant irreducible background in this channel is from non-resonant ZZ production (with both Z bosons decaying to either 2e, or 2µ, or 2τ with the tausdecaying leptonically) and is estimated from simulation. The smaller reducible backgroundswith jets misidentified as leptons, e.g. Z + jets, are estimated from data.

In the H→ ZZ→ 2`2ν search [79], we select events with a lepton pair (ee or µµ), with invariantmass consistent with that of an on-shell Z boson, and a large Emiss

T . We then define a transverseinvariant mass mT from the dilepton momenta and Emiss

T , assuming that EmissT arises from a

Z→ νν decay. We search for a broad excess of events in the mT distribution. The non-resonantZZ and WZ backgrounds are taken from simulation, while all other backgrounds are evaluatedfrom control samples in data.

7

In the H → ZZ(∗) → 2`2q search [80], we select events with two leptons (ee or µµ) and twojets with zero, one, or two b-tags, thus defining a total of six exclusive final states. Requiring b-tagging improves the signal-to-background ratio. The two jets are required to form an invariantmass consistent with that of an on-shell Z boson. The aim is to search for a peak in the invariantmass distribution of the dilepton-dijet system, with the background rate and shape estimatedusing control regions in data.

In the H → ZZ → 2`2τ search [81], one Z boson is required to be on-shell and to decay to alepton pair (ee or µµ). The other Z boson is required to decay through a ττ pair to one of thefour final-state signatures eµ, eτh, µτh, τhτh. Thus, eight exclusive sub-channels are defined. Wesearch for a broad excess in the distribution of the dilepton-ditau mass, constructed from thevisible products of the tau decays, neglecting the effect of the accompanying neutrinos. Thedominant background is non-resonant ZZ production whose rate is estimated from simula-tion. The main sub-leading backgrounds with jets misidentified as τ leptons stem from Z+ jets(including ZW) and top-quark events. These backgrounds are estimated from data.

4 Combination methodologyThe combination of the SM Higgs boson searches requires simultaneous analysis of the datafrom all individual search channels, accounting for all statistical and systematic uncertaintiesand their correlations. The results presented here are based on a combination of Higgs bosonsearches in a total of 50 exclusive sub-channels described in Section 3. Depending on the sub-channel, the input to the combination may be a total number of selected events or an eventdistribution for the final discriminating variable. Either binned or unbinned distributions areused, depending upon the particular search sub-channel.

The number of sources of systematic uncertainties considered in the combination ranges from156 to 222, depending on the Higgs boson mass. A large fraction of these uncertainties arecorrelated across different channels and between signal and backgrounds within a given chan-nel. Uncertainties considered include: theoretical uncertainties on the expected cross sectionsand acceptances for signal and background processes, experimental uncertainties arising frommodelling of the detector response (event reconstruction and selection efficiencies, energy scaleand resolution), and statistical uncertainties associated with either ancillary measurements ofbackgrounds in control regions or selection efficiencies obtained using simulated events. Sys-tematic uncertainties can affect either the shape of distributions, or event yields, or both.

The combination is repeated for 183 Higgs boson mass hypotheses in the range 110–600 GeV.The step size in this scan varies [83] across the mass range and is determined by the Higgsboson mass resolution. The minimum step size is 0.5 GeV at lower masses, where it is com-mensurate with the mass resolution of the γγ and 4` channels. The maximum step size is20 GeV at large masses, where the intrinsic Higgs boson width is the limiting factor.

4.1 General framework

The overall statistical methodology used in this combination was developed by the CMS andATLAS collaborations in the context of the LHC Higgs Combination Group. The detailed de-scription of the methodology can be found in Ref. [83]. Below we outline the basic steps in thecombination procedure.

Firstly, a signal strength modifier µ is introduced that multiplies the expected SM Higgs bosoncross section such that σ = µ · σSM.

8 4 Combination methodology

Secondly, each independent source of systematic uncertainty is assigned a nuisance parameterθi. The expected Higgs boson and background yields are functions of these nuisance parame-ters, and are written as µ · s(θ) and b(θ), respectively. Most nuisance parameters are constrainedby other measurements. They are encoded in the probability density functions pi(θi|θi) describ-ing the probability to measure a value θi of the i-th nuisance parameter, given its true value θi.

Next, we define the likelihood L, given the data and the measurements θ:

L(data | µ·s(θ) + b(θ)) = P(data | µ·s(θ) + b(θ)) · p(θ|θ) , (1)

where P(data | µ·s(θ) + b(θ)) is a product of probabilities over all bins of discriminant variabledistributions in all channels (or over all events for sub-channels with unbinned distributions),and p(θ|θ) is the probability density function for all nuisance parameter measurements.

In order to test a Higgs boson production hypothesis for a given mass, we construct an ap-propriate test statistic. The test statistic is a single number encompassing information on theobserved data, expected signal, expected background, and all uncertainties associated withthese expectations. It allows one to rank all possible experimental observations according towhether they are more consistent with the background-only or with the signal+backgroundhypotheses.

Finally, in order to infer the presence or absence of a signal in the data, we compare the ob-served value of the test statistic with the distribution of values expected under the background-only and under the signal+background hypotheses. The expected distributions are obtainedby generating pseudo-datasets from the probability density functions P (data | µ · s(θ) + b(θ) )and p(θ|θ). The values of the nuisance parameters θ used for generating pseudo-datasetsare obtained by maximizing the likelihood L under the background-only or under the sig-nal+background hypotheses.

4.2 Quantifying an excess

In order to quantify the statistical significance of an excess over the background-only expecta-tion, we define a test statistic q0 as:

q0 = −2 lnL(data | b(θ0) )

L(data | µ·s(θ) + b(θ) ), µ ≥ 0, (2)

where θ0, θ, and µ are the values of the parameters θ and µ that maximise the likelihoods inthe numerator and denominator, and the subscript in θ0 indicates that the maximization inthe numerator is done under the background-only hypothesis (µ = 0). Since the Higgs bosonsignal cannot be negative, the allowed range for µ is µ ≥ 0. With this definition, a signal-likeexcess, µ > 0, corresponds to a positive value of q0. In the absence of an excess, µ is zero (thelowest allowed value), the likelihood ratio becomes equal to one, and q0 = 0.

An excess can be quantified in terms of the p-value p0, which is the probability to obtain avalue of q0 at least as large as the one observed in data, qobs

0 , under the background-only (b)hypothesis:

p0 = P(

q0 ≥ qobs0 | b

). (3)

We choose to relate the significance Z of an excess to the p-value via the Gaussian one-sidedtail integral:

p0 =∫ ∞

Z

1√2π

exp(−x2/2) dx. (4)

4.3 Quantifying the absence of a signal 9

The test statistic q0 has one degree of freedom (µ) and, in the limit of a large number of events,its distribution under the background-only hypothesis converges to a half of the χ2 distribu-tion for one degree of freedom plus 0.5 · δ(q0) [84]. The term with the delta function δ(q0)corresponds to the 50% probability not to observe an excess under the background-only hy-pothesis. This asymptotic property allows the significance to be evaluated directly from theobserved test statistic qobs

0 as [84]:

Z =√

qobs0 (5)

When the observed event yield lies below the expectation under the background-only hypothe-sis, µ is at its minimum allowed value of µ = 0, the test statistic qobs

µ = 0 (Eq. (2)), the asymptoticsignificance Z = 0 (Eq. (5)), and the corresponding p-value p0 = 0.5 (Eq. (4)).

The local p-value p0 characterises the probability of a background fluctuation resembling asignal-like excess for a given value of the Higgs boson mass. The probability for a backgroundfluctuation to be at least as large as the observed maximum excess anywhere in a specified massrange is given by the global probability or global p-value. This probability can be evaluatedby generating pseudo-datasets incorporating all correlations between analyses optimized fordifferent Higgs boson masses. It can also be estimated from the data by counting the numberof transitions from deficit to excess in a specified Higgs boson mass range [83, 85]. The globalsignificance is computed from the global p-value using Eq. (4).

4.3 Quantifying the absence of a signal

In order to set exclusion limits on a Higgs boson hypothesis, we define a test statistic qµ, whichdepends on the hypothesised signal rate µ. The definition of qµ makes use of a likelihood ratiosimilar to the one for q0, but uses instead the signal+background model in the numerator:

qµ = −2 lnL(data | µ·s(θµ) + b(θµ) )

L(data | µ·s(θ) + b(θ) ), 0 ≤ µ < µ, (6)

where the subscript µ in θµ indicates that, in this case, the maximisation of the likelihood in thenumerator is done under the hypothesis of a signal of strength µ. In order to force one-sidedlimits on the Higgs boson production rate, we constrain µ < µ.

This definition of the test statistic differs slightly from the one used in searches at LEP andthe Tevatron, where the background-only hypothesis was used in the denominator. With thedefinition of the test statistic given in Eq. (6), in the asymptotic limit of a large number ofbackground events, the expected distributions of qµ under the signal+background and underthe background-only hypotheses are known analytically [84].

For the calculation of the exclusion limit, we adopt the modified frequentist construction CLs [86,87]. We define two tail probabilities associated with the observed data; namely, the probabil-ity to obtain a value for the test statistic qµ larger than the observed value qobs

µ for the sig-nal+background (µ·s + b) and for the background-only (b) hypotheses:

CLs+b = P(

qµ ≥ qobsµ | µ·s + b

), (7)

CLb = P(

qµ ≥ qobsµ | b

), (8)

and obtain the CLs value from the ratio

CLs =CLs+b

CLb. (9)

10 5 Results

If CLs ≤ α for µ = 1, we determine that the SM Higgs boson is excluded at the 1− α confidencelevel. To quote the upper limit on µ at the 95% confidence level, we adjust µ until we reachCLs = 0.05.

When the observed event yield lies above the expectation under the signal+background hy-pothesis, µ is at its maximum allowed value of µ, the test statistic qobs

µ = 0 (Eq. (6)), and CLs+b,CLb and hence CLs equal unity (Eqs. (7-9)).

5 ResultsCombined results of searches for SM, SM4, and fermiophobic Higgs bosons are presented inthis section. Unless stated otherwise, the following conventions are used. The observed valuesare shown by a solid line. A dashed line indicates the median of the expected results for thebackground-only hypothesis. The green (dark) and yellow (light) bands indicate the ranges inwhich the measured values are expected to reside in at least 68% and 95% of all experimentsunder the background-only hypothesis. The probabilities for an observation to lie above orbelow the 68% (95%) band are at most 16% (2.5%) each.

5.1 SM Higgs boson

The CLs value for the SM Higgs boson hypothesis as a function of its mass is shown in Fig. 4.The observed and median expected values of CLs as well as the 68% and 95% bands are ob-tained by generating ensembles of pseudo-datasets. The thick red horizontal lines indicate CLsvalues of 0.10, 0.05, and 0.01. The mass regions where the observed CLs values are below theselines are excluded with the corresponding (1− CLs) confidence levels of 90%, 95%, and 99%,respectively. We exclude a SM Higgs boson at 95% CL in the mass range 127.5–600 GeV. At99% CL, we exclude it in the mass range 129–525 GeV.

Figure 5 shows the 95% CL upper limits on the signal strength modifier, µ = σ/σSM, obtainedby generating ensembles of pseudo-datasets, as a function of mH. The ordinate thus shows the

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Figure 4: The observed and expected CLs values for the SM Higgs boson hypothesis as a func-tion of the Higgs boson mass in the range 110–600 GeV (left) and 110–145 GeV (right). Thethree horizontal lines on the CLs plot show confidence levels of 90%, 95%, and 99%, defined as(1−CLs).

5.1 SM Higgs boson 11

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Figure 5: The observed and expected 95% CL upper limits on the signal strength parameterµ = σ/σSM for the SM Higgs boson hypothesis as a function of the Higgs boson mass in therange 110–600 GeV (left) and 110–145 GeV (right).

Higgs boson cross section that is excluded at 95% CL, expressed as a multiple of the SM Higgsboson cross section.

The median expected exclusion range of mH at 95% CL in the absence of a signal is 114.5–543 GeV. The differences between the observed and expected limits are consistent with statisti-cal fluctuations since the observed limits are generally within the green (68%) or yellow (95%)bands of the expected limit values. For the largest values of mH, we observe fewer events thanthe median expected number for the background-only hypothesis, which makes the observedlimits in that range stronger than expected. However, at small mH we observe an excess ofevents. This makes the observed limits weaker than expected in the absence of a SM Higgsboson.

Figure 6 shows the observed/expected limits for the five individual decay channels studied,and their combination. For masses beyond 200 GeV, the limits are driven mostly by the H→ ZZdecay channels, while in the range 125–200 GeV, the limits are largely defined by the H→WWdecay mode. For the mass range below 120 GeV, the dominant contributor to the sensitivity isthe H → γγ channel. The results shown are calculated using the asymptotic formula for theCLs method.

To quantify the consistency of the observed excesses with the background-only hypothesis, weshow in Fig. 7 (left) a scan of the combined local p-value p0 in the low-mass region. The localp-values shown in Fig. 7 are obtained with the asymptotic formula (lines) and validated bygenerating ensembles of background-only pseudo-datasets (points).

A broad offset of about one standard deviation, caused by excesses in the channels with poormass resolution (bb, ττ, WW), is complemented by localized excesses observed in the ZZ →4` and γγ channels. The largest excess in the combination is at 125 GeV and arises mostlyfrom the observed excess in the γγ channel. The narrow feature in the H → ZZ(∗) → 4`channel at 119.5 GeV, associated with three ZZ → 4` events, is considerably reduced in thecombination, mostly by the H → γγ channel that has a better sensitivity and actually showsa deficit of events for that mass. Figure 8 shows the interplay of contributing channels forthe two Higgs boson mass hypotheses mH = 119.5 and 125 GeV. The plots show the level of

12 5 Results

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Figure 6: The observed and expected 95% CL upper limits on the signal strength parameterµ = σ/σSM as a function of the Higgs boson mass in the range 110–600 GeV (left) and 110–145 GeV (right) for the five explored Higgs boson decay modes and their combination.

statistical compatibility between the channels contributing to the combination.

The minimum local p-value pmin = 0.003 at mH ' 125 GeV corresponds to a local significanceZmax of 2.8σ. The global significance of the observed excess for the entire search range of 110–600 GeV is estimated directly from the data following the method described in Ref. [83] andcorresponds to about 0.8σ. For a restricted range of interest, the global p-value is evaluatedusing pseudo-datasets. For the mass range 110–145 GeV, it yields a significance of 2.1σ.

The p-value characterises the probability of background producing an observed excess of events,but it does not give information about the compatibility of an excess with an expected signal.The latter is provided by the best fit µ value, shown in Fig. 7 (right). In this fit the constraintµ ≥ 0 is not applied, so that a negative value of µ indicates an observation below the expec-tation from the background-only hypothesis. The band corresponds to the ±1σ uncertainty(statistical+systematic) on the value of µ obtained from a change in qµ by one unit (∆qµ = 1),after removing the µ constraint in Eq. (6). The observed µ values are within 1σ of unity in themass range from 121–126 GeV.

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Figure 7: The observed local p-value p0 (left) and best-fit µ = σ/σSM (right) as a function ofthe SM Higgs boson mass in the range 110–145 GeV. The local p-values for individual channelsand their combination are obtained with the asymptotic formula (lines); the combined local p-value is validated by generating ensembles of background-only pseudo-datasets (points). Thedashed line shows the expected local p-values p0(mH), should a Higgs boson with a mass mHexist. The band in the right plot corresponds to the ±1σ uncertainties on the µ values.

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Figure 8: Values of µ = σ/σSM for the combination (solid vertical line) and for contribut-ing channels (points) for two hypothesized Higgs boson masses: 119.5 GeV (left) and 125 GeV(right). The band corresponds to ±1σ uncertainties on the overall µ value. The horizontal barsindicate ±1σ uncertainties on the µ values for individual channels.

14 5 Results

5.2 SM4 Higgs boson

Figure 9 (left) shows the 95% CL upper limits on the signal strength modifier, µ = σ/σSM4,obtained by generating ensembles of pseudo-datasets, as a function of mH. We exclude theSM4 Higgs boson at 95% CL in the mass range 120–600 GeV.

Figure 9 (right) shows the expected and observed limits for individual SM4 Higgs boson decaymodes as well as for their combination. In contrast with the SM Higgs boson search (cf. Fig. 6),in the SM4 scenario the H → ττ search becomes the most sensitive channel in the low Higgsboson mass range. This is not unexpected, given the changed values of the Higgs boson crosssections and branching fractions seen in Fig. 2.

The local p-value as a function of the Higgs boson mass for the individual decay modes andfor their combination for the low mass range is shown in Fig. 10 (left) The excesses observedin the H → γγ channel contribute very little to the combination, given that this channel has amuch smaller sensitivity in the SM4 context. Overall, the excess observed in the combinationof all channels is too weak to be consistent with the SM4 Higgs boson signal, as can be seen inFig. 10 (right).

At 99% CL, we exclude the SM4 Higgs boson in the range 125–600 GeV.

5.3 Fermiophobic Higgs boson

Figure 11 (left) shows the 95% CL upper limits on the signal strength modifier, µ = σ/σFP,obtained by generating ensembles of pseudo-datasets, as a function of mH. The fermiophobicHiggs boson is excluded at 95% CL in the mass range 110–192 GeV. At 99% CL, we exclude thefermiophobic Higgs boson in the range 110–188 GeV, with the exception of two gaps: 124.5–128 and 148–154 GeV.

Figure 11 (right) shows the expected and observed 95% CL limits for individual fermiophobicHiggs boson decay modes as well as for their combination.

Figure 12 (left) shows the local p-value as a function of the Higgs boson mass for individualdecay modes and for their combination. The local excess at mH ∼ 125 GeV is almost as pro-nounced as in the SM Higgs combination. However, this excess is too weak to be consistentwith the fermiophobic Higgs boson signal, as can be seen in Fig. 12 (right).

5.3 Fermiophobic Higgs boson 15

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Figure 9: (Left) The observed and expected 95% CL upper limits on the signal strength pa-rameter µ = σ/σSM4 for the SM4 Higgs boson hypothesis as a function of the Higgs bosonmass (Right) The observed and expected 95% CL upper limits on the signal strength parameterµ = σ/σSM4 as a function of the SM4 Higgs boson mass for the five explored Higgs boson decaymodes and their combination.

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Figure 10: (Left) The observed and expected local p-values p0(mH) as a function of Higgs bo-son mass mH for the SM4 Higgs boson search. The local p-values for the five Higgs bosondecay modes and their combination are obtained with the asymptotic formula (lines); the com-bined local p-value is validated by generating ensembles of background-only pseudo-datasets(points). The dashed line indicates the expected combined local p-values, should a SM4 Higgsboson with a mass mH exist. (Right) The best-fit value of a signal strength modifier µ = σ/σSM4as a function of Higgs boson mass mH for the SM4 Higgs boson search.

16 5 Results

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Figure 11: (Left) The observed and expected 95% CL upper limits on the signal strength param-eter µ = σ/σFP for the fermiophobic Higgs boson hypothesis as a function of the Higgs bosonmass (Right) The observed and expected 95% CL upper limits on the signal strength parameterµ = σ/σFP as a function of the fermiophobic Higgs boson mass for the three explored Higgsboson decay modes and their combination.

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Figure 12: (Left) The observed and expected local p-values p0(mH) as a function of Higgs bosonmass mH for the fermiophobic Higgs boson search. The local p-values for the three Higgs bosondecay modes channels and their combination are obtained with the asymptotic formula (lines);the combined local p-value is validated by generating ensembles of background-only pseudo-datasets (points). The dashed line indicates the expected combined local p-values, should afermiophobic Higgs boson with a mass mH exist. (Right) The best-fit value of a signal strengthmodifier µ = σ/σFP as a function of Higgs boson mass mH for the fermiophobic Higgs bosonsearch.

17

6 SummaryCombined results are reported from searches for a Higgs boson in proton-proton collisions at√

s = 7 TeV in five Higgs boson decay modes: γγ, bb, ττ, WW, and ZZ. The explored Higgsboson mass range is 110–600 GeV. The analysed data correspond to an integrated luminosity of4.6–4.8 fb−1. The expected excluded mass range in the absence of the standard model Higgs bo-son is 114.5–543 GeV at 95% CL. The observed results exclude the standard model Higgs bosonin the mass range 127.5–600 GeV at 95% CL, and in the mass range 129–525 GeV at 99% CL. Anexcess of events above the expected standard model background is observed at the low end ofthe explored mass range making the observed limits weaker than expected in the absence of asignal. The largest excess, with a local significance of 2.8σ, is observed for a Higgs boson masshypothesis of 125 GeV. The global significance of observing an excess with a local significance≥2.8σ anywhere in the search range 110–600 (110–145) GeV is estimated to be 0.8σ (2.1σ). Moredata are required to ascertain the origin of the observed excess. For an extension of the stan-dard model including a fourth generation of fermions (SM4), the SM4 Higgs boson is excludedin the mass range 120–600 GeV at 95% CL. In the fermiophobic (FP) Higgs boson scenario, theFP Higgs boson is excluded in the mass range 110–192 GeV at 95% CL.

18 6 Summary

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