Standard Model Higgs Combination from CMS with up to 1.7 fb-1 of data

The combination is presented of searches for a standard model (SM) Higgs boson in eight decay modes: H->gamma,gamma, H->tau,tau, H->bb, H->WW->2l2nu, H->ZZ->4l, H->ZZ->2l2tau, H->ZZ->2l2nu, and H->ZZ->2l2q. The searches were performed by the CMS Collaboration using 1.1-1.7 fb-1 of integrated luminosity, depending on the analysis. No excess compatible with a SM Higgs signal has been observed; the largest excursion of the observed data from the expected background has a probability of 0.4 after taking into account the look-elsewhere effect. The SM Higgs boson is excluded at 95% C.L. in three mass ranges 145-216, 226-288, and 310-400 GeV/c2, while the expected exclusion range is 130-440 GeV/c2.


Introduction
Understanding of the mechanism of electroweak symmetry breaking is one of the main goals of the CMS physics program. In the standard model (SM) the electroweak symmetry breaking is described by so-called Higgs mechanism which leads to prediction of one scalar particle -a Higgs boson (H) [1,2,3,4,5,6]. So far, experimental searches for this particle have given negative results allowing to exclude its mass below m H < 114.4 GeV/c 2 (LEP experiments [7]) and for m H ∈ 100-108 GeV/c 2 and m H ∈ 156-177 GeV/c 2 (Tevatron experiments [8]). Indirect searches using fits to precise measurements predict relatively light Higgs boson with m H < 158 GeV/c 2 [9].
The cross sections for Higgs boson production, its decay branching fractions, and their uncertainties are taken from the report prepared by LHC Higgs Cross Section group [10].
In Section 2 an overview of all eight analysis used in the combination is provided, then in Section 3 a statistical methodology used in this work is briefly described, and finally in Section 4 the combined result is presented.

Channels used in the combined search
The combination presented in this report bases on eight analyses corresponding to main decay modes of the Higgs boson as summarised in Table 1. In the following subsections a brief description is provided of each individual analysis.

H → γγ channel [11]
The H → γγ analysis is a search for a narrow peak in the diphoton mass m γγ distribution on top of a large falling backa On leave from NCBJ, Warsaw, Poland b e-mail: michal.bluj@cern.ch ground. It is the most sensitive channel at low masses despite a small branching fraction (Br(H → γγ) ∼ 1−2 × 10 −3 ). All events are divided into eight categories based on whether the transverse momentum of the di-photon system p γγ T > 40 GeV/c, whether both photons are in the central part of the CMS detector, and whether both photons are unconverted (have compact electromagnetic showers). The categorisation is motivated by different resolution in each category (1-3%).
The background under the expected signal peak is derived from sidebands without use of Monte Carlo simulation.

H → ττ channel [12]
In this analysis a broad excess in the visible di-tau mass m vis ττ distribution is looked for (resolution of m vis ττ ∼ 20%). Three di-tau final states are used: eµ, eτ h , µτ h (τ h stands for a τ decaying hadronically). Each of of these three categories is further divided into two mutually exclusive subcategories: events with the Vector Boson Fusion (VBF) signature (two jets separated in pseudorapidity with no additional jets in between), and events with less than two jets or with exactly two jets that fail VBF requirements.
The main irreducible background is Z → ττ with normalisation taken from the Z → ℓℓ cross section measurement and shape of m vis ττ modelled using simulated events. The reducible backgrounds (W+jets, QCD, tt, Z → ℓℓ) are evaluated basing on data.

H → bb channel [13]
The H → bb search exploits the Higgs boson production in association with W or Z bosons (V). The following W and Z boson decay modes are considered: W → ℓν and Z → ℓℓ, νν (ℓ = e, µ). It is required that the system of two b-tagged jets (a Higgs boson decay candidate) is boosted in the transverse plane, which reduces background and improves the di-jet mass resolution. The result of the analysis bases on event count in signal regions defined by the output of a multivariate analysis classifier (MVA). The classifier was trained for a number of Higgs boson masses.
The rates of the main backgrounds V+jets, Vbb, and tt are estimated from control samples and then applied to simulation. The WZ and ZZ backgrounds with Z → bb, and the single-top background are modelled with Monte Carlo simulation.

H → WW * → 2ℓ2ν channel [14]
The signature of the H → WW * → 2ℓ2ν signal is the presence of exactly two opposite sign, isolated leptons and significant E miss T . There is no signal mass pick due to escaping energy due to presence of two neutrinos from W decays. The search is based on event counting.
Events are split into three categories basing on a jet multiplicity in the event (0, 1 or 2 jets) with different signal-tobackground ratios. For the 0-jet category the main background is the electroweak WW production; for the 1-jet category the WW and tt processes. Both the 0-and 1-jet categories are further split into same-flavour and oppositeflavour di-lepton sub-channels, since different contribution of the Drell-Yan background. The 2-jet category is optimised to take advantage of the VBF production signature (jets separation in pseudorapidity). The main background for this category is tt.
To separate the H → WW signal from the electroweak WW background the scalar nature of the Higgs boson is explored.
Contributions from all main backgrounds are estimated basing on data.

H → ZZ * → 4ℓ channel [15]
The H → ZZ * → 4ℓ analysis is a search for a four-lepton mass peak over the continuum background. Three final states 4e, 4µ, 2e2µ are considered separately, as each of them has a different resolution of m 4ℓ and a different composition of background with jets faking leptons.
The dominant irreducible background is the electroweak ZZ production. Its contribution is modelled using simulation and normalised using the measured yield of Z → ℓℓ events scaled by the ratio of ZZ and Z cross sections. The reducible backgrounds with jets faking leptons (Z+jets, Zbb, tt) are evaluated from data using control regions. Their contribution was found to be small.

H → ZZ → 2ℓ2τ channel [16]
In the H → ZZ → 2ℓ2τ search, the presence is required of one di-lepton pair (ee or µµ) forming an on-shell Z boson. Then a second Z boson is required to decay to τ-pair, with one of the following four decay modes: eµ, eτ h , µτ h , τ h τ h (τ h stands for a τ decaying hadronically). It makes eight exclusive sub-channels. In the analysis, the mass of two leptons and visible products of two tau decays (without accounting for missing neutrinos) is a final observable.
The dominant background is the electroweak ZZ production which is taken from simulation and normalised using the measured yield of Z → ℓℓ events scaled by the ratio of ZZ and Z cross sections. The sub-leading backgrounds with jets faking tau come from Z+jets (including ZW) and tt, are evaluated from data using fake-rate method.

H → ZZ → 2ℓ2ν channel [17]
In the H → ZZ → 2ℓ2ν analysis, events with one di-lepton pair (ee or µµ) consistent with an on-shell Z boson, and significant E miss T are selected. Then the transverse mass m T from the di-lepton pair momenta and E miss T is constructed assuming that E miss T arises from the Z → νν decay 1 . Finally, events are counted in a m H dependent window in the m T distribution.
The main ZZ and WZ backgrounds are taken from simulation, while all other backgrounds are evaluated from control samples.

H → ZZ → 2ℓ2q channel [18]
The H → ZZ → 2ℓ2q analysis is a search for a peak in the mass of the di-lepton plus di-jet system (m 2ℓ2j ). There are six exclusive final states used in the search with the lepton pair in one of two possible flavours (ee or µµ) and the jet pair with 0, 1 or 2 b-tags. Both lepton and jet pairs are required to be consistent with the Z boson mass. Background is further suppressed by employing a multivariate angular likelihood constructed from the kinematic variables of the two leptons and the two jets.
The background m 2ℓ2j distribution is obtained using control regions in data.

Statistical methodology
The modified frequentist construction CLs [19,20] is used for calculations of exclusion limits presented in this report. To completely define the method, one needs to make a choice of test statistic and of treatment of the systematic uncertainties in the construction of the test statistic and in generating pseudo-data. Here the LHC Higgs Combination Group prescription [21] is followed.
The likelihood L(data | µ, θ) used to construct the test statistic is defined as follows: The 2011 Hadron Collider Physics symposium (HCP-2011),Paris, France, November 14-18 2011 where Poisson (data|µ · s(θ) + b(θ) ) is the Poisson probability to observe "data", assuming signal and background models, s(θ) and b(θ), that depend on some nuisance parameters θ. The free parameter µ is a common signal strength modifier affecting signal event yields in all production modes (σ/σ SM ). Nuisance parameters θ correspond with independent sources of systematic uncertainties. The probability of "measuring"θ which is best known estimate of true value θ is p(θ|θ) and describes the scale of the systematic uncertainty. Then, the test statistics is definied as: where "data" stands either for the real observation or pseudodata. Both the denominator and numerator are maximized.
In the numerator, µ is fixed and only the nuisance parameters θ can float. Their values at which L reaches the maximum are denoted asθ µ . In the denominator, both µ and θ are allowed to float in the fit, andμ andθ are parameters at which L reaches its global maximum. The lower constraint onμ (0 ≤μ) is imposed as the signal rate cannot be negative; the upper constraint (μ ≤ µ) forces the limit to be one-sided. The value of the test statistic for the real observation is denoted as q obs .
In the next step, the values of the nuisance parametersθ obs 0 andθ obs µ best describing the observed data (maximizing L) are obtained for the background-only and signal+background hypotheses, respectively. Using these best-fit values of the nuisance parameters, toy Monte Carlo pseudo-data is generated to construct the test statistic sampling distributions for the both signal+background hypothesis (with signal strength µ) and for the background-only hypothesis (µ=0). The "measurements"θ are also randomized in each pseudodata.
With signal+background and background-only sampling distributions for the test statistic q µ one can find the probability to obtain a test statistic value as high as, or higher than, the one observed in data, under the signal+background hypothesis, and obtain CLs(µ) from the ratio The CLs ≤ α for a given µ means that the signal with strenth µ is excluded at the (1 − α) confidence level (C.L.). To quote the 95% C.L. upper limit on µ, we adjust µ until we reach CLs = 1 − 0.95.
To quantify an excess of events the alternative test statistic q 0 is used: This test statistic allows to evaluate significances (Z) and p-values (p 0 ) from the asymptotic formula: where q obs 0 is the observed test statistic for µ = 0.

Result of combined search
The combined result of the search for the SM boson is presented in Figure 1   The differences between the observed and expected limits are consistent with statistical fluctuations, as the observed limits lie within the 68% and 95% bands. For the low Higgs boson mass range, we observe an excess of events which leads to weaker observed limit than expected in the absence of the SM Higgs boson. The observed local p-value p 0 which quantifies the consistency of the observed excesses with the background-only hypothesis, is shown in Figure 3 (top panel) for the combined search, and split into individual decay modes in Figure 4. A broad offset for low masses, of about 1σ, corresponds to the excesses seen in the H → WW * → 2ℓ2ν channel characterised by poor mass resolution. The excesses observed in the H → ZZ → 4ℓ and the H → γγ channels result two narrow minima of the pvalue. The minimal p-value is p min ∼ 0.01, but after accounting for the look-elsewhere effect which is important for this study, it is reduced to a global probability p global ∼ 0.4. The look-elsewhere effect was esimeted for the whole explored mass range 110-600 GeV/c 2 . The best-fit value of σ/σ SM is also presented in Figure 3 (bottom panel). The best-fit value is a factor by which the SM Higgs boson cross section has to be rescaled to best describe observed data. In the mass range between 115 and 125 GeV/c 2 the best-fit value agrees within uncertainty with 1 (σ = σ SM ), but as discussed above, with the analysed amount of data the excess is not significant. More data will increase the statistical accuracy of the search thus improve its sensitivity.

Conclusions
The combined search for the standard model Higgs boson performed by the CMS Collaboration with up to 1.7 fb −1 of data was presented. The expected exclusion mass range is 130-440 GeV/c 2 . The observed data allowed to exclude the SM Higgs boson at 95% C.L. in three mass ranges 145-216, 226-288, and 310-400 GeV/c 2 . The largest excursion of the observed data from the expected background has a probability of 0.4 after taking into account the lookelsewhere effect for the whole explored mass range (110-600 GeV/c 2 ).