The Standard Model Higgs boson has been searched for by the four LEP
experiments in the last twelve years. The data collected at LEP in the year
2000 suggest the first observation of a Higgs boson. In this letter, I describe
the basic concepts of the Higgs search at LEP, with emphasis in the statistical
method used to combine the results from the LEP experiments.Comment: 4 pages, 8 figures, submitted to Moriond QCD 200

Garcia-Abia, Pablo

English

arXiv

The Standard Model Higgs boson has been searched for by the four LEP experiments in the last twelve years. The data collected at LEP in the year 2000 suggest the first observation of a Higgs boson. In this letter, I describe the basic concepts of the Higgs search at LEP, with emphasis in the statistical method used to combine the results from the LEP experiments.The Standard Model Higgs boson has been searched for by the four LEP experiments in the last twelve years. The data collected at LEP in the year 2000 suggest the first observation of a Higgs boson. In this letter, I describe the basic concepts of the Higgs search at LEP, with emphasis in the statistical method used to combine the results from the LEP experiments

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STANDARD MODEL HIGGS SEARCH STRATEGY AT LEPP. GARCIA-ABIAaCERN, EP Division, J21300, CH-1211-Geneva 23, SwitzerlandOn behalf of the LEP CollaborationsThe Standard Model Higgs boson has been searched for by the four LEP experiments in thelast twelve years. The data collected at LEP in the year 2000 suggest the first observation ofa Higgs boson. In this letter, I describe the basic concepts of the Higgs search at LEP, withemphasis in the statistical method used to combine the results from the LEP experiments.1 IntroductionIn 12 years of running, the LEP collider at CERN has produced e+e− collisions in the interactionregion of the four detectors ALEPH, DELPHI, L3 and OPAL. The centre-of-mass energy of theinteractions varied from about 90 to 210 GeV. The large amount of data collected at theseenergies has allowed the experiments to measure the most relevant parameters of the StandardModel 1 with very high accuracy, establishing the success of the model.However, the Standard Model does not provide an answer to a fundamental problem: in agauge invariant theory all fundamental particles should be massless, in contradiction with theobservation of the heavy W and Z bosons. Currently, there is no direct evidence of electroweaksymmetry breaking and the generation of masses of the gauge bosons. The Higgs mechanism isintroduced in the model to let particles acquire mass by interaction with the Higgs eld. As aresult, there should be a new particle of a completely new kind, the Higgs boson, whose mass isnot predicted by the theory.2 Higgs Production at LEPThe dominant Higgs production mode at LEP is the Higgsstrahlung process, e+e− ! Z ! HZ(Figure 1 (left)). The processes W+W− and ZZ fusion, giving rise to the H and He+e−aOn leave from the Institute of Physics of the University of Basel (Switzerland).Z*Ze+e− HW, ZW, Ze+e−ν_e, e+νe, e−HHiggsstrahlung diagramFusion diagram10-310-210-11100 110 120 130MH   [GeV]Cross section  [pb]Total cross sectionHiggsstrahlungFusion + interference√s = 206.6 GeVFigure 1: Higgs production modes (left) and cross section as function of the Higgs mass (right).channels, contribute with smaller rate to the Higgs production cross section (Figure 1 (right)).The integrated luminosity collected by the four experiments at LEP in the year 2000 amountsto 870 pb−1, at centre-of-mass energy between 200 and 209 GeV. At these energies, Higgsbosons of 116 GeV mass or heavier are dicult to be detected, as they would be producedbeyond the kinematic limit. As an example, assuming a Higgs of 115 GeV mass, a luminosity of500 pb−1collected atps  207 GeV and a detection eciency of 50 %, the number of expectedsignal events is 12.5.The Higgs boson is predicted to decay mainly in b-quark pairs for masses below 120 GeV.The Z boson decays into hadrons, neutrinos and leptons with branching fractions 69.6%, 20%and 10.1%, respectively. The search for the Higgs boson is based on the study of four distinctevent topologies representing approximately 80% of the HZ decay modes in the mass range ofinterest: bbqq (4-jet channel), bb (missing energy channel), qq‘+‘− (‘ = e; ; ) and +−qq(lepton and tau channels, respectively). With the exception of the HZ ! +−qq decay mode,all the analyses are optimised for H!bb decay.Figure 2 (left) displays the topology of the four search channels, together with their branchingratios. The expected signal events for a 115 GeV mass Higgs are: 6.5 from the 4-jet channel,1.9 from the missing energy channel, 1 from taus and 0.6 from leptons (e+), that is 10 eventsin total.The main backgrounds are events from e+e− ! qq(γ), W+W− and ZZ processes (Figure 2(right)). The tagging of jets originating from b-quarks plays a crucial role in the identicationof signal events. After the nal selections, typically few hundred events are expected frombackground processes. The detailed description of the analyses of the dierent channels can befound elsewhere in these proceedings 2,3.3 The Statistical Method: −2 ln(Q)Each of the four LEP experiments performs the Higgs search in four analysis channels, with datacollected at several centre-of-mass energies. A simple statistical method 4 has been developedby the experiments in order to treat LEP as a single search analysis.The results of the individual analyses are expressed in terms of one (or more) nal variable,4-jetleptons (e+µ)missing energytaus52%5%15%8%Z→ qq_H→ bb_Z→ l+l− H→ bb_Z→ νν_H→ bb_Z→ τ+τ− H→ bb_H→ τ+τ− Z→ qq_10-410-310-210-111080 100 120 140 160 180 200 220s [nb]s [GeV]mH  =114 GeVe+e– → g /Z → qq_(g )e+e– → HZ → qq_qq_s' / s > 0.85e+e–→ W+W-→ qq_qq_e+e–→ ZZ→ qq_qq_e+e– → e+e–hadronsWgg > 5 GeVL3Figure 2: Left, topology of the four search channels, together with the branching ratio and the conventional nameof the channel. Right, cross section of the background processes.also called discriminant, which is calculated for the signal and background expectations as wellas for the data. How this nal variable is calculated for each channel is explained elsewhere 2,3.The shape of the distributions depends on the Higgs mass hypothesis.The ratio between the expected number of signal and background events (the so called s/bratio) for a given value of the nal variable reflects the likelihood for an event being signal orbackground-like. Events from dierent experiments and channels with the same value of thes/b ratio are combined together, as they have the same sensitivity (discriminating power) toa possible Higgs signal. As an example, Figure 3 shows typical distributions of a discriminantvariable (left) and the s/b ratio (right) for data, signal and background events. Events at highvalues of s/b are more signal-like.In order to quantify the signal-likeness of the data, the Likelihood Ratio 4 test-statistic isdened as the ratio of the Poisson probabilities of data to be consistent with either the signal10-310-210-111010 20 1 2 3 4DiscriminantEvents / 0.25DataBackgroundHqq_ signal  (115 GeV)10-210-1110-1 0 1log10(S/B)Events / 0.15DataBackgroundSignalFigure 3: Typical distributions of a discriminant variable (left) and the s/b ratio (right) for data, signal andbackground events.-20 -10 0 10-2 ln(Q)Probability densityobservedsignal+background backgroundCLs+b1-CLb-10-7.5-5-2.502.557.510110 112 114 116 118Background OnlyBackground+SignalEXAMPLEObservedMH (GeV)-2ln(Q)Figure 4: Left, example distributions of −2 ln(Q) for the background and signal plus background hypotheses, aswell as for the data, for a given Higgs mass. The definition of the confidence levels of the background (CLb) andthe signal plus background (CLs+b) are also shown. Right, example distribution of −2 ln(Q) as function of theHiggs mass. The colour bands are the 1σ and 2σ bands for the background expectation.plus background hypothesis or the background only hypothesis:Q =L(s + b)L(b)Each bin in the s/b ratio distribution (i) is treated as a Poisson counting experiment:ln(Q) = −stot +N∑i=1ni ln(1 +sibi)where ni is the number of observed events, si the expected signal and bi the expected backgroundin a given bin. The sum runs over all the bins in the s/b distribution, i.e. all the observed eventsenter the likelihood calculation. The value of Q, and hence its discrimination power, dependson the Higgs mass hypothesis and on the Higgs production cross section (stot). In the highstatistics limit −2 ln(Q) approaches the dierence in 2 of the two hypotheses, that is why thisconvention is adopted.The results of the LEP combination using this statistical method are presented in detailelsewhere in these proceedings 5.References1. S.L. Glashow, Nucl. Phys. 22, 579 (1961), S. Weinberg, Phys. Rev. Lett. 19, 1264(1967), A. Salam, \Weak and Electromagnetic Interactions", in Elementary Particle The-ory, edited by N. Svartholm, page 367, Stockholm, 1969, Almqvist and Wiksell.2. G. Davies, \Selecting Standard Model Higgs candidates in the 4-jet channel at LEP", theseproceedings.3. E. Piotto, \Selecting Standard Model Higgs candidates in other channels at LEP", theseproceedings.4. ALEPH, DELPHI, L3 and OPAL Collab., The LEP Working Group for Higgs BosonSearches, Preprint CERN-EP/2000-055.5. A. Okpara, \Standard Model Higgs at LEP: combined results", these proceedings.

Standard Model Higgs Search Strategy at LEP

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Standard Model Higgs Search Strategy at LEP

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