European Organisation for Nuclear Research CERN-EP/2000-156 22 December, 2000 Search for the Standard Model Higgs Boson in e+e Collisions at √s 192–209 GeV 1 − 0 ≈ 0 2 n a The OPAL Collaboration J 1 1 1 v 4 1 Abstract 0 1 0 Asearch fortheStandardModelHiggsbosonhasbeenperformedwiththeOPAL detector 1 at LEP based on the full data sample collected at √s 192–209 GeV in 1999 and 2000, /0 corresponding to an integrated luminosity of approx≈imately 426 pb−1. The data are x examined for their consistency with the background-only hypothesis and various Higgs e - boson mass hypotheses. A lower bound of 109.7 GeV is obtained on the Higgs boson p e mass at the 95% confidence level. At higher masses, the data are consistent with both h the background and the signal-plus-background hypotheses. : v i X r a (Accepted by Physics Letters B) This work is dedicated to the memory of our friends and collaborators, Professors Shuji Orito and George A. Snow. The OPAL Collaboration G.Abbiendi2, C.Ainsley5, P.F.˚Akesson3, G.Alexander22, J.Allison16, G.Anagnostou1, K.J.Anderson9, S.Arcelli17, S.Asai23, D.Axen27, G.Azuelos18,a, I.Bailey26, A.H.Ball8, E.Barberio8, R.J.Barlow16, R.J.Batley5, T.Behnke25, K.W.Bell20, G.Bella22, A.Bellerive9, G.Benelli2, S.Bethke32, O.Biebel32, I.J.Bloodworth1, O.Boeriu10, P.Bock11, J.B¨ohme25, D.Bonacorsi2, M.Boutemeur31, S.Braibant8, P.Bright-Thomas1, L.Brigliadori2, R.M.Brown20, H.J.Burckhart8, J.Cammin3, P.Capiluppi2, R.K.Carnegie6, B.Caron28, A.A.Carter13, J.R.Carter5, C.Y.Chang17, D.G.Charlton1,b, P.E.L.Clarke15, E.Clay15, I.Cohen22, J.Couchman15, A.Csilling15,i, M.Cuffiani2, S.Dado21, G.M.Dallavalle2, S.Dallison16, A.De Roeck8, E.A.De Wolf8, P.Dervan15, K.Desch25, B.Dienes30,f, M.S.Dixit7, M.Donkers6, J.Dubbert31, E.Duchovni24, G.Duckeck31, I.P.Duerdoth16, P.G.Estabrooks6, E.Etzion22, F.Fabbri2, M.Fanti2, L.Feld10, P.Ferrari12, F.Fiedler8, I.Fleck10, M.Ford5, A.Frey8, A.Fu¨rtjes8, D.I.Futyan16, P.Gagnon12, J.W.Gary4, G.Gaycken25, C.Geich-Gimbel3, G.Giacomelli2, P.Giacomelli8, D.Glenzinski9, J.Goldberg21, C.Grandi2, K.Graham26, E.Gross24, J.Grunhaus22, M.Gruw´e08, P.O.Gu¨nther3, A.Gupta9, C.Hajdu29, G.G.Hanson12, K.Harder25, A.Harel21, M.Harin-Dirac4, M.Hauschild8, C.M.Hawkes1, R.Hawkings8, R.J.Hemingway6, C.Hensel25, G.Herten10, R.D.Heuer25, J.C.Hill5, K.Hoffman8, R.J.Homer1, A.K.Honma8, D.Horv´ath29,c, K.R.Hossain28, R.Howard27, P.Hu¨ntemeyer25, P.Igo-Kemenes11, K.Ishii23, A.Jawahery17, H.Jeremie18, C.R.Jones5, P.Jovanovic1, T.R.Junk6, N.Kanaya23, J.Kanzaki23, G.Karapetian18, D.Karlen6, V.Kartvelishvili16, K.Kawagoe23, T.Kawamoto23, R.K.Keeler26, R.G.Kellogg17, B.W.Kennedy20, D.H.Kim19, K.Klein11, A.Klier24, S.Kluth32, T.Kobayashi23, M.Kobel3, T.P.Kokott3, S.Komamiya23, R.V.Kowalewski26, T.K¨amer25, T.Kress4, P.Krieger6, J.von Krogh11, D.Krop12, T.Kuhl3, M.Kupper24, P.Kyberd13, G.D.Lafferty16, H.Landsman21, D.Lanske14, I.Lawson26, J.G.Layter4, A.Leins31, D.Lellouch24, J.Letts12, L.Levinson24, R.Liebisch11, J.Lillich10, C.Littlewood5, A.W.Lloyd1, S.L.Lloyd13, F.K.Loebinger16, G.D.Long26, M.J.Losty7, J.Lu27, J.Ludwig10, A.Macchiolo18, A.Macpherson28,l, W.Mader3, S.Marcellini2, T.E.Marchant16, A.J.Martin13, J.P.Martin18, G.Martinez17, T.Mashimo23, P.M¨attig24, W.J.McDonald28, J.McKenna27, T.J.McMahon1, R.A.McPherson26, F.Meijers8, P.Mendez-Lorenzo31, W.Menges25, F.S.Merritt9, H.Mes7, A.Michelini2, S.Mihara23, G.Mikenberg24, D.J.Miller15, W.Mohr10, A.Montanari2, T.Mori23, K.Nagai13, I.Nakamura23, H.A.Neal33, R.Nisius8, S.W.O’Neale1, F.G.Oakham7, F.Odorici2, A.Oh8, A.Okpara11, M.J.Oreglia9, S.Orito23, C.Pahl32, G.P´asztor8,i, J.R.Pater16, G.N.Patrick20, J.E.Pilcher9, J.Pinfold28, D.E.Plane8, B.Poli2, J.Polok8, O.Pooth8, A.Quadt8, K.Rabbertz8, C.Rembser8, P.Renkel24, H.Rick4, N.Rodning28, J.M.Roney26, S.Rosati3, K.Roscoe16, A.M.Rossi2, Y.Rozen21, K.Runge10, O.Runolfsson8, D.R.Rust12, K.Sachs6, T.Saeki23, O.Sahr31, E.K.G.Sarkisyan8,m, C.Sbarra26, A.D.Schaile31, O.Schaile31, P.Scharff-Hansen8, M.Schr¨oder8, M.Schumacher25, C.Schwick8, W.G.Scott20, R.Seuster14,g, T.G.Shears8,j, B.C.Shen4, C.H.Shepherd-Themistocleous5, P.Sherwood15, G.P.Siroli2, A.Skuja17, A.M.Smith8, G.A.Snow17, R.Sobie26, S.S¨oldner-Rembold10,e, S.Spagnolo20, F.Spano9, M.Sproston20, A.Stahl3, K.Stephens16, D.Strom19, R.Str¨ohmer31, L.Stumpf26, B.Surrow8, S.D.Talbot1, S.Tarem21, M.Tasevsky8, R.J.Taylor15, R.Teuscher9, J.Thomas15, M.A.Thomson5, E.Torrence9, S.Towers6, D.Toya23, T.Trefzger31, I.Trigger8, Z.Tr´ocs´anyi30,f, E.Tsur22, M.F.Turner-Watson1, I.Ueda23, B.Vachon26, C.F.Vollmer31, P.Vannerem10, M.Verzocchi8, H.Voss8, J.Vossebeld8, D.Waller6, C.P.Ward5, D.R.Ward5, P.M.Watkins1, A.T.Watson1, N.K.Watson1, P.S.Wells8, T.Wengler8, N.Wermes3, D.Wetterling11 J.S.White6, G.W.Wilson16, J.A.Wilson1, T.R.Wyatt16, S.Yamashita23, V.Zacek18, D.Zer-Zion8,k 1School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK 2Dipartimento di Fisica dell’ Universit`a di Bologna and INFN, I-40126 Bologna, Italy 3Physikalisches Institut, Universit¨at Bonn, D-53115 Bonn, Germany 4Department of Physics, University of California, Riverside CA 92521, USA 5Cavendish Laboratory, Cambridge CB3 0HE, UK 6Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ot- tawa, Ontario K1S 5B6, Canada 7Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada 8CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerland 9Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USA 10Fakult¨at fu¨r Physik, Albert Ludwigs Universit¨at, D-79104 Freiburg, Germany 11Physikalisches Institut, Universit¨at Heidelberg, D-69120 Heidelberg, Germany 12IndianaUniversity, DepartmentofPhysics, SwainHallWest117,BloomingtonIN47405, USA 13Queen Mary and Westfield College, University of London, London E1 4NS, UK 14Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D- 52056 Aachen, Germany 15University College London, London WC1E 6BT, UK 16Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK 17Department of Physics, University of Maryland, College Park, MD 20742, USA 18Laboratoirede Physique Nucl´eaire, Universit´e de Montr´eal, Montr´eal, Quebec H3C 3J7, Canada 19University of Oregon, Department of Physics, Eugene OR 97403, USA 20CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK 21Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel 22Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel 23International Centre for Elementary Particle Physics and Department of Physics, Uni- versity of Tokyo, Tokyo 113-0033, and Kobe University, Kobe 657-8501, Japan 24Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel 25Universit¨at Hamburg/DESY, II Institut fu¨r Experimental Physik, Notkestrasse 85, D- 22607 Hamburg, Germany 26University of Victoria, Department of Physics, P O Box 3055, Victoria BC V8W 3P6, Canada 27UniversityofBritishColumbia,DepartmentofPhysics, VancouverBCV6T1Z1,Canada 28University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada 29Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P O Box 49, Hungary 30Institute of Nuclear Research, H-4001 Debrecen, P O Box 51, Hungary 31Ludwigs-Maximilians-Universit¨at Mu¨nchen, Sektion Physik, Am Coulombwall 1, D- 85748 Garching, Germany 32Max-Planck-Institute fu¨r Physik, F¨ohring Ring 6, 80805 Mu¨nchen, Germany 33Yale University,Department of Physics,New Haven, CT 06520, USA a and at TRIUMF, Vancouver, Canada V6T 2A3 b and Royal Society University Research Fellow c and Institute of Nuclear Research, Debrecen, Hungary e and Heisenberg Fellow f and Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hun- gary g and MPI Mu¨nchen i and Research Institute for Particle and Nuclear Physics, Budapest, Hungary j now at University of Liverpool, Dept of Physics, Liverpool L69 3BX, UK k and University of California, Riverside, High Energy Physics Group, CA 92521, USA l and CERN, EP Div, 1211 Geneva 23 m and Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel. 1 Introduction In the Standard Model [1], the Higgs mechanism [2] gives mass to the electroweak gauge bosons,thusallowingtheunificationoftheelectromagneticandweakinteractions. Whether the Higgs boson exists is one of the most important open questions in particle physics. A number of improvements were made to the LEP collider for the year 2000 data tak- ing, which increased the Higgs discovery potential, extending the sensitivity of the Higgs boson search to approximately 115 GeV if the data from all four LEP experiments are combined. The combination of the preliminary Higgs boson search results of the four LEP experiments [3,4] shows an excess of candidates which may indicate the production of a Standard Model Higgs boson with a mass near 115 GeV. In this letter we present the results of a search for the Standard Model Higgs boson with the OPAL detector at LEP, considering particularly the mass hypothesis of 115 GeV. Approximately 426pb−1 ofe+e− annihilationdatawerecollectedbyOPALintheyears 1999 and 2000 at centre-of-mass energies in the range 192–209 GeV; this data sample is used for the analyses presented in this letter. Searches are performed for the “Higgs- strahlung” process e+e− H0Z0 H0f¯f, where H0 is the Standard Model Higgs boson, and f¯f is a fermion-antiferm→ion pair→from the Z0 decay. For the H0νν¯ (H0e+e−) final state, the contribution from the W+W− (Z0Z0) fusion process is also taken into account. Only the decays of the Higgs boson into bb¯ and τ+τ− are considered here. OPAL has already reported results from the Standard Model Higgs boson search at e+e− centre-of-mass energies up to 189 GeV [5,6], where a lower mass limit of m > 91.0 GeV was obtained H at the 95% confidence level. A similar search procedure is applied here. All data were processedwiththemostup-to-datedetectorcalibrationsavailable. Forfuturepublications more refined analyses and the final detector calibrations will be used. 2 OPAL Detector, Data and Monte Carlo Samples DetailsoftheOPALdetectorcanbefoundin[7]. Thedatausedintheanalysescorrespond to integrated luminosities of approximately 216 pb−1 at 192–202GeV, 80 pb−1 at 203–206 GeV, and 130 pb−1 at centre-of-mass energies higher than 206 GeV. The total luminosity used to search for the Higgs boson varies by 2% from channel to channel, due to slightly ± different requirements on the operational status of different detector elements. During 2000 (1999), data were taken at √s = 200-209 GeV (192-202 GeV) with a luminosity- weighted mean centre-of-mass energy of 206.1 (197.6) GeV. A variety of Monte Carlo samples was generated at centre-of-mass energies between 192 and 210 GeV. Higgs boson production is modelled with the HZHA3 generator [8] for a wide range of Higgs boson masses. The size of these samples varies from 2000 to 10000 events for each mass and at each centre-of-mass energy. The background processes are simulated with typically more than 50 times the statistics of the corresponding data sam- ∗ ple. The process (Z/γ) qq¯(γ) is modelled with the KK2f generator using CEEX [9] for → the modelling of the initial state radiation. The four-fermion processes (4f) are simulated using grc4f[10]. Thetwo-photonandother two-fermionprocesses haveanegligible impact on the results. The hadronisation process is simulated with JETSET/PYTHIA [11] with parameters described in [12]. In each search channel, the estimates of the signal efficiency and the selected background rate depend strongly on the centre-of-mass energy and are thus interpolated on a fine grid. For each Monte Carlo sample, the full detector response is simulated in detail as described in [13]. 3 Analysis Procedures We search for Higgs production in the following final states: H0Z0 bb¯qq¯ (four-jet chan- nel), H0Z0 bb¯νν¯ (missing-energy channel), H0Z0 bb¯τ+τ− and τ→+τ−qq¯ (tau channels), H0Z0 bb¯e→+e− and bb¯µ+µ− (electron and muon c→hannels). In each channel, a preselec- → tion is applied to ensure that the events are well measured and are consistent with the desired signal topology. A likelihood selection combining 6 to 10 variables depending on the search channel is then used to further enrich the signal. We use the same analysis techniques described in a previous publication [5], namely event reconstruction, b-flavour tagging,lepton(electron, muonandtau)identification and kinematic fits to reconstruct the Higgs boson mass. The b-tagging variable is evaluated B for each jet to distinguish jets containing b-hadrons from those that do not. The tracking and b-tagging performance in the Monte Carlo simulation are tuned using 8.2 pb−1 of calibration data collected at √s m at intervals during 1999 and 2000 with the same Z ≈ detector configuration and operating conditions as the high-energy data. Figure 1(a) shows the distribution of for the calibration data. Comparisons between the data and B the Monte Carlo simulation are shown in Figure 1(b) for jets which are found opposite to jets passing or failing the b-tagging requirement. The tagging efficiency for b-flavoured (udsc-flavoured) jets is modelled by the Monte Carlo simulation to within an accuracy of 2% (5%). The performance of the b-tagging for the data taken at √s 192 GeV is checked ≥ with samples of qq¯(γ) events by selecting hadronic events with the mass of the qq¯ system near m . Figure 1(c) shows the b-tagging variable for jets opposite b-tagged jets in Z B the 2000 sample. The efficiency for tagging udsc flavours is also checked by computing for the jets in a sample of W+W− qqℓν (ℓ=e or µ) obtained with the selection used tBo measure the W+W− cross-section [→14] as shown in Figure 1(d). The expectation from the Standard Model Monte Carlo describes the data within the relative statistical uncertainty of5–10%. Theresultsofthesecross-checks arenotusedintheevaluationofthesystematic uncertainties described below. Sources of systematic uncertainties are investigated for their effect on the signal de- tection efficiencies and the Standard Model backgrounds. The error from the modelling of the likelihood selection input variables on the background (signal) rates is 4–8% (1– 4%), depending on the channel. These uncertainties are evaluated based on comparisons of the distributions of the variables in the data and the Monte Carlo. Comparisons of alternative Monte Carlo generators for the backgrounds [9–11,15] account for an addi- tional 3–11% uncertainty in the background rates. The uncertainty in the four-fermion cross-section is taken to be 2% [16]. The uncertainties on the detector performance, ± such as the spatial resolution of the tracking and the modelling of the efficiency of the silicon microvertex detector, are evaluated source by source with Monte Carlo studies. Recent improvements in the knowledge of heavy quark production processes and decays, such as the b-hadron charged decay multiplicity [17] and the gluon splitting rate to heavy quarks [18], are taken into account in the analyses by reweighting Monte Carlo events. The modelling of the b-hadron production and decay processes is constrained by various measurements summarized in [17]; residual uncertainties in these measurements result in systematic uncertainties here. In particular, the b-hadron charged decay multiplicity n B is varied within n = 4.955 0.062. The uncertainties from the fragmentation functions B ± for b- and c-quarks are obtained by adjusting the mean energy x within the range al- E h i lowed by the measurements. The charm and bottom-flavoured hadron lifetimes are varied within their errors with negligible effect on all search channels. The total uncertainties on the background (signal) rates are 11–15% (5–6%) varying from channel to channel. 3.1 Event Selections and Mass Reconstruction Thepreselection requirements inthefour-jetchannelareidenticaltothoseof[5]. Afterthe preselection, a likelihood selection based on eight variables is applied. For each selected candidate, two of the jets are associated to the H0 using a likelihood method based on the kinematic fit result and the b-tagging information. The mass determined by a H0Z0 5C kinematic fit for the chosen jet pair gives the reconstructed mass of the Higgs boson candidate, mrec. Because of the constraints of the kinematic fit, mrec < √s m . The H H Z − variables used in the likelihood selection for the 1999 data are the same as those used in our earlier analysis [5]. For the 2000 data, however, one variable, the χ2 probability of the H0Z0 5C kinematic fit, is replaced by the χ2 probability of a fit imposing an equal-mass constraint as used in the OPAL W mass measurement [19] in order to further suppress the Z0Z0 background. The selection of the missing-energy channel is very similar to [5]. The notable changes are: 1) tightening the requirement on the maximum fraction of the visible energy in the angular region cosθ > 0.90 from 50% to 20% in order to further suppress qq¯(γ) back- | | ground (changed only in the 2000 analysis); 2) a looser requirement on the missing mass which is now selected in the range from 40 to 140 GeV. Other small changes correspond to the scaling of cut values with √s for variables related to the visible momenta. In the construction of the likelihood selection, two new variables are included: 1) the thrust value of the event, and 2) the angle between the missing momentum and the direction of the most energetic jet. This last variable adds discrimination power especially against the process W+W− qqℓν in which the charged lepton is close to one of the jet axes. → The reconstructed Higgs boson mass mrec is evaluated using a kinematic fit constraining H the missing mass to the Z0 mass. Because of the fit constraints, mrec < √s m . H Z − The event selections in the tau, electron and muon channels are identical to the ones used in [5]. For the tau channel the reconstructed Higgs boson mass is evaluated (see [5]) withthe3Ckinematicfitwiththelargestχ2 probabilityfixingeither thetaupairinvariant mass or the jet pair invariant mass to the Z0 mass. The reconstructed Higgs boson mass is determined by the recoil mass of the electron pair in the electron channel, and with the results of a 4C kinematic fit constraining energy and momentum in the muon channel. There is no upper bound of mrec at √s m in the electron and muon channels. H Z − The numbers of events selected in each analysis after preselection and after the final likelihood selection are shown in Table 1 for the data taken at √s 192 209 GeV. ≈ − The errors on the background and signal expectations are the sums in quadrature of the individual systematic uncertainties. Distributions of the selection likelihood values H0Z0 L in all channels are shown in Figure 2. The number of selected events in all search channels is 156 with 146.1 11.9 expected from Standard Model background processes. ± The distributions of the reconstructed masses of the selected events are shown in Fig- ure 3. Note that all data taken in the wide √s range from 192 to 209 GeV are summed in the figure, while the expected signal rates strongly depend on √s. The method used to optimise the sensitivity to the signal is described in Section 3.2. The background accumu- lation at high reconstructed mass in the four-jet channel is dominated by qq¯ events and jet-pairing combinatorial backgrounds from the Z0Z0 process. The qq¯ background in the missing-energy channel also clusters at high reconstructed mass because qq¯ events passing the selection requirements are largely composed of events with two or more undetected, energetic initial state radiation photons with a small momentum sum along the beam direction. The jets in such events are nearly back-to-back, which results in values of mrec H near the maximum kinematically allowed in the fits, √s m . Z − 3.2 Confidence Level Calculations After the event selections, all results from the various search channels are combined to test for the presence of a Standard Model Higgs boson signal. Previous data taken at centre-of-mass energies near or below 189 GeV have a negligible impact on the sensitivity to Higgs boson signals with m > 100 GeV and are not included. The cross-sections used H in computing the confidence level (CL) include the effects of W+W− and Z0Z0 fusion processes and their interference with the H0Z0 process in the missing-energy and electron channels respectively, as calculated using HZHA3 [8]. In order to compute the confidence levels, a test statistic is defined which expresses how signal-like the data are. The confidence levels are computed from the test statistic of the observed data and the expected distributions of the test statistic in a large number of simulated experiments under two hypotheses: the background-only hypothesis and the signal+background hypothesis. The test statistic chosen is the likelihood ratio Q, the ratio of the probability of observing the data given the signal+background hypothesis to the probability of observing the data given the background-only hypothesis [20,21]. The results of all search channels are expressed in fine bins of discriminating variables, such as mrec. The expected signal strength depends strongly on √s, hence the results H are considered separately in fine divisions of √s. In each bin of each channel at each √s the expected Higgs boson signal, s , and the Standard Model background rate, b , i i are estimated, and the observed data counts, n , are reported. The s depend on the i i mass of the Higgs boson under study (the “test mass”). Each bin is considered to be a statistically independent search obeying Poisson statistics. The likelihood ratio Q can then be computed [21] as lnQ = P s +P n ln(1+s /b ). Each event has a weight in i i i i i i − the sum which depends on the signal-to-background ratio in the bin in which it is found; events may be classified by their local s/b values. The confidence level for the background hypothesis is (1 CL ) [21] which is the probability in an ensemble of background-only b − experiments of observing a more signal-like Q than is actually observed: 1 CL = b − P(Q > Q background). A low value of (1 CL ) indicates an excess of candidates obs b | − in data compared to the expectation from background. The distribution of (1 CL ) is b − uniform between 0 and 1 in an ensemble of background-only experiments. Similarly, theconfidencelevelforthesignal+backgroundhypothesisisCL = P(Q s+b ≤ Q signal+background), and is used to exclude the signal+background hypothesis if it obs | has a small value. To eliminate the possibility of excluding a signal to which there is no sensitivity, a third quantity is defined CL = CL /CL [21]. Results are also presented s s+b b in terms of the signal rate limit n95 = gminPisi, where gmin is the smallest number such that the signal hypothesis consisting of g s in each bin yields CL = 0.05. The signal min i s rate limit n depends on the test mass. The technique used to perform the computation 95 of the confidence levels is the same as is used in [6]. In our previous papers, the only discriminating variables used were the values of mrec. H Here, the discriminating power is improved by combining mrec with other variables. In H the four-jet channel, after the jet pairing assignment and mass determination, a new test-mass-dependent variable is formed using a likelihood technique in order to mass D investigate the compatibility with the signal production hypothesis for a Higgs boson of a specific test mass. The variable is based on the following four quantities: 1) the mass D combined b-tagging variable H defined by H /( +(1 ) (1 )) B2jet B2jet ≡ B1·B2 B1·B2 −B1 · −B2 for the two jets with the most significant b tags; 2) the energy difference between the most energetic and the least energetic jets in the event; 3) β , a selection likelihood min variable (see [6]); and 4) the reconstructed Higgs boson mass mrec. Signal Monte Carlo H sampleswere generatedwithHiggsbosonmasses in1GeVsteps, and isinterpolated mass D between neighbouring test masses. The distribution of is shown for a test mass of mass D 115 GeV in Figure 4(a). In the missing-energy, electron and muon channels, the selection likelihood value, H0Z0, is used to form a two-dimensional discriminant ( H0Z0, mrec). The cut on H0Z0 is H L L L chosen to optimise the sensitivity of this new discriminant. In Figures 4(b) and (c), the reconstructed mass distributions are shown in slices of the selection likelihoods for the electron and muon channels, and for the missing-energy channel, respectively. In each channel, the enrichment of the signal depends on both the likelihood value and on mrec. H For the tau channels, only the reconstructed mass is used for the discriminant as in [5]. The systematic uncertainties on the signal and background expectations in each chan- nelaretreated using anextension ofthemethoddescribed in[22]. Uncertainties described in Section 3 are assumed to be 100% correlated if they arise from the same source in dif- ferent channels, in the signal and background estimations, and at different centre-of-mass energies. The current uncertainty on the beam energy for the 2000 data is expected to be of the order of 100 MeV, and would therefore affect the limits by 200 MeV. The ∼ uncertainty on the integrated luminosity is estimated to be 0.3%. Both of these errors are neglected. 4 Results Figure 5(a) shows (1 CL ) as a function of the test mass m . It attains its lowest value b H − of 0.02 at m = 107 GeV, indicating a local excess of candidates. The probability to H observe such an excess anywhere in the range of test masses between 100 and 120 GeV is approximately 10%, estimated from the size of the range and the reconstructed mass resolution. The value of (1 CL ) observed at m =115 GeV is 0.2. Figure 5(a) also b H − shows the expected (1 CL ) in the presence of a 115 GeV Higgs boson signal. b − The signal rate limit n is shown as a function of m in Figure 5 (b) together with 95 H its median expectation in an ensemble of background-only experiments. Figure 5 (b) also shows the expected accepted signal rate. Where the signal rate curve crosses the n curve is the 95% CL exclusion limit on m , and the expected limit is where the 95 H median expected n curve crosses the accepted signal rate curve. A lower mass bound of 95 109.7 GeV is obtained, and the expected limit is 112.5 GeV. In particular, the hypothesis m =107 GeV is excluded at the 98% CL (CL = 0.02) even in the presence of the excess H s candidates because the excess in the data is not large enough to be consistent with the expected signal rate from a Standard Model Higgs boson of that mass. The candidates with the largest weights, ln(1+s/b), in each channel for test masses of 115 GeV are listed in Table 2. Figure 6 shows the distributions of ln(1+s/b) of each candidate as a function of the Higgs boson test mass for the candidates collected in 1999 and 2000. The region of test mass for which a candidate’s contribution is significant depends on the mass resolution of the candidates in the channel, and the normalization of thecurve depends onthe candidateb-tags, the kinematic variables, theHiggsbosoncross- section and the local background near the reconstructed candidate mass. Deviations from smoothness of the curves are due to Monte Carlo statistics; this uncertainty is included in the confidence level computation. The most significant candidate for a Higgs boson search for a test mass m = 115 GeV H (candidate #1) is found in the four-jet channel. For the jet-pairing chosen by the jet- pairing likelihood function, the event has a reconstructed Higgs boson mass of 110.7 GeV. The second most significant candidate (#2) is also found in the four-jet channel, with a reconstructed mass of 112.6 GeV. No jet pairing yields a reconstructed Higgs boson mass close to the Z0 mass in either of these two candidates. The observed low value of (1 CL ) at 107 GeV is caused by candidates which have b − relatively high weights at around 105–110 GeV seen in Figure 6. For the tau channel candidate #5, the reconstructed mass is taken from the invariant mass of the jets after a 3C kinematic fit where the tau pair mass is constrained to the Z0 mass. The tau pair mass is 91 GeV if a 2C fit [5] is performed. The muon channel candidate #7 significantly affects the results of the confidence level calculations around 100–105 GeV since its likelihood H0Z0 is very close to one. L The observed 2lnQ is shown as a function of the test mass m in Figure 7 (a). Also H − shown are the 68% and 95% probability contours centred on the median expectation. Fig- ure 7 (b) shows the probability density functions of 2lnQ for the signal+background − hypothesis with m = 115 GeV, and also for the background hypothesis. The separation H between the two hypotheses is not strong. The background confidence level (1 CL )=0.2 b − is the integral of the background-only probability density to the left of the data obser- vation, and CL = 0.4 is the integral to the right of the data observation of the sig- s+b nal+background curve. The data are slightly more consistent with the presence of a 115 GeV Higgs boson than with the background alone. 5 Conclusions A search for the Standard Model Higgs boson has been performed with the OPAL de- tector at LEP based on the full data sample collected at √s 192–209 GeV in 1999 and ≈ 2000. The largest deviation with respect to the expected Standard Model background in the confidence level for the background hypothesis, (1 CL ), is observed for a Higgs b − boson mass of 107 GeV with a minimum (1 CL ) of 0.02, but the observed excess is less b − significant than is expected for a Standard Model Higgs boson with a 107 GeV mass. A lower bound of 109.7 GeV on the mass of the Standard Model Higgs boson is obtained at the95%confidence level while themedianexpectation forthebackground-onlyhypothesis is 112.5 GeV. For a Higgs boson with a mass of 115 GeV, (1 CL ) is approximately 0.2 b − while CL is approximately 0.4, indicating that the data slightly favour the hypothesis s+b that a signal is present, but also that the data are consistent with the background hy- pothesis. These data alone provide little discrimination between the signal+background and background hypotheses for Higgs boson masses above 112 GeV, but more statistically