1 Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA2 Physics Department, University Instelling Antwerpen, Universiteitsplein 1, 2610 Wilrijk, Belgium
and IIHE, ULB-VUB, Pleinlaan 2, 1050 Brussels, Belgiumand Faculte des Sciences, University de l’Etat Mons, Av. Maistriau 19, 7000 Mons, Belgium
3 Physics Laboratory, University of Athens, Solonos Str. 104, 10680 Athens, Greece4 Department of Physics, University of Bergen, Allegaten 55, 5007 Bergen, Norway5 Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna, Italy6 Centro Brasileiro de Pesquisas Fısicas, rua Xavier Sigaud 150, 22290 Rio de Janeiro, Brazil
and Depto. de Fısica, Pont. University Catolica, C.P. 38071, 22453 Rio de Janeiro, Braziland Inst. de Fısica, University Estadual do Rio de Janeiro, rua Sao Francisco Xavier 524, Rio de Janeiro, Brazil
7 Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, 84215 Bratislava, Slovakia8 College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, 75231 Paris Cedex 05, France9 CERN, 1211 Geneva 23, Switzerland
10 Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, 67037 Strasbourg Cedex, France11 Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, 15310 Athens, Greece12 FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic13 Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, 16146 Genova, Italy14 Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, 38026 Grenoble Cedex, France15 Helsinki Institute of Physics, HIP, P.O. Box 9, 00014 Helsinki, Finland16 Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation17 Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany18 Institute of Nuclear Physics and University of Mining and Metalurgy, Ul. Kawiory 26a, 30055 Krakow, Poland19 Universite de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. 200, 91405 Orsay Cedex, France20 School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK21 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, 1000 Lisboa Codex, Portugal22 Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK23 LPNHE, IN2P3-CNRS, University Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, 75252 Paris Cedex 05, France24 Department of Physics, University of Lund, Solvegatan 14, 223 63 Lund, Sweden25 Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, 69622 Villeurbanne Cedex, France26 University d’Aix - Marseille II - CPP, IN2P3-CNRS, 13288 Marseille Cedex 09, France27 Dipartimento di Fisica, Universita di Milano and INFN, Via Celoria 16, 20133 Milan, Italy28 Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark29 NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic30 NIKHEF, Postbus 41882, 1009 DB Amsterdam, The Netherlands31 National Technical University, Physics Department, Zografou Campus, 15773 Athens, Greece32 Physics Department, University of Oslo, Blindern, 1000 Oslo 3, Norway33 Dpto. Fisica, University Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain34 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK35 Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, 35131 Padua, Italy36 Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK37 Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, 00173 Rome, Italy38 Dipartimento di Fisica, Universita di Roma III and INFN, Via della Vasca Navale 84, 00146 Rome, Italy
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 565
39 DAPNIA/Service de Physique des Particules, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France40 Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, 39006 Santander, Spain41 Dipartimento di Fisica, Universita degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy42 Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation43 J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics,
Nova Gorica Polytechnic, Kostanjeviska 16a, 5000 Nova Gorica, Slovenia,and Department of Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
44 Fysikum, Stockholm University, Box 6730, 113 85 Stockholm, Sweden45 Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, 10125 Turin, Italy46 Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, 34127 Trieste, Italy
and Istituto di Fisica, Universita di Udine, 33100 Udine, Italy47 University Federal do Rio de Janeiro, C.P. 68528 Cidade University, Ilha do Fundao 21945-970 Rio de Janeiro, Brazil48 Department of Radiation Sciences, University of Uppsala, P.O. Box 535, 751 21 Uppsala, Sweden49 IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, 46100 Burjassot (Valencia), Spain50 Institut fur Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, 1050 Vienna, Austria51 Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, 00681 Warsaw, Poland52 Fachbereich Physik, University of Wuppertal, Postfach 100 127, 42097 Wuppertal, Germany53 On leave of absence from IHEP Serpukhov54 Now at University of Florida
Received: 9 February 1999 / Published online: 28 September 1999
Abstract. Neutral Higgs bosons were searched for in the data collected by DELPHI at a centre-of-massenergy of 183 GeV, corresponding to an integrated luminosity of 54 pb−1. The production of the lightestneutral Higgs boson with either an on-shell Z boson or a neutral pseudo-scalar Higgs boson was anal-ysed. Lower limits at the 95% confidence level were obtained on the Higgs boson masses. The limits are85.7 GeV/c2 for the Standard Model Higgs boson and 74.4 GeV/c2 for the scalar and 75.3 GeV/c2 forthe pseudo-scalar Higgs bosons as predicted by the minimal super-symmetric extension of the StandardModel with commonly used assumptions on the model parameters, plus the assumption that the mass ofthe pseudo-scalar boson is greater than 20 GeV/c2. These results significantly improve the limits reachedwith previous data.
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 565
1 Introduction
In the framework of the Standard Model (SM) there isone physical Higgs boson, H, which is a neutral CP-evenscalar. At LEP II the most likely production process isthrough the s-channel, e+e−→ Z∗ →ZH. There are alsoW+W− and ZZ fusion t-channel production processes insome of the channels described here, but their contributionto the cross-section is at most 10%.
In the Minimal Super-symmetric Standard Model(MSSM) five physical Higgs bosons are predicted, butonly two are likely to be accessible at LEP II. There isone scalar boson, the h, analogous to the SM Higgs, butbounded in mass to be less than mZ at tree level. Afterradiative corrections its mass may be larger. The results ofthe search for the SM Higgs are also interpreted in termsof this boson. The CP-odd pseudo-scalar, A, would beproduced mostly in the e+e− →hA process.
We have previously [1] excluded a Standard Model Hwith mass less than 66.2 GeV/c2, and set limits on hand A of the MSSM of 59.5 GeV/c2 and 51.0 GeV/c2respectively. The present analyses therefore concentrateon masses between these and the kinematic limit. Notethat the LEP Higgs working group [2] has found a masslimit on H of 77.5 GeV/c2 when combining the limits ofthe four experiments from data taken up to 172 GeV.
All known decays of the Z boson have been taken intoaccount (hadrons, charged leptons and neutrinos) while
the analyses have been optimized either for decays of theHiggs into bb, making use of the expected high branchingfraction of this mode, or for Higgs boson decays into a pairof τ ’s.
The analysis is divided according to the decay productsof the Higgs and Z bosons. Some common features arediscussed in Sect. 4, the Hµ+µ− and He+e− channels inSect. 5, Hνν in Sect. 6, and channels involving jets andτ ’s in Sect. 7. Purely hadronic final states are discussed inSect. 8. The results are presented in Sect. 9.
2 Collected data overview
For most of the data collected in 1997, LEP was runningat energies around 183 GeV. DELPHI recorded an inte-grated luminosity of 54.0±0.5 pb−1 at a mean energy of182.7 GeV.
Large numbers of background and signal events havebeen produced by Monte Carlo simulation using the DEL-PHI detector simulation program [3]. The available statis-tics of the background are given in Table 1. The back-ground events have been generated with PYTHIA [4] andKORALZ [5] for (e+e− → qq(γ) ), PYTHIA and EXCALIBUR [6]for the four-fermion background and TWOGAM [7] and BDK[8] for two-photon processes. BABAMC [9] is used to simulateBhabha events in the main acceptance region. In generalthe events generated with PYTHIA have been used to esti-
566 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Table 1. Statistics for the various simulated backgrounds. The cross-sectionsrefer to an energy of 183 GeV
Type of background generator cross section simulated luminosity
e+e− → qq(γ) PYTHIA 107.5 pb 10000 pb−1
e+e− →W+W− PYTHIA 15.4 pb 2800 pb−1
e+e−→ ZZ∗ or Zγ∗ PYTHIA 1.25 pb 13500 pb−1
e+e− →Zee PYTHIA 6.8 pb 375 pb−1
e+e− →Weν PYTHIA 0.6 pb 15000 pb−1
e+e− → 4 fermion EXCALIBUR 18.46 pb 2400 pb−1
Bhabha events BABAMC 1261 pb 72 pb−1
γγQCD TWOGAM 2307 pb 154 pb−1
γγQPM BDK 988 pb 729 pb−1
γγVDM TWOGAM 7500 pb 56 pb−1
mate the four-fermion background, but if this shows thatZZ and Zee survive at significant rates then the EXCALIBURsamples, which include interference between these states,are used instead. Some studies have also been done withthe GRC4F [10] and WPHACT [11] generators. It is alwaysassumed that ‘gluonic returns’, where a quark loop fromthe s-channel produces two gluons and an on-shell Z, arenegligible.
Signal events have been produced using the HZHA [12]generator. For the SM process the Higgs mass has beenvaried in 5 GeV/c2 steps from 60 GeV/c2 to 95 GeV/c2,while for hA of the MSSM, the A mass has been variedbetween 55 and 85 GeV/c2 with tanβ (the ratio of thevacuum expectation values of the two doublets) either 2or 20. This fixes the h mass.
The ZH simulated samples are organised by the Higgsand Z boson decay modes. For He+e−, Hµ+µ− and Hννthe natural mix of H decay modes is permitted. In the Hqqchannel the ττ decay mode is removed, and we generateseparately the two channels involving τ leptons for whichone of the bosons is forced to decay to τ ’s and the otherhadronically. Finally, for the hA simulations final statesinvolving either four b quarks or two b quarks and twoτ ’s are simulated. Efficiencies are defined relative to thesestates.
3 The DELPHI detector
The detector consists of a cylindrical part covering thebarrel region (with polar angle, θ, typically from 40◦ to140◦) and two end caps covering the forward regions. Alarge super-conducting solenoid provides a magnetic fieldof 1.2 T inside the central tracking volume. In the bar-rel region, tracks of charged particles are reconstructedin the microvertex detector, the inner detector, the timeprojection chamber (TPC) and the outer detector, reach-ing an average inverse momentum resolution, σ(1/p), of0.57 · 10−3 ( GeV/c )−1 for 45 GeV/c muons. In the for-ward region, the reconstruction is achieved by the timeprojection chamber, the inner detector and forward drift
chambers called A (which are just behind the TPC end-plates) and B (which are in front of the forward elec-tromagnetic calorimeter) with a momentum resolution of1.31 ·10−3 ( GeV/c )−1. The polar angle acceptance of thewhole tracking system is 20◦ < θ < 160◦.
The microvertex detector, as well as improving the mo-mentum resolution by a factor of two, also provides pre-cise measurements of impact parameters and secondaryvertices. As compared to the setup described in [13], thethree layers of the microvertex detector have been ex-tended down to 25◦ in θ. Typical precisions of the im-pact parameter measurements are 26µm in the transverseplane, and 47µm along the beam direction for high mo-mentum particles emitted at 90◦ in θ. The time projectionchamber can also provide charged particle identificationby measurement of the energy loss.
Neutral and charged particle energies are measured inthe electromagnetic and hadronic calorimeters, whose cov-erage in θ starts at 8◦ and 11◦ respectively. The fractionalenergy resolutions are 0.32/
√E and 0.12/
√E in the bar-
rel and forward electromagnetic calorimeters, respectively,and 1.3/
√E (E in GeV) in the hadron calorimeter. Par-
ticles emitted at small angles are detected in the smallangle calorimeter (STIC) devoted to luminosity measure-ment, whose acceptance lies between 1.69◦ and 10.8◦. Thehermeticity of the electromagnetic calorimetry is improvedby photon taggers which cover the gap between the bar-rel and forward regions at θ ' 40◦, the weak region atθ '90◦ and some azimuthal gaps in the barrel calorimeteracceptance.
Finally, muons are identified by their penetrationthrough the iron yoke of the hadron calorimeter to planesof drift chambers located partly inside and partly outsidethe yoke. The barrel region is equipped with three setsof drift chambers while the end caps each contain twoplanes. One surrounding layer of limited streamer tubescompletes the coverage between the barrel and forwardregions at θ ' 50◦.
More details about the apparatus and its performancecan be found in references [13,14].
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 567
The luminosity used by most analyses was 54 pb−1.Following the quality control on the DELPHI subdetec-tors, the requirement of full detector performance reducedthe luminosities in the Hνν and He+e− search to 50.6 pb−1
and 52.3 pb−1 respectively.
4 Common features for all channels
4.1 Particle selection
In all analyses, charged particles are selected if their mo-mentum is greater than 100 MeV/c and if they originatefrom the interaction region (within 10 cm along the beamdirection and within 4 cm in the transverse plane). Neu-tral particles are defined either as energy clusters in thecalorimeters not associated to charged particle tracks, oras reconstructed vertices of photon conversions, interac-tions of neutral hadrons or decays of neutral particles inthe tracking volume. All neutral clusters of energy greaterthan 200 MeV (electromagnetic) or 500 MeV (hadronic)are used; clusters in the range 100-500 MeV are consid-ered with specific quality criteria in some analyses. Theπ± mass is used for all charged particles except identi-fied leptons, while zero mass is used for electromagneticclusters and the K0 mass is assigned to hadronic clusters.
4.2 b-quark identification
The method of separation of b quarks from other flavoursis described in [15], where the various differences betweenB-hadrons and other particles are accumulated in a singlevariable, hereafter denoted xb for an event and xi
b for jeti. One input to the combined variable is the probabilitythat all tracks in a group originate from the interactionpoint. This is called PE for all tracks in a jet or event,and P+
E for those particles with a positive lifetime-sign,and approaches zero for b quarks. xb combines P+
E withinformation from secondary vertices (the mass computedfrom the particles assigned to the secondary vertex, therapidity of those particles, and the fraction of the jet mo-mentum carried by them) by computing the ratio of likeli-hood distributions for the signal and for the background.The procedure is calibrated on events recorded at the Zresonance, where the jets have similar characteristics tothose from ZZ or ZH. The suppression of various back-grounds is illustrated in Fig. 1. The combined b-taggingprovides a substantial gain in rejection of background ascompared to the b-tagging using only impact parameterinformation [16,1].
4.3 Constrained fits
In all channels a constrained fit [17] is performed to extractthe Higgs mass, and often to reject background processesas well. If only total energy and momentum conservationare imposed then the fit is referred to as ‘4-C’, while somefits require the Z mass as well, either as a fixed value,
or taking into account the Breit–Wigner shape of the Zresonance. In both cases such fits are referred to as ‘5-C’.The hadronic system assigned to the Higgs is forced totwo jets for the fits. The treatment of an object in the fitdepends upon whether it is an electron, µ, τ or hadronicjet candidate.
4.4 Confidence levels and the choiceof selection criteria
Selection criteria have been tuned in order to optimize theexpected exclusion of the Higgs signals using confidencelevel computations. The confidence with which the signalhypothesis can be rejected, CLs, is calculated using thelikelihood ratio technique [18]. This means that we findL, the ratio of the likelihood of the observed candidatesassuming signal plus background to that found using thebackground only hypothesis:
L = e−SΠisi + bibi
,
where S is the total expected signal, and si and bi are thesignal and background densities in mass for each candi-date i. This therefore includes the information obtainedfrom the reconstructed masses of any candidates. Combi-nation of channels is achieved seamlessly because the onlyrelevant criterion is the signal to background ration foreach event.
We calculate CLb and CLsb:
CLb = P(Lbackground < Lobs)
CLsb = P(Lsignal+background < Lobs).
i.e. the fraction of gedanken experiments with backgroundonly or signal and background which give smaller valuesof L than that observed. We then make the conservativestep of defining CLs as the ratio of these probabilities:
CLs =CLsb
CLb
Note that the CLs is the confidence in the signal hy-poythis; this must fall below 5% for an exclusion confi-dence of 95%.
The required gedanken experiments are made by MonteCarlo simulation, using the background and signal massdistributions estimated herein. The signal mass distribu-tions which are simulated at 5 GeV intervals are interpo-lated for intermediate values [19]. The signal efficienciesare fitted with simple functions, to obtain the expectedsignal rate at any given mass.
Errors on the background rate and signal efficiency areincluded by taking values for each gedanken experimentwhich are chosen from the distribution allowed by the er-ror. The effect on the mass limit is rather small, as will beseen in Sect. 9.3.
568 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 1a,b. Performance of the combined b-tagging at√s = 183 GeV: fraction of background events remaining after a b-tagging
requirement as a function of the corresponding signal efficiency. Full curves are shown for simulated hadronic four-jet eventsfrom W+W− pairs, ZZ pairs and qq(γ) background events, as a function of the efficiency for detecting four-jet events from aZH signal and b hA signal. The rejection of W+W− pairs is easiest, because these contain very few b quarks. The dotted curveshows the efficiency for the signal, for reference. The background is smaller in the channels because these events contain moreb-quarks
4.5 Analysis optimization
We wish to set the efficiencies of each channel so that thesensitivity of the combination is maximised. The choiceof the final working point for each analysis is made withan automated optimization procedure, using the expected(mean) confidence 〈CLs〉 in the signal hypothesis if thereis no signal taking into account all ZH (or hA) channels.The minimum value of this is found by varying the workingpoints of all channels. This is done only once, using a Higgsmass of 85 GeV/c2, which is close to the expected limitin the SM Higgs boson case. More details are given inSect. 4.4.
Finally, some of the analyses, such as discriminantanalyses or neural networks, use selection techniques in-ternally where the shapes of the Monte Carlo samples areused to generate selection criteria. With such techniquesthere is a danger of over-training the selection criteria byusing random fluctuations in the simulated data sets. Thisis controlled by splitting the simulation into two halveswith one half used to train the analysis and the other totest the outcome.
5 Higgs boson searches in events with jetsand electrons or muons
The Hµ+µ− and He+e− channels together represent 6.7%of the ZH final states. The experimental signature is a pairof jets recoiling against a pair of high momentum andisolated leptons where the invariant mass of the leptonpair is close to the Z mass.
5.1 Lepton identification and jet reconstruction
Muon identification is provided primarily by the algo-rithm described in [13] which relies on the association ofcharged particle tracks to signals in the barrel and for-ward muon chambers. The same algorithm was also ex-tended to the surrounding muon chambers. The longitudi-nal profile of the energy deposit in the hadron calorimeteris also used to improve the efficiency of muon identifica-tion. Since 1997, detailed information about the shape ofthe hadronic shower provided by the new HCAL cathodereadout has been included in the muon identification al-gorithm. The performance of the muon identification at
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 569
183 GeV has been evaluated using Z → µ+µ−(γ) and Z→ τ+τ−(γ) simulated events. The efficiency correspondsto the fraction of charged particles in µ+µ−(γ) events,with momentum above 10 GeV/c, which are identified asmuons by the algorithm. The misidentification probabilityis defined as the fraction of kaons and pions in the samemomentum range coming from simulated τ+τ−(γ) eventswhich are misidentified as muons by the algorithm. Differ-ent possible working points of the algorithm are presentedin Fig. 2 a).
A specific electron identification algorithm was devel-oped for Higgs boson searches with the emphasis on ef-ficiency rather than purity, as electrons in the ZH chan-nel are expected to be isolated. Electrons are identifiedas charged particle tracks with an energy deposit above3 GeV in the electromagnetic calorimeter, below 1.6 GeVbeyond the first layer of the hadronic calorimeter, andwith a ratio of calorimeter energy to momentum fromtracking above 0.3. A charged particle track pointing toan insensitive calorimeter region is also accepted providedit is not identified as a muon and is either associatedwith a hit in the hermeticity taggers or has an energyloss in the TPC in agreement with that expected for anelectron. In both cases, electrons from gamma conversionat large radius are rejected by requiring the track recon-struction to include points in the TPC or, if the particlepasses between the modules of the TPC, points both inthe microvertex and inner detectors. In the forward re-gion (θ < 43◦ and θ > 137◦) the track is only required toinclude points in the microvertex detector.
The energy of an electron candidate in the barrel re-gion is defined by a weighted average of the calorimeterenergy and the momentum given by the tracking detec-tors (using weights tuned on real and simulated Bhabhaevents) except if the track points to an insensitive regionof the calorimeters, in which case only the momentum isused. The electron identification efficiency, measured ona sample of simulated He+e− events, is 94% within theacceptance of the tracking system. The price of such ahigh efficiency is a probability of misidentifying a pion asan electron of 16%. When accepting only tracks linked toan electromagnetic shower the efficiency is 83% and themisidentification probability is 13%. A cross-check of thedata, based on the selection of Bhabha events where oneelectron is used as a trigger and the other as a member ofthe test sample, has confirmed this efficiency.
5.2 Muon channel
Events are required to have at least four charged particlesand a total energy from charged particles above 0.30
√s.
The total energy in the barrel electromagnetic calorimetermust be less than 100 GeV and at least two charged par-ticles must be reconstructed in the barrel region. This re-jects 99.9% of Bhabha and γγ events. Among the chargedparticles, two of them must have opposite charges andmomenta greater than 10 GeV/c. In order to take into ac-count possible final-state radiation, any photon collinearwith a muon candidate and having an energy larger than
2.5 GeV has its energy added to the muon momentumand the corresponding error is modified accordingly. Inthe case of low multiplicity events (charged multiplicitybelow ten) the acollinearity of the selected pair must begreater than 2◦ to remove µµ(γ) and ττ(γ) events. Afterthis preselection, the expected background is dominatedby qq(γ) and W+W− events.
Each pair of particles satisfying these criteria is thenconsidered in turn. The momentum (including anycollinear radiation) of the faster particle of the pair mustbe greater than 39 GeV/c, and the slower one above15 GeV/c. The opening angle between the particles mustbe greater than 109◦. Muon identification is required forboth particles of the pair. A search for jets is then per-formed in the system recoiling from the muon pair, usingthe DURHAM algorithm [20] with a resolution parameter of0.12. Events are selected if at least two jets are recon-structed and if there is at least one charged particle inthe second most energetic jet. This last criterion is intro-duced to avoid fake jets caused by noise or by photonsshowering in the detector. Finally, the isolation angles tothe closest jet, ψjet of the two muon candidates are re-quired to be more than 15◦ and 9◦. A 5-C kinematic fitis then performed, which, in addition to total energy andmomentum conservation, requires the mass of the muonpair to be consistent with mZ, taking into account theBreit–Wigner shape of the Z resonance. Events are onlykept if the fit probability is higher than 10−6. After the fit,the dominant background is made up of ZZ events, withone Z decaying into µ+µ− and the other into hadrons. Theb-tagging procedure is then used to discriminate the lightquark decays of the Z from a Higgs boson decay into bb.In order not to lose efficiency in signal mass zones far fromZ mass, a b-tagging cut is applied only if the measured re-coiling mass to the di-muon is above 84 GeV/c2. A looseb-tag probability cut is used; it is the minimum value ofP+
E and PE for the event being required to be below0.10. Events are kept if the above criteria are fulfilled forat least one muon pair.
The values of the above selection cuts were obtained bya procedure which optimizes them one after another. Thevalue of each selection cut is varied over a given range andonly those corresponding to the best efficiency for a givenbackground are retained. The optimization was performedon half of the simulation samples and the optimal sets ofcuts were applied to the remaining simulation samples todefine the final efficiencies and backgrounds. All Higgs bo-son masses from 60 to 95 GeV/c2 were taken into accountin the optimization. The curve of efficiency as a functionof background number of events, obtained after optimiza-tion, is presented in Fig. 2 b). The final working point isdetermined by the global optimization procedure at mH=85 GeV/c2 as described in Sect. 4.5.
Table 2 details the effect of the selection cuts on dataand simulated samples of background and signal events.The agreement of simulation with data is good. This canalso be seen in Fig. 3, which shows the distributions ofthe momenta and isolation angles of the high-momentumparticles at the preselection level, except that the acolin-
570 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 2a,b. Hµ+µ− channel: a the performance of the muon identification. Efficiency is given for muons with momentum above10 GeV/c coming from Z → µ+µ−(γ) events at 183 GeV. The probability of misidentifying a charged hadron as a muon ismeasured using charged kaons and pions coming from Z→ τ+τ−(γ) events. The kinks correspond to changes in the way theinformation is combined. b Expected background as a function of the maximal efficiency obtained at each background level fora Higgs signal of mH= 85 GeV/c2. Statistical errors are indicated by the narrow band around the curve. Stars correspond to thenumber of observed data events for a given working point. Notice that the working point definition involves optimizing severalcuts simultaneously, and not a cut on just one variable. Thus the events selected at any given efficiency need not be a subset ofthose at higher efficiencies, and this explains the overlap when 4 or 5 events are observed
Table 2. Hµ+µ− channel: effect of the selection cuts on data, simulated background and simulated signal events at√s = 183 GeV with mH = 85 GeV/c2. Efficiencies are given for the signal simulation
Selection Data Total qq(γ) 4 fermion l+l−(γ) γγ Hµ+µ−
earity cut has not been applied. There us a small excess athigh momentum, which is due to low-multiplicity eventssuch as Bhabhas where a photon has converted and fouror more charged tracks are seen. This is removed by theacilinearity cut. At the end of the analysis, the expectedbackground comes mainly from ZZ events, and amountsto 0.49± 0.06 (stat.) ±0.17 (syst.) events. The mass res-olution of the selected events is about 2 GeV/c2[1].
Because of the finite size of the Monte Carlo data sam-ples, zero quantities appear in the background estimatesat different levels of the selection. To check that these ze-roes are realistic, a second estimator of the backgroundwas used. Muon identification was removed from the se-
lection and, for each background process, the backgroundafter the remaining selection cuts was multiplied by theefficiency of the muon identification step, taken from Ta-ble 2. This leads to a total background of 0.36±0.06 (stat.)event, in good agreement with the previous one. The con-tributions from qq(γ) and W+W− background are 0.004±0.003 (stat.) and 0.024± 0.007 (stat.) events respectively,confirming that the ZZ background dominates the sample.
Two events are left in the data after selection, com-pared to 0.49 expected from the simulation. The first onehas two muons of momenta 60 and 35 GeV/c with aninvariant mass of 89.5 GeV/c2 and a recoiling mass of82.9 GeV/c2 after the kinematic fit. This event shows no
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 571
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Fig. 3a–h. Hµ+µ− channel: distributions of some analysis variables as described in the text. Plots a to d show a comparisonbetween 183 GeV data (points) and simulated background events (solid line) normalized to the experimental luminosity. Theshaded area represents the contribution of the dominant qq(γ) background. Plots e to h show the (unnormalized) expecteddistributions for a Higgs boson of 85 GeV/c2
b-quark signature and no secondary vertex was found. Alongitudinal view of the event is shown in Fig. 4. The otherevent has two clearly identified muons in the barrel muonchamber. A dimuon mass of 89.9 GeV/c2 and a recoil-ing mass of 89.9 GeV/c2 are obtained after kinematic fit.This event has a significant b-tag, and 4 tracks are foundto form a secondary vertex. A transverse view of the event
is shown in Fig. 5. The main characteristics of the eventsare summarized in Table 3.
The signal efficiencies for different Higgs boson massesare given in Table 4 and shown graphically in Fig. 29. Thedecrease of the efficiency at low mass is due to the largerboost of the Higgs boson which makes the requirementson the number of jets less efficient. The decrease of the
572 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Table 3. Characteristics of the selected events in the Hµ+µ−channel: the muon momentaand angles of isolation from closest jet (ψ), dimuon and recoiling mass after kinematicfit and b-tagging probability are quoted. The first event has a low mass, and so theb-tagging requirement is not made
Fig. 4. Hµ+µ− channel: longitudinal view of the event with little evidence for b quarks. The reconstructed charged particletracks, energy deposits and the geometry of the forward electromagnetic calorimeters (EMF) are displayed. The two muoncandidates are the tracks isolated from the jets
efficiency at high mass is, on one hand, due to b-taggingwhich is only applied to recoiling masses close to mZ, and,on the other hand, to the kinematic fit which rejects eventswhere the Z boson is off shell, which becomes more likelyas the mass of the Higgs rises and the available energyshrinks.
A first source of systematic effects is the imperfect sim-ulation of the detector response. The agreement of realand simulated distributions for the analysis variables was
checked at the preselection level, and no crucial discrep-ancy was found.
For each continuous variable used in the optimization,the mean values in the real data and the simulated sam-ples are compared. The systematic uncertainties are thenestimated by varying the cuts on each of these variablesby the difference in the mean. The corresponding changesin the efficiencies and background estimates obtained foreach variable are finally added quadratically. To take intoaccount possible differences between data and simulation
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 573
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Fig. 5. Hµ+µ−channel: transverse view of the event with high b-quark content
Table 4. Hµ+µ− channel: efficiency of the Higgs boson selection at√s = 183 GeV as a function of the mass of the Higgs boson. The first
uncertainty quoted is statistical, the second is systematic
in the muon identification, a relative 1% uncertainty [13]has been added quadratically to get the final systematicuncertainties on the efficiencies, which are given in Ta-ble 4.
The errors on background estimates given by the previ-ous method are found to be negligible in comparison to theeffect of a possible incorrect simulation of standard pro-cesses. The simulated distributions for the analysis vari-ables of four-fermion processes obtained with PYTHIA andEXCALIBUR have been compared at each step of the selec-tion. Good agreement is observed for all variables exceptdimuon masses and hence for the fit probability. After theisolation cut, the total background predicted by PYTHIA is
1.56±0.15 (stat.), close to the 1.78±0.23 (stat.) given byEXCALIBUR. This agreement has been checked for differentsets of cuts and is always correct before kinematic fit vari-able cuts. The discrepancy observed in the dimuon massdistribution, which is broader in PYTHIA samples than inEXCALIBUR ones, could be due to the lack of final-stateradiation simulation in EXCALIBUR. This affects the kine-matic fit procedure and leads to a final background pre-dicted by EXCALIBUR of 0.65±0.11 (stat.), one third largerthan the PYTHIA estimate. To take this difference into ac-count, a systematic uncertainty of ±0.17 has finally beengiven to the expected background.
574 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
5.3 Electron channel
Candidates for e+e− → He+e− are preselected by requir-ing five or more charged particles and a total energy above0.12
√s. Among the charged particles of the event, two are
required to have a momentum above 10 GeV/c and musteither be associated with a shower in the electromagneticcalorimeter or point to an insensitive calorimeter region.It is also required that the sum of the energies of othercharged particles within a cone of 5◦ around either elec-tron be less than 8 GeV. Furthermore, the sum of the en-ergy deposits in the electromagnetic calorimeters from thetwo electrons has to be above 10 GeV. The LUCLUS algo-rithm [21], with the resolution parameter set to 4 GeV/c,is applied to the system recoiling from the electron pair.Events must have at least two reconstructed jets with thesecond most energetic jet containing at least two chargedparticles.
All pairs of particles satisfying the above criteria arethen considered as electron candidates. Both particlesmust satisfy the electron identification described above,with the restriction that the two particles are not allowedto point simultaneously to insensitive calorimeter regions.Events are kept if at least one pair of oppositely chargedelectron candidates is found. If the higher energy electroncandidate is over 65 GeV, and is at less than 25◦ to thebeam axis, it is rejected as a Bhabha candidate. The en-ergy of the slower (faster) electron is required to be above15(32) GeV. Global 5-C kinematic fits are performed, withthe e+e− mass fixed to a range of values between 60 and120 GeV/c2. A combined variable is defined which is theproduct of the χ2 probability of the fit times the prob-ability (found using all simulated He+e− samples) thatan He+e− event should have the difference between themass of the e+e− system and mZ at least as large as thatobserved. This quantity is used as an estimator of thegoodness of the fit, and the recoil mass corresponding toits highest value is taken as the estimator of the Higgsmass. Events with a probability product below 10−22 arerejected.
Electron isolation angles with respect to the closest jetare required to be larger than 20◦ for the more isolatedelectron and more than 10◦ for the other. As the searchis restricted to high mass Higgs bosons, the mass of therecoiling system, as given by the kinematic fit, is requiredto be above 50 GeV/c2. The final selection is an eventb-tag, based on the minimum of P+
E and PE , in order tokeep the main background source (i.e. ZZ production) atan acceptable level. Since the b-tagging selection concernsmainly the ZZ background, it is applied only for fittedrecoil masses above 80 GeV/c2. The value of the b-taggingselection is chosen by the global optimization procedureof Sect. 4.5 and set to min(PE ,P+
E ) < 0.005.Figure 6 shows the distributions of the main analysis
variables after preselection, for 183 GeV data, simulatedbackground and signal events at 85 GeV/c2. The agree-ment between data and background expectation is good.
Table 5 shows the effect of the selection cuts on data,simulated background and signal events. Backgrounds notquoted in the table (e.g. two-photon processes leading to
leptonic final states) are negligible after the selections. Thefinal background amounts to 0.68±0.12 (stat.)+0.09
−0.10 (syst.)events, and is mainly due to e+e−qq events, with the ZZprocess dominant. Fig. 7 illustrates the distribution of re-constructed Higgs boson masses as given by the kinematicfit in simulated background and signal events.
Table 6 and Fig. 29 show the selection efficiency fordifferent masses at the working point selected by the globaloptimization.
The systematic uncertainties have been evaluated byconsidering both the difference between data and simu-lation in the distributions of each analysis variable andthe sensitivity of the selection criteria to such variables.The variables included in this procedure are the continu-ous variables used in the electron identification and in thekinematic requirements.
In a similar way the systematic errors on the expectedbackground have been estimated. A detailed comparisonof PYTHIA to four-fermion generators for final states ofthe type e+e−qq has shown significant discrepancies thathave been attributed to the less complete nature of theprocess described by PYTHIA. On the other hand no sig-nificant discrepancy, outside the statistical accuracy, hasbeen observed between different four-fermion generators(EXCALIBUR, GRC4F and WPHACT). For this reason ourbackground estimates for four-fermion final states arebased on samples from four-fermion generators. The ab-sence of FSR in EXCALIBUR, referred to in the Hµ+µ−search, is of less relevance in the electron channel, whereit is minor in comparison to bremsstrahlung in the detec-tor material.
One event fulfils the selection criteria. The electronenergies are 19.6 and 55.6 GeV and the maximum andminimum jet isolation angles are 82.7◦ and 32.2◦. The 4-C fit gives an e+e− mass of 68.5 GeV/c2 and a recoil massof 87.5 GeV/c2 with a fit probability of 4.5%. When the5-C fit is performed, these numbers become 70.0 GeV/c2,86.5 GeV/c2 and 0.8% respectively. This event is depictedin Fig. 8.
6 Neutral Higgs boson searches in eventswith jets and missing energy
This topology corresponds to 20% of the ZH final states.The experimental signature is a pair of acollinear jets,acoplanar with the beam, coming mostly from b quarks,with a recoiling mass compatible with expectation from Z→ νν decays.
A sample of hadronic events was defined by the follow-ing two criteria:– at least nine charged particles were required, and at
least one of them had to originate from the recon-structed event primary vertex with an Rφ impact pa-rameter less than 200 µm;
– the total energy of detected charged particles had toexceed 0.1·√s .A veto based on hermeticity counters was applied to
these events to reject events with an on-shell Z and pho-
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 575
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tons at angles with poor electromagnetic calorimetry cov-erage. The total cross-section for bbγ(γ) events with anenergetic radiated photon in the detector acceptance isabout 7 pb. Without the veto, these would give a back-ground of 0.47 ± 0.06 events with partially reconstructedenergetic photons in the candidate sample. The veto algo-rithm considers signals from hermeticity counters installed
at polar angles of 40◦ and 90◦. Events with such signalswere rejected if topologically and kinematically consistentwith the hypothesis that jets accompanied by one photonin the direction of the counter give a signal and anotherphoton (possibly of very low energy) is lost in the beam di-rection. The background due to poorly reconstructed pho-tons is suppressed down to the level of 2 fb, i.e. 0.12 ± 0.03
576 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Table 5. He+e− channel: the numbers of events passing each selection. Efficiencies are given for the signal withmH = 85 GeV/c2 at
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Selection Data Total qq(γ) ll(γ) 4 fermion γγ → He+e−
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 577
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expected events in the final selection, with a loss of 8%(relative) in efficiency.
6.1 Iterative discriminant analysis
Eleven variables were used to exploit the differences be-tween the Higgs signal and the various background pro-cesses.
– Eγ/EZγ : the normalized energy of a photon, assumed
to have escaped in the beam direction. It was com-puted from the polar angles of the two main jet di-rections in the event. The two jet directions were com-puted by forcing the event into two jets with theLUCLUS routine [21]. The estimated photon energy wasnormalized to the expected energy for a photon recoil-ing against an on-shell Z.
– | cos θP | : the absolute value of the cosine of the polarangle of the missing momentum.
– Ef/Etot : the fraction of the total reconstructed energybelow a polar angle of 20◦.
– Econe/piso : the energy sum in a double cone, aroundthe most isolated particle, divided by its momentum.The lower half opening angle was 5◦ and the upper oneis αmax. In the momentum interval 2-5 GeV/c , αmax
was set to 60◦ in order to maximise the sensitivity toisolated particles from W+W− → qqτν events, whileαmax = 25◦ was used for higher momenta. The mostisolated particle was defined as the particle with mo-mentum above 2 GeV/c with the smallest Econe/piso .
– The momentum of the most isolated particle, as de-fined above.
– Etot : the total reconstructed energy of the event.– Mvis : the reconstructed invariant mass of the event.– log[∆φ · sin θmin
jet ] : the logarithm to base ten of thescaled acoplanarity. Acoplanarity was defined as ∆φ,the complement of the difference in azimuthal anglebetween the two jets in degrees, when forcing the re-construction to have exactly two jets. In order to com-pensate for the geometrical instability of this variablefor jets at low polar angles, it was multiplied by thesine of the smaller polar angle of the two jets.
– The sum of the two smallest differences in cos θ be-tween a jet and a region of weaker energy resolution(40◦ and 90◦ polar angles).
– The thrust computed in the rest frame of the visi-ble system. The transformation into the rest framewas made in order to compensate the smearing dueto acollinearity of the jet system.
– xb : the combined event b-tagging defined in Sect. 4.2.
The invariant mass of the visible system given by a 1-Cfit where the recoil system is an on shell Z boson, M1C
vis ,was also computed for selected events. The first column ofFig. 9 shows the distributions of | cos θP | ,log[∆φ · sin θmin
jet ] , Mvis , and xb following the hadronicpreselection for real data, simulated background, and sim-ulated signal.
Events which fell in the extreme tails of the selectionvariable distributions were removed. These ‘tail cut’ re-quirements (see Table 7) emphasize the signal region of
578 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Fig. 9a–h. Hνν channel: a to d show distributions of the four event variables used after hadronic preselection and e to h after‘tail cut’ selection (see Table 7). for real data (dots) and simulated background. The thick dashed histogram contour shows theexpected signal for mH = 85 GeV/c2 scaled up by factors of 500 at the preselection and 50 at the tail cuts stage
the variable space in the discriminant analysis and avoidthe effect of any badly reconstructed events with extremevariable values.
The right column of Fig. 9 shows the distributions offour event variables following the ‘tail cut’ selection forreal data, simulated background, and simulated signal.The overall agreement in the number of events for realand simulated data was within about 15% at this stage,with 239 observed events and 214 expected.
The remaining selection cuts are made with an Iter-ative Discriminant Analysis (IDA) [22,23]. A step in an
IDA consists of defining a polynomial of event variables,such that the separation between signal and backgroundis maximised [24]. The analysis used here consisted of twosuch steps, using quadratic discriminant functions on allthe variables introduced in this section. After the first stepthe value of the discriminant function was required to ex-ceed a value such that the efficiency is reduced by 30% onaverage for the signal samples. This left a much smallersample where the background is suppressed relative to apossible signal. A second discriminant function was op-timized for this sample. The distribution of its value for
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 579
Table 7. Hνν channel: requirements made to remove eventsin tails of signal distributions
Fig. 10. Hνν channel: distribution of the final discriminantoutput for those events which passed the first step in the It-erative Discriminant Analysis selection for data, background,and the expected signal for mH = 85 GeV/c2
events passing the first IDA step is shown in Fig. 10 fordata, simulated background and signal.
The background versus efficiency curve obtained byvarying the requirement on the second discriminant stepcan be seen in Fig. 11 for a Higgs mass of 85 GeV/c2.The final selection in the second IDA output has beenchosen by the global optimization procedure (Sect. 4.5)and corresponds to a minimal value of 0.265. Table 8 andFig. 29 show the efficiency, and Table 9 shows the numberof events expected and observed at different stages in theanalysis. Fig. 12 shows the selected candidate event. It hasa visible mass of 77 GeV/c2, which becomes 88 GeV/c2after the constrained fit, and xb is 1.2. | cos θP | is 0.42, andlog[∆φ · sin θmin
jet ] is 0.82. The output weight from the sec-ond IDA is 0.37.
At the end of the analysis, the Higgs boson mass is re-constructed as the mass of the visible system, found usinga 1-C fit with the constraints of energy and momentum
databackground
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conservation and the constraint that the invisible systemis an on-shell Z. The distributions of the reconstructedHiggs boson mass expected for the signal and the back-ground are shown in Fig. 13.
6.2 Systematic uncertainties
Estimates for signal efficiencies and background have beenmonitored by comparison of real and simulated data atall stages of the analysis (see Fig. 9 and Table 9). Sev-eral additional cross-checks, based on test samples, wereperformed in order to constrain the uncertainties in the fi-nal selection. Test samples were necessary to avoid biasessince the statistics are low and the IDA might have beentrained to recognise individual simulated signal events.
They were constructed from well-understood back-ground processes and passed through the selection. Dis-crepancies between real and simulated data are expectedto affect the test samples and the final sample in the nor-mal selection in a similar way. The signal efficiencies werecross-checked using a test sample of events with hadronicsystems recoiling against an isolated particle, such asW+W− → qqlνl events and qq production with an iso-lated photon from initial state radiation. The isolated par-ticle was used as a tag, and all the event variables wererecomputed using the hadronic system only, which resem-
580 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 12. Hνν channel: longitudinal and transverse views of the selected candidate. The absence of signal in the forward detectorsshows that there were no signals in these devices. The missing momentum in this event is indicated by the large arrow
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Table 8. Hνν channel: the efficiency for various Higgs masses at theselected working point. The first uncertainties are due to Monte Carlostatistics, the second estimates give the systematic uncertainties. 85 GeVhave been checked
Table 9. Hνν channel: the reduction for different background processes. The bb(γ) sample has beenseparated from the light quark qq(γ) sample. The column ‘Others’ includes two-photon processes, Zee andBhabha scattering. The signal efficiency column is for mH= 85 GeV/c2. Uncertainties include simulationstatistics
Data Total bb(γ) qq(γ) W+W− ZZ Weν Others Hννbackground ε(%)
bles a signal event. As an additional check, in order toincrease the statistics late in the selection, the value of xb
was systematically shifted to higher values. Good agree-ment between data and simulation was found for the ratesand shapes of distributions including the b-tagging andevent weights, as seen in Fig. 14 a and b and Table 10,first row.
The uncertainties in the signal efficiencies due to eventreconstruction are limited to ±10% relative, based on thelast selection applied to the events tagged by isolated par-ticles in Table 10, where 108 events were observed com-pared with 112 expected. In addition, the efficiency uncer-tainties due to fusion production graphs have been checkedwith the WPHACT [11] generator and found to be well withinthis range.
The background estimate in a missing energy searchdepends strongly on the modelling of rare occurrences inthe detector, leading to lost or spurious particles. Theprecision in this modelling was evaluated using eventswhich survive the tail-cut selection but were rejected in thefirst IDA step. Many of these events had a low b-taggingweight, xb . By artifically increasing xb , a more signal-likesample was obtained, dominated by qq(nγ), W+W−andWeν events. These events had kinematic properties thatwere very close to the residual actual background. Theobserved and expected rates for this sample, shown in Ta-ble 10, second row, and their b-tagging and IDA weightdistributions, shown in Fig. 14 c)-d), are in good agree-ment. As a specific check of the important backgroundfrom bb events with photons lost in the beam directions,high-energy deposits in the STIC were used to tag radi-ated photons which were then assumed lost in computingthe event variables. Three events were observed after thefirst IDA step for an expected 3.1 ± 0.2 events (see Ta-
ble 10, last row and Fig. 14 e)-f)). The uncertainty ofthe background in the final selection is estimated to be±20%, corresponding to the statistical uncertainty of the29 events in the test sample.
7 Neutral Higgs boson searches in eventswith jets and taus
This topology includes 8.5% of the ZH final states andtypically 14% of the hA final states. The experimentalsignature is two jets and two isolated τ leptons, which arereconstructed exclusively.
7.1 Preselection
Hadronic events are selected by requiring at least sevencharged particles and, either a total energy carried bycharged particles greater than 0.15
√s, or a total energy
greater than 0.3√s and forward and backward energies
greater than 0.03√s. After this hadronic selection, an ex-
clusive search for τ leptons is applied. A cone algorithmis used to define clusters in the event. The two free pa-rameters of the algorithm are the minimum energy in thecone (Emin) and the cone half opening angle (θ1/2). Theirvalues (Emin = 1.3 GeV and θ1/2 = 0.2 rad (11.5◦) havebeen determined by optimizing the signal over backgroundratio for this analysis.
The angles between all possible pairs of cones are com-puted using as possible τ candidates only cones with noother particles within 15◦ of the cone axis. The principalτ decays are then tagged by means of several algorithms,depending on the charged and neutral multiplicities in the
582 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Table 10. Hνν channel: the numbers of observed and expected events in testsamples consisting of hadronic systems recoiling against an isolated particletag (upper part) of events rejected by the first discriminant iteration andxb artificially increased (middle part) and of hadronic systems recoiling againsta photon tag in STIC (lower part). The columns give rates after the selectionof tail cuts, the first iteration (‘Step 1’) and in the final sample (‘Final’)
Test events, tagged by isolated particlesData 533 43 170 14 108Simulation 475±5 42±1 154±2 16.3±0.5 112±2Test events, rejected by the first discriminant analysis stepData 211 0 29 0 14Simulation 195±4 0 28.8±1.3 0 12.2 ±0.6Test events, tagged by a large STIC energy depositData 80 3 0Simulation 57±2 3.1±0.5 0.93±0.5
cones. The different algorithms are, by order of applica-tion, i.e. order of decreasing purity, as follows.
1. Lepton algorithm: lepton identification [13] is used to-gether with an upper limit on the lepton momentumto reject decays of W or Z bosons to leptons.
2. ρ algorithm: three different algorithms were designed,depending on the number of neutrals in the cone (one,two or more than two). Selection cuts are applied onthe invariant mass and total momentum of the parti-cles in the cone, as well as on the maximum openingangle between them.
3. π± algorithm: this is the most difficult channel dueto the contamination from pions in hadronic jets. Asthese are softer than pions from τ decays, a minimumvalue is required for the pion momentum. A maximumvalue is also imposed to reject direct leptons from Wdecays not selected by the lepton algorithms.
4. Three prong algorithm: the three charged particles inthe cone are required to form a secondary vertex within1.9 mm of the primary vertex, to be isolated from therest of the event and to be at small angles with respectto one another.
The one-prong algorithms (1 to 3) have a selection ef-ficiency from 50% to 67% for one-prong τ decays, whilethe three-prong algorithm has an efficiency of 28%. Thecontamination from fake τ candidates reconstructed fromhadronic particles of a jet ranges from 5% in the µ channel,through 11% in the electron channel, 15% in the π± chan-nel, 16-22% for the ρ channel to 28% for the 3π channel.More details can be found in [25].
Events with no τ candidate are rejected. Events withtwo or more τ candidates are kept for the analysis andmake a sample that will be called 2τ in the following (ap-proximately 30% of the signal). In the case of more thantwo candidates, the candidates selected by the less efficientand less pure algorithms are not considered further.
In order to increase the signal efficiency, events withonly one τ candidate are kept and a second τ is searchedfor with a looser selection than before: identified leptonswith moderate momenta or well isolated cones failing theτ algorithm selection cuts are again considered and keptif they are of opposite charge to the first τ candidateand isolated from it. If no second τ is found, the missingmomentum direction is used to define a preferred regionin which an isolated track of moderate momentum withcharge opposite to that of the first τ candidate is consid-ered as a second τ candidate. This constitutes a samplecalled (1+1)τ in the following (approximately 50% of thesignal).
In both samples, the preselection is completed by a re-quirement on the effective centre-of-mass energy
√s′[26]
to reduce the background further. The effect of the pres-election is shown in Table 11. At this level, the dominantbackgrounds are W+W− and qq(γ) events. The agree-ment between data and background simulation is good.
Before channel-dependent selection cuts, all particlesexcept those belonging to the two τ candidates are forcedinto two jets with the DURHAM algorithm [20]. Masses de-rived from application of a 4-C kinematic fit are used inthe event selection, while the estimator of the Higgs bosonmass used for the limit is the 5-C fit value.
7.2 The ZH channel
7.2.1 H decaying into τ+τ−
In the ZH channel with H decaying into τ+τ−, the 2τsample is used to achieve a good purity, for lack of otherpowerful discriminating variables to reject four-fermionevents, and especially WW pairs. The details of the se-lection cuts as well as their effect on data and simulatedevents are given in Table 12. The background is reducedby requiring the momentum of the less energetic jet, Pq2,
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Fig. 14a–f. Hνν channel: distributions of beauty event tag in the test sample of hadronic systems recoiling against an isolatedparticle a, in the sample of hadronic systems recoiling against an isolated particle in the STIC acceptance b, and in the sampleof events surviving the tail cuts but rejected after the first IDA step c. Distributions of the IDA weights for these test samples,are shown in d–f, respectively. The beauty weights are shifted up in computing the IDA function values in d and f. The arrowsshow the position of the final selection. The observed and expected event rates are listed in Table 10
584 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 14a–f. (continued)
Table 11. τ+τ−qq channel: effect of the preselection on data and simulated background at√s = 183 GeV. The
cut on√s′ is in GeV. Efficiencies are given for signals at 85 GeV/c2 in the ZH channel, and at 70 GeV/c2 in the
hA channel
Selection Data Total qq(γ) W+W− ZZ Zee Weν γγ ZHbackground → had. ε(%)
to be bounded, the mass of the τ pair, Mττ , to be high(since the search is restricted to high mass Higgs bosons)and the mass of the hadronic system, Mqq, to be compat-ible with mZ. The final two selection cuts use the open-ing angle of the τ pair, expected to be large if the Higgsboson is massive, and the difference between the secondand fourth Fox-Wolfram moments of the hadronic system,H2−H4, expected to be larger for the signal than for thebackground. Their values have been varied and the finalchoice determined in the global optimization procedure.
Table 13 and Fig. 29 show the signal efficiencies for dif-ferent Higgs boson masses. The agreement between dataand background simulation is illustrated in Fig. 15 at pre-selection level.
The expected background is 0.74± 0.09± 0.08 mainlyfrom ZZ events. The one event selected in the data isshown in Fig. 16. The τ candidates are selected by thethree prong channel and by the ρ algorithm with at least
three neutrals. The event corresponds to a reconstructedHiggs boson mass of 72 GeV/c2 after the 5-C fit.
7.2.2 Z decaying into τ+τ−
When the Z decays into a τ+τ− pair, the hadronic sys-tem is expected to come from the Higgs boson and thusto contain beauty hadrons. B-tagging is expected to be apowerful tool against background and the full preselected(1+1)τ sample is used in this analysis. Background re-duction is achieved by requiring the mass of the hadronicsystem to be large and that of the τ pair to be compatiblewith mZ. The final two selection cuts apply on the open-ing angle of the τ pair and the event combined b-taggingvariable. Their values have been varied and the final choicedetermined by the global optimization procedure. The re-sult is indicated in Table 14, while Table 15 and Fig. 29
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 585
Table 12. (H → τ+τ−)qq channel: effect of the final selection cuts in data and simulated background. Efficiencies aregiven for a signal of 85 GeV/c2
selection data total qq(γ) W+W− ZZ Zee Weν γγ ZHbackground → had. ε(%)
Table 14. (H → qq)τ+τ− channel: effect of the final selection cuts in real and simulated data at√s = 183 GeV. Efficiencies are given for a signal of 85 GeV/c2
Selection Data Total qq(γ) 4 fermions γγ ZHBackground → had. ε(%)
give the selection efficiency as a function of the Higgs bo-son mass. The four-fermion generator has been discussedin Sect. 2.
The data and simulated background after the preselec-tion are compared in Fig. 17. Distributions of two variablesused in the channel-dependent analysis are shown. Thereis no selected event in the data for an expected backgroundof 0.34 ± 0.07 (stat.) ± 0.04 (sys.) events, mainly due toqq(γ) events.
7.3 The hA channel
In the hA channel, the cross-section is typically maximumat large tanβ, i.e. when the two Higgs bosons are almostdegenerate in mass. In that case, the masses of the pairof hadronic jets and of the τ+τ− pair are expected tobe close. In addition, one Higgs boson is expected to de-cay into a bb pair. The starting sample is thus the entire(1+1)τ sample.
Background reduction is achieved through selectioncuts in the acollinearity between the two hadronic jets,Acolhad., in the first Fox-Wolfram moment of the hadronic
586 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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signal at 85 GeV/c2 are given
Table 16. hA → τ+τ−qq channel: effect of the final selection cuts in real and simulated data at√s = 183 GeV.
Efficiencies are given for a signal of 70 GeV/c2 and tanβ of 20
Selection Data Total qq(γ) W+W− ZZ Zee Weν γγ hAbackground → had. ε(%)
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 587
τ → ρ
τ → 3π
HCAL
HPC
TPC
Fig. 16. (H → τ+τ−)qq channel: ZH candidate. One τ candidate (τ → ρ) goes to the upper right, where a high momentumcharged particle can be seen to coincide with a large energy deposit in the electromagnetic calorimeter (HPC). The other(τ → 3π) can be seen in the lower right part of the figure. Three of the charged particles all have a common initial direction.The missing neutrinos are allowed for in the analysis
system, H1, in the mass of the τ pair and the difference inmass between the τ pair and the hadronic system, ∆M ,and in the combined event b-tagging. The effect of theselection cuts on real and simulated data are given inTable 16. The last three requirements in the table havebeen determined through the global optimization proce-dure. The selection efficiencies as functions of the Higgsboson mass are given in Table 17 for two values of tanβ.
Figure 18 shows good agreement between data andsimulated background for three analysis variables at thepreselection level. At the end of the analysis, no event isselected in the data for an expected background of 0.47±0.07(stat.) ± 0.05(sys.), mainly due to qq(γ) events.
7.4 Systematic errors
A 1% systematic error is assumed on the background pro-cesses cross-sections. For each variable, the difference inthe mean values of the distributions in data and simulated
Table 17. hA → τ+τ−qq channel: efficiency of the Higgs bo-son selection at
√s = 183 GeV, as a function of the common
Higgs boson mass mA. The first uncertainty quoted is statisti-cal, the second is systematic
background is applied as a shift in the selection and thecorresponding change in signal efficiency and backgroundexpectation is taken as the systematic uncertainty. Thetotal error due to this is ±6%. The signal samples are gen-
588 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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erated without τ polarization. A sample with one Higgsmass was generated with τ polarization included, and therelative change in efficiency of 5% is taken as the error dueto ignoring this effect.
All uncertainties are then summed quadratically. Thisleads to a ±10% relative systematic error on the back-ground expectations, and a ±7.2% relative error on signalefficiencies.
8 Higgs boson searches in four-jet final states
The preselection procedure is the same for all four-jetchannels. Its aim is to reduce the qq(γ) background whilekeeping most of the Higgs boson signal.
The first step is to select hadronic events by requiringat least eighteen charged particles, a total energy above0.6√s and a total neutral energy below 0.5
√s. This se-
lection eliminates all Bhabha events and almost all two-photon events without affecting the signal.
To reject events where an on-shell Z is produced witha real γ, it is required that no photon with more than30 GeV is present. This is applied either to photons ob-served in the calorimeters, or initial state radiation impliedby a 3C kinematic fit to the observed jets.
Then four-jet events are selected by demanding threeconditions: firstly, the sum of the Fox-Wolfram momentsof order two and four has to be less than 1.1; secondly, thethrust of the event has to be less than 0.92. Finally, theDURHAM [20] algorithm is applied, forcing the clusters intoa four-jet configuration. These jets are then used in boththe following analyses. Each jet is required to contain atleast one charged particle and have a mass greater than1.5 GeV/c2. Figure 19 shows the distributions of some ofthese variables.
Table 18 summarises the four-jet preselection perfor-mance. The systematic errors have been estimated by tak-ing into account the errors on the cross-sections and theobserved differences between generators (2%), and the sys-tematic discrepancy found during the selection (slight ex-cess of data at the multi-hadron level and slight loss ofdata at the four-jet selection level, estimated to be of theorder of 3%) resulting in a total relative systematic errorof 4%. The efficiencies for the generated signal samplesrange from 81% to 93%.
8.1 The Standard Model Higgs selection
A probabilistic analysis has been used to search for aZH signal in the four-jet channel. In order to reduce the
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Fig. 18a–i. hA → τ+τ−qq channel: in plots a to c), data (dots) are compared to expected background distributions (solid line)at
√s = 183 GeV/c2. The clear histogram is all other backgrounds. The shapes of the distributions (unnormalized) expected
for a Higgs signal at 75 GeV/c2, tanβ = 20 are shown in d to f and tanβ = 2 in g to i
Table 18. Hqq channel: remaining simulated background event rates and simulated signal efficien-cies after each step of the four-jet selection. The first error is statistical and the second is systematic.The signal efficiencies are quoted for a SM Higgs of mass 85 GeV/c2
590 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 19a–h. Hqq channel: distributions of some four-jet preselection variables. Plots a to d show comparisons between data(dots) and all simulated background events (solid line) as well as the qq(γ) background (shaded histogram) normalized to theexperimental integrated luminosity. Plots e to h show the (unnormalized) expected distributions for the hqq process with mH=85 GeV/c2, and the hA processes with tanβ = 2 and tanβ = 20, which are all similar. a and b are made after the initialmulti-hadronic selection; the other plots have the non-radiative requirement in addition
The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 591
main background sources (e+e−→ qq(γ), W+W− andZZ) topological, kinematical and b-tagging informationhave been used.
8.1.1 Finding the best jet pairing
In a four-jet final state there are six combinations of jetpairs which are possible for the Higgs and the Z bosons.For a signal event, by definition, i and j jet indices willbe used for the Higgs bosons whereas k and l indices cor-respond to the Z decays.Pb(xi
b) is the probability density of the measured value,xi
b, for the b-tagging variable for the jet i coming from ab quark jet. This probability density has been evaluatedusing simulated samples of e+e− to b and non-b quarksgenerated at the Z peak. It has been checked that theprobabilities for b and non-b quark jets of genuine fourjet final states at high energy are essentially identical tothese.
Effects from the acceptance of the VD have been in-cluded by considering three intervals in polar angle in-side which the shapes of Pb(xi
b) have been independentlyadjusted. These intervals are θ ≤ 30◦, 30◦ ≤ θ ≤ 40◦,θ ≥ 40◦ and the symmetric intervals obtained by reflec-tion through the origin.
To test the signal hypothesis it has been assumed thatthe jets (i,j) from the Higgs boson candidate are from bquarks. The two jets from the Z decays can be initiated byb or lighter flavours with respective probabilities Pb
Z and(1-Pb
Z), given by the Z couplings to the different hadronicfinal states. Finally the χ2 probability of the 5C fit, ob-tained by imposing that the mass of the di-jet (k,l) beequal to the Z mass, is included to define the probabilitythat the four jets present in the event correspond to thechannel e+e− → ZH:
PbZH(x1
b , x2b , x
3b , x
4b) =
∑Pb(xi
b)Pb(xjb)
×[(1− PbZ)Pq(xk
b )Pq(xlb)
+PbZPb(xk
b )Pb(xlb)]
× P5Cχ2 (mkl = mZ)
The sum runs over the six different possible pairings ofthe jets i, j, k, l. In this expression Pb
Z = 0.216, Pq(xlb) =
1−Pb(xlb) and the sum, over the six combinations, of the
5C fit χ2 probabilities has been normalized to unity.In a similar way, the probability that the observed
event comes from the qq(γ) background has been eval-uated:
Pbqq(γ)(x
1b , x
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4b)
=16
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jb)Pq(xk
b )Pq(xlb)
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b)Pb(xjb)Pq(xk
b )Pq(xlb)]
In this expression the fraction of bb jets in a di-jet, Pbγ , the
fraction of jets in qq(γ) events which are from b quarks,
has been taken from the simulation (Pbγ = 0.175). The
(i,j) and (k,l) masses are not constrained.For W+W− events, neglecting the very small W− →
bc(u) couplings and the difference between the fractionsof c quarks in W and in Z decays which was assumed todefine Pb(xi
b), the following expression is obtained:
PbWW (x1
b , x2b , x
3b , x
4b) = Pq(x1
b)Pq(x2b)Pq(x3
b)Pq(x4b)
To verify the validity of the approximations concern-ing the description of W decays, the b-tag probability dis-tributions have also been determined separately for light,charm and b flavours and the different branching fractionsof W bosons into q1q2 pairs have been used. The χ2 prob-ability of a 5C fit, in which the equality of (i,j) and (k,l)di-jet masses is required, has also been tried in the ex-pression for Pb
WW . As no significant improvement in thebackground rejection was found, the simpler expressionabove was adopted.
No separate PZZ probability has been calculated.The jet pairing which maximises the term of the expres-sion of Pb
ZH is selected and the Higgs boson candidatemass is given by the 5C fit.
8.1.2 Contributions from the shape variables
The previous expressions for PbZH , Pb
qq(γ) and PbWW have
been multiplied by the probability densities observed forshape variables in the signal and in the two backgroundcomponents. Five variables have been used:
– the minimum di-jet mass;– αminEmin, which is the product of the minimum jet
energy and the minimum opening angle between twojets,
– (H2+H4)/H0, the normalized sum of two Fox-Wolframmoments;
– βmin · Emax/Emin where βmin is the minimum anglebetween the most energetic jet, of energy Emax, andthe others;
– the value of the cut in the jet algorithm, y34, corre-sponding to the transition between three- and four-jettopologies for the studied event.
The distributions of these variables are shown in Fig. 20at the level of the preselection. A good agreement betweendata and simulation in the variables used is observed. Dis-tant tails in these distributions have been replaced by aconstant level in the parametrization functions. All thesignal simulations for different values of the Higgs bosonmass between 70 and 95 GeV/c2 have been used to pro-duce the signal shapes. This ensures a rather constantacceptance of the signal inside this mass range.
8.1.3 Final event selection
A discriminating variable has been defined as the ratio oftwo likelihood distributions obtained, respectively, for sig-nal and background simulated events. The discriminating
592 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV 593
Table 19. Hqq channel: number of selected multi-hadronic events in data and corresponding expectations fromthe simulation at different levels of the analysis. The last column gives the selection efficiency for the channele+e−→ ZH → hadrons, using mH = 85 GeV/c2
PW is the fraction of W+W− pairs in the preselectedsample (PW = 0.575) deduced from the simulation. Thequantities PZH , PWW and Pqq(γ) are the products ofthe expressions Pb(xb
1, xb2, x
b3, x
b4) defined previously by the
probability distributions for the shape variables obtainedfor the three classes of events. The background compo-nent coming from production of two neutral bosons (Z’sor γ’s) has not been considered in the expression of thebackground probability distribution because it behaveslike qq(γ) events (Zγ∗ component) or like signal events(on-shell ZZ pair events when a Z decays into bb). Thedistributions of the decimal logarithm of the discriminat-ing variable obtained in data and in simulated events arecompared in Fig. 21.
8.1.4 Comparison between data and simulation
The final event selection is made through a cut on thediscriminating variable. The efficiency and background asa function of the cut can be seen in Fig. 22. The efficien-cies at different levels of this selection, for a Higgs bosonof 85 GeV/c2 mass, and the number of kept events fromthe different background components are summarized inTable 19, for three different values of the cut.
The value of the final cut on this variable is fixed bythe global optimization algorithm. A requirement Xdisc >100 is found to correspond to the optimal working point,selecting one event in the data while 3.74 ± 0.20 ± 0.18are expected from standard processes. The values of thecorresponding efficiencies to the signal, for different valuesof the Higgs boson mass can be found in Table 20 and
Table 21. Fitted and expected numbers of events correspond-ing to the different background components
NWW Nqq(γ) NZZ
Measured 366+21−22 227+22
−21 6+13−6
Expected 364.6 234.6 19.1
Fig. 29. The mass distributions of the selected Higgs di-jet candidates, obtained after the 5-C fit, in data and inthe simulation have been compared at different levels ofthe selection in Fig. 23. The data event passing throughthe selection has a measured Higgs mass of 89.4 GeV/c2and a log10(Xdisc) of 4.4. It can be seen in Fig. 24.
8.1.5 Systematic uncertainties
Systematic uncertainties on the background evaluationmay originate from differences between data and simula-tion in the rates, event shape or b-tagging distributions forthe different components. All studied distributions in dataand simulation have been found to be in agreement withinstatistics. A ±4% systematic uncertainty has been evalu-ated on the preselection requirements (Sect. 8). The dis-criminating variable (shown in Fig. 21) has a different be-haviour for qq(γ) , W+W− and ZZ events and the relativefractions of the three components have been fitted to dataafter the preselection and found to be in agreement withexpectations (Table 21). This fit assumed no Higgs bo-son production, but much of the information comes fromregions of low log10(Xdisc), which are not affected by apossible signal.
From this result, which is also sensitive to possible dif-ferences in event shapes between the data and the simu-lation, relative uncertainties of ±6% and ±10% have beenestimated respectively on the relative rates of W+W− and
594 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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obtained by varying the cut on the log10(Xdisc) vari-able. The expected numbers of qq(γ), WW and ZZbackground events are shown separately. Statisticalerrors on the expected number of background eventsare indicated by the hatched band corresponding tothe sum of all background components
qq(γ) backgrounds. No systematic uncertainty needs tobe added for the ZZ component because the uncertaintyon its importance is, at present, naturally dominated bystatistics. The present evaluation quoted in Table 21 in-dicates that there is no large discrepancy as comparedto expectations for this component. The distributions ofthe b-tag variable measured in data and in the simulationhave been compared for preselected events (see Fig. 25).A difference is observed in the region dominated by lightflavours. To gain in statistics, in the region mainly popu-lated by b quarks, similar distributions have been studiedusing Z decays. They confirm the effect observed at highenergy in the light flavour populated region, and do notshow evidence for a discrepancy in the b-quark region.Simulated events have been modified to correct for theobserved difference. The measured relative variations onthe efficiency of the signal and the expected backgroundare respectively ±1.3% and ±2.2%, and these are includedin the quoted systematics.
8.2 The hA four-b channel
A neural network has been used to search for hA produc-tion in the four-jet channel. The common four-jet selec-tion criteria are applied to preselect relevant events withthe exception of the requirement on H2 + H4. Instead,this quantity is used as input for the neural network. Theresulting number of expected events and the signal effi-ciencies after the preselection are given in Table 22.
8.2.1 Input variables for the neural network
The input variables were selected in a pre-analysis usinga discriminant analysis technique. The following 14 vari-ables are used:
– ln(6+xb),– ln(5+xi
b,1 +xib,2), where xi
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– combined jet b-tag of the jet with highest b-tag prob-ability,
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Fig. 23a–d. Hqq channel: mass spectra measured in data and in the expected background for the Higgs di-jet candidate atdifferent levels of the selection: a efficiency ∼ 85%, b efficiency ∼ 79% and c optimal working point. Dots are the data, andthe solid line is the total background. Shaded histograms correspond to the qq(γ) background component, and the arrow in cshows the position of the candidate. The lower right histogram d corresponds to the expected mass spectrum for a 85 GeV/c2
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Table 22. hA 4b channel: the number of expected background events after thepreselection. The number of events found in data is also given
Total hA Efficiency (%)Data background qq(γ) WW ZZ mA = 70 GeV/c2, tanβ = 20655 686± 27 311 355 20 93%
Table 23. hA 4b channel: efficiency for different masses of thepseudo-scalar Higgs. Errors are statistical and systematic
– combined jet b-tag of the jet with third highest b-tagprobability,
– number of secondary vertices,– thrust,– 2−H2 −H4,– minimal jet charged multiplicity,– − log10(y34) (DURHAM),– minimal di-jet mass– βmin, defined as the minimal angle between the most
energetic jet and the three remaining jets,– maximum jet energy,– minimum jet energy,– minimum angle between any two jets.
Event b-tag variables are transformed as given above inorder to have less peaked distributions. All inputs are nor-malized to lie in the region between zero and one. Thenthey are fed into a fully connected three-layer feed-forwardpercepton with 14 nodes in the input, 15 nodes in the hid-den and 1 node in the output layer, using the JETNETpackage [27]. The training sample has been subdivided
596 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
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Fig. 24. Hqq channel: transverse view of the surviving candidate. The arrows show the jet directions and momenta, and thetracks in each of the four jets are shaded differently
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is shown in c and d for tanβ = 20 and e and f for tanβ = 2. In the first case the mass of the h is 69.7 GeV, while in thesecond it is 60.8 GeV and the larger difference explains the larger width in f. The distributions are given for the jet pairingswith the smallest mass difference
598 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Table 24. Expected background with statistical and systematic errors, in-tegrated luminosity, number of observed events and signal expectation in allchannels. The number of signal events is given at 85 GeV/c2 in the ZH searchand 70 GeV/c2 in the hA
Fig. 28. Global optimization: variation of the expected per-formance of the total analysis for mH= 85 GeV/c2 with theHνν efficiency, while all others are at the global optimum. Thedots show the expected 〈CLs〉 at each signal rate, and the dot-ted line shows the expected background. The working point isthe smallest 〈CLs〉
into two subsamples, one of them is used for the train-ing, and the second one to monitor the performance ofthe network. The two samples included 3000 qq(γ) , 3000WW and 1000 ZZ events for the background, and 900events for each of the Higgs masses from 60 to 85 GeV/c2(tanβ = 20).
Figure 26 a shows the network output for a natu-ral mixture of the three background types qq(γ) , WW
and ZZ. The output distribution for a signal with mA =70 GeV/c2 and tanβ = 20 is also given.
8.2.2 Final optimization
The final selection on the neural network output is chosenby the global optimization procedure (see Sect. 4.5) andcorresponds to a requirement at 0.877. This yields a totalresulting background of 1.46 ± 0.13 events, coming fromqq(γ) (0.906 ± 0.071), WW (0.155 ± 0.058) and ZZ (0.403± 0.097). No events are selected in the data. Efficienciesobtained for all masses and tanβ are summarized in Ta-ble 23. Figure 27 shows the distributions of the sum andthe difference of the di-jet masses at the end of the analysisfor mA = 70 GeV/c2 and tanβ = 2 or 20. In these dis-tributions, the jet pairing is that with the smallest di-jetmass difference. Figure 27 shows that this pairing allowsfor a good reconstruction of the sum of the di-jet masseseven when the h and A bosons have a (moderate) massdifference.
8.2.3 Systematic errors
The distributions of the input variables show no signifi-cant difference between data and simulation after prese-lection. A small discrepancy is observed in the highest jetb-tag probability distribution in the light quark region.An additional preselection cut which removes this regiondoes not affect signal and background selection efficien-cies. Each event of the testing sub-sample (Sect. 8.2.1)has been shifted by the difference of the mean values be-tween simulation and data. Then the shifted events havebeen moved randomly fifty times within the error of themean value of the data distribution. Correlations of theinput variables are taken from Monte Carlo simulation.The mean shift of the resulting efficiencies is taken as sys-tematic uncertainty.
To check systematic uncertainties on the total back-ground due to the training procedure the training and the
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validation sample have been exchanged and the trainingwas repeated. The uncertainty on the total backgrounddue to this is of the order 4%. An additional uncertaintyon the input variables of 4% at preselection level has beentaken from Sect. 8. Summing all errors in quadrature yieldsa relative error of 12% on the total background.
9 Global optimization and results
As there is no evidence for a signal, the results of thesearches presented in the previous sections translate intoexclusion limits on the masses of the neutral Higgs bosonsin the SM and MSSM. The procedure used to set the limitis the same as that first used to optimize the expectedlimit. The results of the global optimization are reportedfirst.
9.1 Optimization results
The final optimization procedure for the SM Higgs is per-formed for two simulated Higgs masses: 85 GeV/c2 and90 GeV/c2, using 183 GeV data alone. This gives a 〈CLs〉of 2.2% at 85 GeV/c2 and 19% at 90 GeV/c2. This indi-cates that the closest simulated mass to the expected 95%limit is 85 GeV/c2. We thus chose the working points se-lected by the optimization at 85 GeV/c2. Note that thisset of individual selection cuts is very close to that ob-tained from the optimization at 90 GeV/c2 and that itsexpected performance at that mass is similar to the opti-mal one. To illustrate the procedure, the convergence ofthis optimization with Hνν selection efficiency is shown inFig. 28 for mH= 85 GeV/c2.
In the hA mode, the optimization is performed for70 GeV/c2 and 75 GeV/c2 in mA and tanβ of 20, wherehA dominates, leading to a 〈CLs〉 of 4.7% at 70 GeV/c2and 13.0% at 75 GeV/c2. The expected limit from 183 GeVdata alone is thus close to 70 GeV/c2 and we chose the setof working points obtained when optimizing at that mass.This leads to a 〈CLs〉 at 75 GeV/c2 of 13.3%, slightly de-graded with respect to the optimal solution at that mass.
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9.2 Summary
For each analysis of the ZH and hA channels at 183 GeV,Table 24 summarises the expected backgrounds and theirerrors, the integrated luminosity and number of observedevents. The efficiency versus Higgs mass can be seen for allSM channels in Fig. 29. The errors are obtained by sum-ming the statistical and systematic uncertainties quadrat-ically. The total number of events observed in all chan-nels is six, which is consistent with the 8.4 expected back-
600 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Table 25. An overview of the candidates. For the ττqq chan-nel no b-content is expected, and so the b tagging is not rele-vant. Each of the other channels uses only one of the b-taggingvariables
Channel Mass xb min(PE ,P+E )
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τ+τ−qq 72.4 – –Hqq 89.4 +3.97 6.3 · 10−16
ground, but this consistency is shown more precisely bythe CLb, as will be detailed in the next section. Signalexpectations at the reference masses are also given. Anoverview of the candidates is given in Table 25.
Figure 30 shows the distribution of the reconstructedHiggs boson mass found in the ZH channel after all se-lection criteria for data, simulated background and signalevents.
9.3 The SM Higgs boson
The confidence levels CLb, CLsb and CLs are computed asdescribed in Sect. 4.4. In the presence of a sizeable Higgssignal the value of the observed CLb would approach one,because it measures the fraction of background-only ex-periments which are less signal-like than the observation.Figure 31 shows that no statistically significant excess isobserved.
We therefore proceed to set a limit on the SM Higgsboson mass, combining these data with those taken at 161and 172 GeV. The improvement on the limit from addingthe lower energy data is approximately 0.1 GeV. The ex-pected cross-sections and branching ratios are taken from[28,29], with the top mass set to 173.9 GeV/c2[32]. Thecombined CLs is shown in Fig. 32. The observed 95% CLlower limit on the mass is
mH > 85.7 GeV/c2
while the expected 95% CL lower limit is
mH > 86.5 GeV/c2.
If errors had not been allowed for, the observed limitwould have been increased by 0.2 GeV/c2 and the effecton the expected limit is less. The limit is worse than ex-pected, despite getting less candidates than expected, be-cause they tend to have high masses.
We also show the effective ∆χ2 (−2 lnL) with whichthe SM Higgs is excluded in Fig. 33. In the event of adiscovery the ∆χ2 would be negative, and could be usedto extract the mass and its error.
9.4 Neutral Higgs bosons in the MSSM
The results in the hZ and hA processes are combined usingthe same statistical method as for the SM. Earlier resultsat√s = 130-136 GeV[30] and 161-172 GeV[1] are also
included.Contrary to the SM case, the production cross-sections
and the Higgs branching fractions are not completely de-termined by the Higgs boson masses but depend on otherparameters through radiative corrections. With universal-ity assumptions, as usually introduced, the free parame-ters beyond tree level are the mass of the top quark, theSUSY Higgs mass parameter µ, the universal sfermionmass term (MS), the universal gaugino mass term (M2)and the universal squark tri-linear coupling (A). The scaleat which the different mass terms in each set are assumedto be unified is either the EW scale or the GUT scale.Once those parameters are set, there are only two free pa-rameters: tanβ and one of the Higgs boson masses,mAandmh, or, alternatively, the two Higgs boson masses.
To obtain the results described hereafter, the parame-ters beyond tree level have been set to the following val-ues [31]: 173.9 GeV/c2 for the top mass, 1 TeV/c2 forMS at the EW scale and 1.6 TeV/c2 for M2 at the EWscale. In addition, three benchmark hypotheses [31] havebeen made for the two parameters A and µ, which deter-mine the mixing in the stop sector: no mixing (A = 0,µ = −100 GeV), maximal mixing (A =
√6MS , µ =
−100 GeV) and typical mixing (A = MS = −µ). In thethree cases, the scale at which the squark tri-linear cou-plings are assumed to be equal is the EW scale, as for MS
and M2. A more general scan over the MSSM parameterswould lead to weaker constraints [33] and is in preparationfor the analysed data set.
Then, the MSSM parameter space is scanned in the(tanβ, mA) plane, assuming a range of variation for mAbetween 20 GeV/c2 and 10 TeV/c2 and a range of varia-tion for tanβ between 0.5 and 50. For the typical mixing,the minimal value of tanβ has been restricted to 1 sincelower values would lead to unphysical Higgs boson masses.At each point of the parameter space, the hZ and hA cross-sections and the Higgs branching fractions are computedwith the HZHA program which uses the results of [34] forthe radiative corrections.
The signal expectations in each channel are derivedfrom the cross-sections, the experimental luminosity andthe efficiencies obtained from the simulation. A correc-tion is applied to account for differing branching fractionsof the Higgs bosons into bb and τ+τ− between the inputpoint and the simulation (e.g. for the hZ process, the simu-lation is done in the SM framework). For the hA channels,as there can be a difference between the masses of the hand A bosons at low tanβ, the set of hA efficiencies ob-tained from the simulation at tanβ = 20 is applied at allpoints with tanβ above 2.5, while the set of efficiencies de-rived from the tanβ = 2 simulation is applied below. Thesame holds for the mass information (see below). The sig-nal expectations, expected backgrounds and numbers ofcandidates are used to compute the observed confidencelevel in the signal hypothesis at the input point, CLs. The
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Fig. 33. The effective ∆χ2 with which each SM Higgsmass is excluded (solid) and the expected value of thesame (dashed). The dotted line shows the expectedvalue if a SM Higgs of mass 85 GeV/c2 were present.Zero is also indicated (solid) because a negative valuewould indicate a mass region more favourable thanno Higgs. It can be seen that masses above about80 GeV/c2 are excluded less strongly than we mightexpect, owing to the clustering of the candidates inthis region
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expected confidence level in the signal hypothesis is alsoderived at each point. The confidence level computationmakes use of the detailed mass information in each chan-nel, for all data except at 130-136 GeV. The reconstructedHiggs boson mass is used in the hZ channels and the sumof the reconstructed h and A masses in the hA channels(for the pairing with minimal mass difference in the four-jet channel).
The results translate into regions of the MSSM pa-rameter space excluded at at least 95% CL. Except formA at low tanβ, they are not strongly dependent on theassumption about the mixing in the stop sector. The re-sults are presented in the (mh, tanβ) plane in Fig. 34,in the (mA, tanβ) plane in Fig. 35 and in the (mA, mh)plane in Fig. 36.
As illustrated in Fig. 36, there is a region of the pa-rameter space where the decay h→AA opens. Once open,this decay in most cases dominates the h→bb decay, sothat the results, which apply only to the other decays,may not be sufficient to reach a 95% CL exclusion. Onthe other hand, as the dominant decay of the A bosonis still into bb in most of the region, the final states re-semble those with h→bb and no analysis dedicated to theh→AA decay seems necessary to cover this region. In or-der to check this, the standard analysis was applied onsimulated samples with h→AA and A→bb and the ef-
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ficiency and mass distributions were determined for thissignal. As the h→AA decay occurs in a region where hAis negligible (typically for tanβ below 1.7) only the dom-inant four-jet hZ analysis was used. The results on a fewpoints are summarized in Table 26 which gives the valueof the observed CLs in each point, in three cases: 1) as-suming no efficiency to the h→AA decay, 2) including theefficiency to the h→AA decay of the analysis at 161 and172 GeV only and 3) including also the efficiency of the183 GeV analysis.
As shown in Table 26, the standard results alone can-not exclude most of the h→AA region. Once the efficiencyof the 161/172 GeV analysis to this decay is included,the whole h→AA region above tanβ = 1 is excluded atmore than 95% CL [1], and, when the efficiency of thepresent analysis is also taken into account, the exclusionextends to lower values of tanβ, more precisely down totanβ = 0.6. For smaller values of tanβ, there are unex-cluded points, due to the decrease of the A→bb branchingratio, and the rise of the A branching ratios into pairs ofc quarks or gluons. The unexcluded area can be seen inFigs. 35 and 36, whereas in Fig. 34 it is not visible sinceit corresponds to points very close in mh.
Finally, the results shown in Figs. 34, 35 and 36 estab-lish 95% CL lower limits on mh and mA, whatever theassumption on the mixing in the stop sector and for allvalues of tanβ greater than or equal to 0.6, but assumingmA> 20 GeV/c2, of:
mh > 74.4 GeV/c2 mA > 75.3 GeV/c2
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Table 26. Examples of points with h→AA: values of tanβ, mA and mh, h branching fractionsinto bb and AA, A branching fraction into bb, efficiency of the standard hZ four-jet analysis tothe final state (h→AA)(Z→qq ), A→bb, and observed confidence level in the signal hypothesisif no efficiency to h→AA is assumed (1), or if the efficiency of the standard analysis to h→AAis included for the 161/172 GeV results only (2) or for the 161/172/183 GeV results (3)
These limits arise from the performance of the searchesat large tanβ, i.e. in the hA channel. The expected limitsare 70.2 GeV/c2 in mh and 70.8 GeV/c2 in mA. For the nomixing assumption, given that mh is tightly constrainedby the theory, all values of mA are excluded in the lowtanβ region, providing an excluded range in tanβ between0.7 and 1.9 (see Fig. 34).
10 Conclusions
From 54 pb−1 of data taken by DELPHI at 182.7 GeV,the lower limit at 95% CL on the mass of the StandardModel Higgs boson is set at:
mH > 85.7 GeV/c2 .
This is an improvement of 18 GeV/c2 over our lastpublication [1]. The MSSM studies described above give,for all values of tanβ in excess of 0.6 and assuming mA >20 GeV/c2:
mh > 74.4 GeV/c2
mA > 75.3 GeV/c2
which is an improvement of 15 to 25 GeV/c2 over our lastresults. These limits can be compared with those found byother collaborations [35–39]. We also deduce that in thelimited scan with no mixing in the stop sector, the valueof tanβ cannot be between 0.7 and 1.9. In other mixingscenarios, no limit on tanβ can be set.
Acknowledgements. We are greatly indebted to our technicalcollaborators, to the members of the CERN-SL Division for theexcellent performance of the LEP collider, and to the fundingagencies for their support in building and operating the DEL-PHI detector. We acknowledge in particular the support of
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tan β ≥ 0.5
50
100
150
200
250
20 40 60 80 100 120
mh (GeV/c2)
mA (
GeV
/c2 )
50
100
150
200
250
20 40 60 80 100 120
DELPHI
Typical mixing
theoretically forbidden
theoretically forbidden
tan β ≥ 1
a)
b)
c)
Fig. 36a–c. Region in the (mA, mh) plane excluded at 95%CL by the result of the searches in the hZ and hA channels at√s= 133 to 183 GeV (in light grey). Three different hypotheses
for the mixing in the stop sector are presented. The regions notallowed by the MSSM model for a top mass of 173.9 GeV/c2
and a SUSY scale of 1 TeV/c2 are shaded. They assume tan βgreater than 0.5 for the maximal and minimal mixings, a andb, and tanβ above 1 for the typical mixing, c. The hatchedarea shows the region where the h→AA decay may occur
604 The DELPHI Collaboration: Search for neutral Higgs bosons in e+e− collisions at√s = 183 GeV
Austrian Federal Ministry of Science and Traffics,GZ 616.364/2-III/2a/98, FNRS–FWO, Belgium, FINEP,CNPq, CAPES, FUJB and FAPERJ, Brazil, Czech Ministryof Industry and Trade, GA CR 202/96/0450 and GA AVCRA1010521, Danish Natural Research Council, Commission ofthe European Communities (DG XII), Direction des Sciencesde la Matiere, CEA, France, Bundesministerium fur Bildung,Wissenschaft, Forschung und Technologie, Germany, GeneralSecretariat for Research and Technology, Greece, National Sci-ence Foundation (NWO) and Foundation for Research on Mat-ter (FOM), The Netherlands, Norwegian Research Council,State Committee for Scientific Research, Poland, 2P03B06015,2P03B03311 and SPUB/P03/178/98, JNICT–Junta Nacionalde Investigacao Cientıfica e Tecnologica, Portugal, Vedeckagrantova agentura MS SR, Slovakia, Nr. 95/5195/134, Min-istry of Science and Technology of the Republic of Slovenia,CICYT, Spain, AEN96–1661 and AEN96-1681, The SwedishNatural Science Research Council, Particle Physics and As-tronomy Research Council, UK, Department of Energy, USA,DE–FG02–94ER40817.
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