EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN–PH–EP/2007–029 DAPNIA–07–150 9 July 2007 8 Higgs boson searches in 0 0 2 CP-conserving and CP-violating n a MSSM scenarios with the DELPHI J 3 2 detector ] x e - DELPHI Collaboration p e h [ 1 v 6 8 Abstract 5 3 . 1 0 This paper presents the final interpretation of the results from DELPHI on 8 the searches for Higgs bosons in the Minimal Supersymmetric extension of the 0 : Standard Model (MSSM). A few representative scenarios are considered, that v include CP conservation and explicit CP violation in the Higgs sector. The i X experimental results encompass the searches for neutral Higgs bosons at LEP1 ar and LEP2 in final states as expected in the MSSM, as well as LEP2 searches for charged Higgs bosons and for neutral Higgs bosons decaying into hadrons independent of the quark flavour. The data reveal no significant excess with respect to background expectations. The results are translated into excluded regions of the parameter space in the various scenarios. In the CP-conserving case, these lead to limits on the masses of the lightest scalar and pseudoscalar Higgs bosons, h and A, and on tanβ. The dependence of these limits on the top quark mass is discussed. Allowing for CP violation reduces the experimental sensitivity to Higgs bosons. It is shown that this effect depends strongly on the values of the parameters responsible for CP violation in the Higgs sector. (Accepted by Eur. Phys. J. C) ii J.Abdallah26,P.Abreu23,W.Adam55,P.Adzic12,T.Albrecht18,R.Alemany-Fernandez9,T.Allmendinger18,P.P.Allport24, U.Amaldi30, N.Amapane48, S.Amato52, E.Anashkin37, A.Andreazza29, S.Andringa23, N.Anjos23, P.Antilogus26, W-D.Apel18, Y.Arnoud15, S.Ask27, B.Asman47, J.E.Augustin26, A.Augustinus9, P.Baillon9, A.Ballestrero49, P.Bambade21, R.Barbier28, D.Bardin17, G.J.Barker57, A.Baroncelli40, M.Battaglia9, M.Baubillier26, K-H.Becks58, M.Begalli7, A.Behrmann58, E.Ben-Haim21, N.Benekos33, A.Benvenuti5, C.Berat15, M.Berggren26, L.Berntzon47, D.Bertrand2, M.Besancon41, N.Besson41, D.Bloch10, M.Blom32, M.Bluj56, M.Bonesini30, M.Boonekamp41, P.S.L.Booth†24, G.Borisov22, O.Botner53, B.Bouquet21, T.J.V.Bowcock24, I.Boyko17, M.Bracko44, R.Brenner53, E.Brodet36, P.Bruckman19, J.M.Brunet8, B.Buschbeck55, P.Buschmann58, M.Calvi30, T.Camporesi9, V.Canale39, F.Carena9, N.Castro23, F.Cavallo5, M.Chapkin43, Ph.Charpentier9, P.Checchia37, R.Chierici9, P.Chliapnikov43, J.Chudoba9, S.U.Chung9, K.Cieslik19, P.Collins9, R.Contri14, G.Cosme21, F.Cossutti50, M.J.Costa54, D.Crennell38, J.Cuevas35, J.D’Hondt2, J.Dalmau47, T.daSilva52, W.DaSilva26, G.DellaRicca50, A.DeAngelis51, W.DeBoer18, C.DeClercq2, B.DeLotto51, N.DeMaria48, A.DeMin37, L.dePaula52, L.DiCiaccio39, A.DiSimone40, K.Doroba56, J.Drees58,9, G.Eigen4, T.Ekelof53, M.Ellert53, M.Elsing9, M.C.EspiritoSanto23, G.Fanourakis12, D.Fassouliotis12,3, M.Feindt18, J.Fernandez42, A.Ferrer54, F.Ferro14, U.Flagmeyer58, H.Foeth9, E.Fokitis33, F.Fulda-Quenzer21, J.Fuster54, M.Gandelman52, C.Garcia54, Ph.Gavillet9, E.Gazis33, R.Gokieli9,56, B.Golob44,46, G.Gomez-Ceballos42, P.Goncalves23, E.Graziani40, G.Grosdidier21, K.Grzelak56, J.Guy38, C.Haag18, A.Hallgren53, K.Hamacher58, K.Hamilton36, S.Haug34, F.Hauler18, V.Hedberg27, M.Hennecke18, H.Herr†9, J.Hoffman56, S-O.Holmgren47, P.J.Holt9, M.A.Houlden24, J.N.Jackson24, G.Jarlskog27, P.Jarry41, D.Jeans36, E.K.Johansson47, P.D.Johansson47, P.Jonsson28, C.Joram9, L.Jungermann18, F.Kapusta26, S.Katsanevas28, E.Katsoufis33, G.Kernel44, B.P.Kersevan44,46, U.Kerzel18, B.T.King24, N.J.Kjaer9, P.Kluit32, P.Kokkinias12, C.Kourkoumelis3, O.Kouznetsov17, Z.Krumstein17, M.Kucharczyk19, J.Lamsa1, G.Leder55, F.Ledroit15, L.Leinonen47, R.Leitner31, J.Lemonne2, V.Lepeltier21, T.Lesiak19, W.Liebig58, D.Liko55, A.Lipniacka47,J.H.Lopes52,J.M.Lopez35,D.Loukas12,P.Lutz41,L.Lyons36,J.MacNaughton55,A.Malek58,S.Maltezos33, F.Mandl55, J.Marco42, R.Marco42, B.Marechal52, M.Margoni37, J-C.Marin9, C.Mariotti9, A.Markou12, C.Martinez-Rivero42, J.Masik13, N.Mastroyiannopoulos12, F.Matorras42, C.Matteuzzi30, F.Mazzucato37, M.Mazzucato37, R.McNulty24, C.Meroni29, E.Migliore48, W.Mitaroff55, U.Mjoernmark27, T.Moa47, M.Moch18, K.Moenig9,11, R.Monge14, J.Montenegro32, D.Moraes52, S.Moreno23, P.Morettini14, U.Mueller58, K.Muenich58, M.Mulders32, L.Mundim7, W.Murray38, B.Muryn20, G.Myatt36, T.Myklebust34, M.Nassiakou12, F.Navarria5, K.Nawrocki56, R.Nicolaidou41, M.Nikolenko17,10, A.Oblakowska-Mucha20, V.Obraztsov43, A.Olshevski17, A.Onofre23, R.Orava16, K.Osterberg16, A.Ouraou41, A.Oyanguren54, M.Paganoni30, S.Paiano5, J.P.Palacios24, H.Palka19, Th.D.Papadopoulou33, L.Pape9, C.Parkes25, F.Parodi14, U.Parzefall9, A.Passeri40, O.Passon58, L.Peralta23, V.Perepelitsa54, A.Perrotta5, A.Petrolini14, J.Piedra42, L.Pieri40, F.Pierre41, M.Pimenta23, E.Piotto9, T.Podobnik44,46, V.Poireau9, M.E.Pol6, G.Polok19, V.Pozdniakov17, N.Pukhaeva17, A.Pullia30, J.Rames13, A.Read34, P.Rebecchi9, J.Rehn18, D.Reid32, R.Reinhardt58, P.Renton36, F.Richard21, J.Ridky13, M.Rivero42, D.Rodriguez42, A.Romero48, P.Ronchese37, P.Roudeau21, T.Rovelli5, V.Ruhlmann-Kleider41, D.Ryabtchikov43, A.Sadovsky17, L.Salmi16, J.Salt54, C.Sander18, A.Savoy-Navarro26, U.Schwickerath9, R.Sekulin38, M.Siebel58, A.Sisakian17, G.Smadja28, O.Smirnova27, A.Sokolov43, A.Sopczak22, R.Sosnowski56, T.Spassov9, M.Stanitzki18, A.Stocchi21, J.Strauss55, B.Stugu4, M.Szczekowski56, M.Szeptycka56, T.Szumlak20, T.Tabarelli30, A.C.Taffard24, F.Tegenfeldt53, J.Timmermans32, L.Tkatchev17,M.Tobin24, S.Todorovova13, B.Tome23, A.Tonazzo30,P.Tortosa54,P.Travnicek13, D.Treille9,G.Tristram8, M.Trochimczuk56, C.Troncon29, M-L.Turluer41, I.A.Tyapkin17, P.Tyapkin17, S.Tzamarias12, V.Uvarov43, G.Valenti5, P.VanDam32, J.VanEldik9, N.vanRemortel16, I.VanVulpen9, G.Vegni29, F.Veloso23, W.Venus38, P.Verdier28, V.Verzi39, D.Vilanova41, L.Vitale50, V.Vrba13, H.Wahlen58, A.J.Washbrook24, C.Weiser18, D.Wicke9, J.Wickens2, G.Wilkinson36, M.Winter10, M.Witek19, O.Yushchenko43, A.Zalewska19, P.Zalewski56, D.Zavrtanik45, V.Zhuravlov17, N.I.Zimin17, A.Zintchenko17, M.Zupan12 iii 1DepartmentofPhysicsandAstronomy,IowaStateUniversity,AmesIA50011-3160, USA 2IIHE,ULB-VUB,Pleinlaan2,B-1050Brussels,Belgium 3PhysicsLaboratory,UniversityofAthens,SolonosStr. 104,GR-10680Athens,Greece 4DepartmentofPhysics,UniversityofBergen,All´egaten55,NO-5007Bergen,Norway 5DipartimentodiFisica,Universita`diBolognaandINFN,ViaIrnerio46,IT-40126Bologna,Italy 6CentroBrasileirodePesquisasF´ısicas,ruaXavierSigaud150,BR-22290RiodeJaneiro,Brazil 7Inst. deF´ısica,Univ. EstadualdoRiodeJaneiro,ruaSa˜oFranciscoXavier524,RiodeJaneiro,Brazil 8Coll`egedeFrance,Lab. dePhysiqueCorpusculaire,IN2P3-CNRS,FR-75231ParisCedex05,France 9CERN,CH-1211Geneva23,Switzerland 10InstitutdeRecherches Subatomiques, IN2P3-CNRS/ULP-BP20,FR-67037StrasbourgCedex,France 11NowatDESY-Zeuthen,Platanenallee 6,D-15735Zeuthen, Germany 12Institute ofNuclearPhysics,N.C.S.R.Demokritos,P.O.Box60228,GR-15310Athens,Greece 13FZU,Inst. ofPhys. oftheC.A.S.HighEnergyPhysicsDivision,NaSlovance2,CZ-18040,Praha8,CzechRepublic 14DipartimentodiFisica,Universita`diGenova andINFN,ViaDodecaneso 33,IT-16146Genova, Italy 15InstitutdesSciences Nucl´eaires,IN2P3-CNRS,Universit´edeGrenoble1,FR-38026GrenobleCedex,France 16Helsinki Institute of Physics and Department of Physical Sciences, P.O. Box 64, FIN-00014 University of Helsinki, Finland 17JointInstituteforNuclearResearch,Dubna,HeadPostOffice,P.O.Box79,RU-101000Moscow,RussianFederation 18Institutfu¨rExperimentelleKernphysik,Universita¨tKarlsruhe,Postfach6980, DE-76128Karlsruhe,Germany 19Institute ofNuclearPhysicsPAN,Ul. Radzikowskiego152,PL-31142Krakow,Poland 20FacultyofPhysicsandNuclearTechniques,UniversityofMiningandMetallurgy,PL-30055Krakow,Poland 21Universit´edeParis-Sud,Lab. del’Acc´el´erateurLin´eaire,IN2P3-CNRS,Baˆt. 200,FR-91405OrsayCedex,France 22SchoolofPhysicsandChemistry,UniversityofLancaster,Lancaster LA14YB,UK 23LIP,IST,FCUL-Av. EliasGarcia,14-1o,PT-1000LisboaCodex,Portugal 24DepartmentofPhysics,UniversityofLiverpool,P.O.Box147,LiverpoolL693BX,UK 25Dept. ofPhysicsandAstronomy,KelvinBuilding,UniversityofGlasgow,GlasgowG128QQ,UK 26LPNHE,IN2P3-CNRS,Univ.ParisVIetVII,Tour33(RdC),4placeJussieu,FR-75252ParisCedex05,France 27DepartmentofPhysics,UniversityofLund,So¨lvegatan 14,SE-22363Lund,Sweden 28Universit´eClaudeBernarddeLyon,IPNL,IN2P3-CNRS,FR-69622VilleurbanneCedex,France 29DipartimentodiFisica,Universita`diMilanoandINFN-MILANO,ViaCeloria16,IT-20133Milan,Italy 30DipartimentodiFisica,Univ. diMilano-BicoccaandINFN-MILANO,PiazzadellaScienza3,IT-20126Milan,Italy 31IPNPofMFF,CharlesUniv.,ArealMFF,VHolesovickach2,CZ-18000,Praha8,CzechRepublic 32NIKHEF,Postbus41882, NL-1009DBAmsterdam,TheNetherlands 33NationalTechnical University,PhysicsDepartment,ZografouCampus,GR-15773Athens,Greece 34PhysicsDepartment,UniversityofOslo,Blindern,NO-0316Oslo,Norway 35Dpto. Fisica,Univ. Oviedo,Avda. CalvoSotelos/n,ES-33007Oviedo,Spain 36DepartmentofPhysics,UniversityofOxford,KebleRoad,OxfordOX13RH,UK 37DipartimentodiFisica,Universita`diPadovaandINFN,ViaMarzolo8,IT-35131Padua,Italy 38RutherfordAppletonLaboratory, Chilton,DidcotOX11OQX,UK 39DipartimentodiFisica,Universita`diRomaIIandINFN,TorVergata, IT-00173Rome,Italy 40DipartimentodiFisica,Universita`diRomaIIIandINFN,ViadellaVascaNavale84,IT-00146Rome,Italy 41DAPNIA/ServicedePhysiquedesParticules,CEA-Saclay,FR-91191Gif-sur-YvetteCedex, France 42InstitutodeFisicadeCantabria(CSIC-UC),Avda. losCastross/n,ES-39006Santander, Spain 43Inst. forHighEnergyPhysics,SerpukovP.O.Box35,Protvino,(MoscowRegion),RussianFederation 44J.StefanInstitute, Jamova39,SI-1000Ljubljana,Slovenia 45LaboratoryforAstroparticlePhysics,UniversityofNovaGorica,Kostanjeviska16a,SI-5000NovaGorica,Slovenia 46DepartmentofPhysics,UniversityofLjubljana,SI-1000Ljubljana,Slovenia 47Fysikum,Stockholm University,Box6730, SE-11385Stockholm,Sweden 48DipartimentodiFisicaSperimentale,Universita`diTorinoandINFN,ViaP.Giuria1,IT-10125Turin,Italy 49INFN,SezionediTorinoandDipartimentodiFisicaTeorica,Universita`diTorino,ViaGiuria1,IT-10125Turin,Italy 50DipartimentodiFisica,Universita`diTriesteandINFN,ViaA.Valerio2,IT-34127Trieste,Italy 51IstitutodiFisica,Universita`diUdineandINFN,IT-33100Udine,Italy 52Univ. FederaldoRiodeJaneiro,C.P.68528CidadeUniv.,IlhadoFunda˜oBR-21945-970RiodeJaneiro,Brazil 53DepartmentofRadiationSciences,UniversityofUppsala,P.O.Box535,SE-75121Uppsala,Sweden 54IFIC,Valencia-CSIC,andD.F.A.M.N.,U.deValencia,Avda. Dr. Moliner50,ES-46100Burjassot(Valencia),Spain 55Institutfu¨rHochenergiephysik, O¨sterr. Akad. d. Wissensch.,Nikolsdorfergasse18,AT-1050Vienna,Austria 56Inst. NuclearStudiesandUniversityofWarsaw,Ul. Hoza69,PL-00681Warsaw,Poland 57NowatUniversityofWarwick,CoventryCV47AL,UK 58FachbereichPhysik,UniversityofWuppertal, Postfach100 127,DE-42097Wuppertal, Germany † deceased 1 1 Introduction This paper presents the final interpretation of the Higgs boson search results from DELPHI in the framework of representative scenarios of the Minimal Supersymmetric Standard Model (MSSM). With respect to the previous MSSM interpretation published in Ref. [1], this analysis uses an enlarged set of experimental results, updated calculations of MSSM radiative corrections and covers more scenarios, including models with CP violation in the Higgs sector. As compared with the Standard Model, the MSSM has an extended Higgs sector with two doublets of complex Higgs fields, leading to five physical Higgs bosons, of which three are neutral. Figure 1: Main production processes of MSSM neutral Higgs bosons at LEP. Left: associated production of a Z and a Higgs boson, which must be one of the CP-even scalars (h or H) if CP is conserved or any Higgs boson (H , H , H ) in the contrary case. 1 2 3 At LEP1, the intermediate Z is on-shell and the final Z is off-shell, while it is the reverse at LEP2. Right: pair-production of neutral Higgs bosons. If CP is conserved, one of them must be CP-even (h or H) and the other one is the CP-odd pseudo-scalar A. If CP is not conserved, the pair can be any couple of different scalars among H , H and 1 2 H . The intermediate Z is on-shell at LEP1. 3 If CP is conserved, two of the three neutral Higgs bosons are CP-even. They are denoted h, for the lighter one, and H. The third one is a CP-odd pseudo-scalar, denoted A. In e+e− collisions, the dominant production mechanisms are the s-channel processes described in Fig. 1, that is the associated production of a Z and a CP-even Higgs boson and the pair production of either CP-even bosontogether with the CP-oddscalar. These processes are complemented by additional t-channel diagrams in the final states where a CP-even Higgs boson is produced with neutrinos or electrons, which proceed through W+W− and ZZ fusions, respectively. These diagrams and their interference with the HZ process have an impact on the production cross-section at masses around the HZ i i kinematic threshold. At LEP2 energies, the only significant effect is from W+W− fusion which doubles the neutrino HZ cross-section at the kinematic threshold. Finally, charged i Higgs bosons, H+ and H−, are produced in pairs through a diagram similar to that in Fig. 1, right, via exchange of a Z boson or a photon. Although CP is conserved at tree level in the MSSM, radiative corrections can in- troduce CP violation through stop and sbottom loops, leading to changes in the neutral Higgs boson sector [2]. If CP is not conserved, the three neutral Higgs bosons are no longer pure CP eigenstates but mixtures of CP-even and CP-odd components. They are 2 usually denoted H , H and H , in increasing mass. The main production mechanisms 1 2 3 are the same as in the CP conserving case, except that, a priori, any scalar can be pro- duced in association with a Z boson or through W+W− and ZZ fusions, and any couple of different Higgs bosons can be pair-produced. The main phenomenological difference with respect to the CP-conserving case lies in the strength of the couplings of the Z boson to the Higgs scalars. In significant regions of the parameter space, CP violation turns off the otherwise dominant coupling between the Z boson and the lightest Higgs boson. In that case, if none of the other processes of Fig. 1 are possible (due e.g. to kinematics), the dominant Higgs boson production mechanism at LEP becomes the Yukawa process of Fig. 2. Of the two phases of LEP, only LEP1 has a significant sensitivity to this process. In the Standard Model, the corresponding cross-sections are negligible, e.g. a fraction of a pb for a few GeV/c2 Higgs boson. In the MSSM, these can be enhanced by up to three orders of magnitude with respect to their Standard Model values, leading to detectable signals which become valuable in the case of CP violation. Figure 2: Additional production process of MSSM neutral Higgs bosons at LEP. The radiation of a Higgs boson off a Z boson decay fermion gives a detectable signal only at LEP1. This signal is exploited in the case of CP violation. The decay properties of the Higgs bosons are moderately affected by CP violation, at leastintherangeofmassesaccessibleatLEP,thatisuptomassesaround100GeV/c2 [2]. InmostoftheMSSMparameterspaceofthescenariosstudiedhereafter,thethreeneutral Higgs bosons decay mainly into the pair of heaviest fermions kinematically permitted, even if CP is not conserved. Below the µ+µ− threshold, a Higgs boson would decay into γγ or e+e− pairs with a significant lifetime. Above the µ+µ− threshold, the lifetime is negligible and Higgs bosons decay at the primary vertex. Up to a mass of 3 GeV/c2 the main decays are into µ+µ− pairs and also into hadronic channels with a large proportion of two-prong final states. Above 3 GeV/c2 the dominant decays are successively into c¯c, τ+τ− and finally bb¯ pairs for Higgs boson masses above 12 GeV/c2. Besides these decays into fermions, there are also regions of the parameter space where one neutral Higgs boson can undergo cascade decays to a pair of Higgs bosons, as for example h AA if CP is conserved or H H H in the contrary case. In some cases, espec→ially if 2 1 1 CP is not conserved, this →mode dominates over the decays into SM particles. In the scenarios considered in this paper, charged Higgs bosons have a mass above 60 GeV/c2 and decay either into the pair of heaviest fermions allowed by kinematics, that is into cs or τν pairs, or into a W∗ and a light Higgs boson, e.g. into a W∗A pair if CP is conserved. Finally, these scenarios do not allow neutral or charged Higgs boson decays 3 into supersymmetric particles such as sfermions, charginos or invisible neutralinos. Note that searches for neutral Higgs bosons decaying into invisible products were performed at LEP, as reported in Ref. [3]. The different decay channels define the topologies that were searched for to cover the MSSM parameter region kinematically accessible at LEP energies. These topologies are described in Section 2. Section 3 summarizes the definition and techniques related to confidence levels used in the statistical interpretation of the searches. The eight CP- conserving MSSMbenchmarkscenarios studiedinthisanalysisarepresented inSection4 and the results obtained in these scenarios when combining all searches are given in Section5. Similarily,theCP-violatingscenariosandthecorrespondingresultsarecovered in Sections 6 and 7. The top quark mass has a significant impact on the properties of the Higgs bosons (e.g. mass spectrum of the neutral Higgs bosons, CP-violating effects). Resultsarethusderived forseveralvaluesofthismass, namely: m =169.2,174.3,179.4 top and 183.0 GeV/c2, which were defined after the measurement of the top quark mass at the Tevatron, run I [4]. Of the two values close to the present experimental measurement of m = 170.9 1.1 1.5 GeV/c2 [5], 174.3 GeV/c2 gives the most conservative results top ± ± and thus was chosen as a reference in most of the exclusion plots and to quote absolute mass and tanβ limits. Readers interested in similar analyses at LEP are referred to Ref. [6,7]. 2 Search channels The different analyses performed to search for neutral and charged Higgs bosons in the whole LEP1 and LEP2 DELPHI data samples are summarized in Table 1 which lists the final states, mass ranges, integrated luminosities and the references for more details about the selections and their performance. Two channels, the τ+τ−bb¯ signal at LEP1 and the (h AA c¯cc¯c) (Z qq¯) signal at A masses below the bb¯ threshold, → → → were analysed for this paper, using selections already published. The efficiencies and the references for the selections can be found in the Appendices 1 and 2 of this paper. In the Table, the notations h and A which label the different analysis channels must be understood as generic notations for any pair of neutral Higgs bosons that could be produced in each of the production processes listed in the Table. As an example, the hZ analyses, originally designed to search for the CP-even h boson in CP-conserving scenarios, can be applied to search for the second CP-even Higgs boson, H, as well as for any of the three Higgs scalars in CP-violating scenarios. It must be noted that the kinematic properties of the signal processes are only slightly affected by CP-violation, since, when CP is not conserved, the production processes still proceed through the CP- even and CP-odd components of the neutral Higgs bosons, as explained in Ref. [7]. The same topological searches can thus be applied whether CP is conserved or not. As compared with our previous publication [1], the following changes were introduced in the experimental results used. The MSSM interpretation in Ref. [1] relied only on searches performed at LEP2 at masses above 12 GeV/c2 in m in the hZ process, with h either direct or cascade decays, and above 40 GeV/c2 in m , m in the hA channels, h A with only direct decays of the Higgs bosons. The corresponding channels have their √s values in bold characters in Table 1. Scans of the MSSM parameter space were thus restricted to m above 12 GeV/c2 and assumed the published LEP1 limits1 to be valid. A Including all LEP1 results, which have a sensitivity starting from vanishing h and A masses, and the additional LEP2 searches of Ref. [21], whose sensitivity in the hA mode 1mh>44(46)GeV/c2 whenmh isabove(below)theAAthreshold[14] √s final state range disc. ref. 4 (GeV) (GeV/c2) (pbL−1) info. hZ with direct decays 91 Z e+e−, µ+µ− <0.21 2.5 no [8] 91 (h→ V0) (Z any) <0.21 2.5 no [8] → → 91 (h 2 prongs) (Z qq¯) 0.21 2. 0.5 no [9] 91 (h → jet) (Z e+e→−, µ+µ−) 1. −20. 0.5 no [9] 91 (h → jet jet)→(Z l+l−, νν¯) >−12. 3.6 no [10] 91 (h → jet jet) (Z→ e+e−, µ+µ−, νν¯) >35. 33.4 no [11] 161,172 (h → bb¯)(Z a→ny), (h τ+τ−)(Z qq¯) >40. 19.9 1d [17] 183 (h → bb¯)(Z → any), (h → τ+τ−)(Z→ qq¯) >55. 52.0 1d [18] 189 (h → bb¯)(Z → any), (h → τ+τ−)(Z→ qq¯) >65. 158.0 2d [19] 192-208 (h → bb¯)(Z → any) → → >12. 452.4 2d [20,1] 192-208 (h → τ+τ−)(→Z qq¯) >50. 452.4 2d [20,1] 189-208 (h → hadrons)(→Z any but τ+τ−) >4. 610.4 mix [22] → → hA with direct decays 91 4 prongs >0.4 5.3 no [12] 91 τ+τ− hadrons >8. 0.5 no [13] 91 τ+τ− jet jet >50 3.6 no [10] 91 bb¯bb¯, bb¯c¯c >30. 33.4 no [14] 91 τ+τ−bb¯ >16. 79.4 no A.1 91 bb¯bb¯ >24. 79.4 no [21] 133 bb¯bb¯ >80. 6.0 no [16] 161,172 bb¯bb¯, τ+τ−bb¯ >80. 20.0 1d [17] 183 bb¯bb¯, τ+τ−bb¯ >100. 54.0 1d [18] 189 bb¯bb¯, τ+τ−bb¯ >130. 158.0 2d [19] 192-208 τ+τ−bb¯ >120. 452.4 2d [20,1] 192-208 bb¯bb¯ >80. 452.4 2d [20,1] 189-208 τ+τ−τ+τ− >8. 570.9 1d [21] 189-208 bb¯bb¯ >24. 610.2 no [21] 189-208 hadrons >8. 610.4 mix [22] hZ or hA with h AA cascade → 91 Z qq¯ <0.21 16.2 no [15] 91 (A→A V0V0) (Z any but τ+τ−) <0.21 9.7 no [15] → → 91 (AA γγ) (Z any or A γγ) <0.21 12.5 no [15] → → → 91 (AA 4 prongs) (Z any or A 2 prongs) >0.21 12.9 no [15] → → → 91 (AA hadrons) (Z νν¯ or A hadrons) >0.21 15.1 no [15] 91 (AA→ τ+τ−τ+τ−)→(Z νν¯ or→A τ+τ−) >3.5 15.1 no [15] → → → 161,172 (AA any) (Z qq¯, νν¯or A any) >20. 20.0 1d [17] 183 (AA→ bb¯bb¯) (Z→ qq¯) → >12. 54.0 1d [18] 192-208 (AA→ bb¯bb¯, bb¯c→¯c, c¯cc¯c) (Z qq¯) >12. 452.4 2d [20,1] → → 192-208 (AA c¯cc¯c) (Z qq¯) >4. 452.4 2d A.2 189-208 (AA→ bb¯bb¯) (Z→ qq¯ or A bb¯) >12. 610.2 no [21] → → → ffh or ffA Yukawa production 91 bb¯(h τ+τ−), bb¯(A τ+τ−) 4. 50. 79.4 no [21] 91 bb¯(h → bb¯), bb¯(A →bb¯) 11.− 50. 79.4 no [21] 91 τ+τ−→(h τ+τ−),→τ+τ−(A τ+τ−) 4. −50. 79.4 no [21] → →H+H− − ∗ ∗ ∗ 189-208 c¯s¯cs, csτντ , W Aτντ , W AW A >40. 610.4 2d [23] 189-208 τ+νττ−ν¯τ >40. 570.8 1d [23] Table 1: List of signals expected from MSSM Higgs bosons that were searched for in the DELPHIdatasample. Indicatedforeachsignalarethecentre-of-massenergy, finalstate, analysed mass range, integrated luminosity, level of discriminant information included in the confidence level estimates (none, one- or two-dimensional) and the reference where detailsoftheanalysisarepublished. HerehandAdenoteanyneutralHiggsbosonallowed to be produced in each of the indicated production processes. The mass range applies to m for hZ production, to m +m for hA production, to m for h AA processes, h h A A to the Higgs boson mass for either Yukawa process and to m for H→+H− production. H± When no upper bound is given, the limit imposed by kinematics or vanishing branching fractions must be understood. 5 complements that of the two other sets of results, allows scans of the MSSM parameter space to be performed with no restriction on masses. Moreover, some of the analyses of Ref. [21] cover production processes which are negligible if CP is conserved but are enhanced by CP violation, such as Yukawa processes or the production of τ+τ−τ+τ− final states. Adding the searches for neutral Higgs bosons decaying into hadrons of any flavour [22] is expected to provide sensitivity in scenarios where the Higgs boson decays ¯ into bb would vanish. As their mass coverage starts at low mass, these analyses also ¯ increase the experimental sensitivity to Higgs bosons below the bb threshold, a region otherwise covered only by analyses of subsets of the LEP1 data. Finally, the charged Higgs boson searches [23] help in a few CP-conserving scenarios in the low m region A where the charged bosons are kinematically accessible at LEP2. Moreover, our previous interpretation was dealing only with the production of the two lightest Higgs bosons, the h and A scalars in CP-conserving scenarios. In this analysis, the production of the third boson, if kinematically accessible, is also accounted for, which can lead to a significant gain in sensitivity in restricted areas of the parameter space. In CP-conserving scenarios, this leads to including the HZ and HA signals besides the usual hZ and hA processes, while in CP-violating models, the H Z and H H signals are 2 1 3 taken into account in addition to the dominant H Z and H H channels (the two other 1 1 2 processes, H Z and H H being out of reach). 3 2 3 3 Tools for the statistical analysis When scanning over the parameter space of a model, confidence levels are computed at each point to test the compatibility of data with the hypothesis of background only and with that of background plus signal as expected from the model. Throughout this section, the notations h, H and A must be understood as generic notations for the three neutral Higgs bosons of any type of MSSM scenario. 3.1 Confidence level definitions and calculations The confidence levels are calculated using a modified frequentist technique based on the extended maximum likelihood ratio [24] which has also been adopted by the LEP Higgs working group. The basis of the calculation is the likelihood ratio test-statistic, : Q s +b i i ln = S +Xln Q − b i i where S is the total signal expected and s and b are the signal and background densities i i for event i. These densities are constructed using either expected rates only or also additional discriminant information, which can be one- or two-dimensional. Table 1 presents the level of discriminant information for each channel: LEP1 results rely on rates only, while LEP2 results mix channels without or with discriminant information. As an example, in neutral Higgs boson channels with discriminant information, the first variable is the reconstructed Higgs boson mass in the hZ analyses and the sum of the reconstructed h and A masses in the hA analyses, while the second variable, if any, is channel-dependent, as specified in the references listed in the Table. Charged Higgs analyses use discriminant informationinasimilar way [23]. Thesearches forHiggsbosons decaying hadronically encompass analyses without or with 1d discriminant information together with analyses whose selections vary with the mass hypothesis [22]. 6 The observed value of is compared with the expected Probability Density Func- Q tions (PDFs) for , which are built using Monte Carlo sampling under the assumptions Q that background processes only or that both signal and background are present. The confidence levels CL and CL are their integrals from to the observed value of b s+b −∞ . Systematic uncertainties in the rates of signal or background events are taken into Q account in the calculation of the PDFs for by randomly varying the expected rates Q while generating the distribution [25], which has the effect of broadening the expected Q distribution and therefore making extreme events seem more probable. CL is the probability of obtaining a result as background-like or more so than the one b observed if the background hypothesis is correct. Similarly, the confidence level for the hypothesis that both signal and background are present, CL , is the probability, in this s+b hypothesis, toobtainmorebackground-likeresultsthanthoseobserved. ThequantityCL s is defined as the ratio of these two probabilities, CL /CL . It is not a true confidence s+b b level, but a conservative pseudo-confidence level for the signal hypothesis. All exclusions discussed hereafter use CL and require it to be 5% for an exclusion confidence of 95%. s As using CL instead of CL is conservative, the rate of fake exclusions is ensured to s s+b be below 5% when CL is equal to 5%. s 3.2 Estimation of expected signal and background densities The expected signal and background densities, which are required to check the con- sistency of the data with the background and signal processes have two components: the overallnormalizationwhich setstheexpected ratesandtheProbabilityDensity Functions (PDF) of the additional discriminant information, if any. The expected background and signal rates were calculated from the number of simu- lated events passing the cuts. For the signal the efficiencies derived from simulations at given mass points had to be interpolated to estimate efficiencies at Higgs boson masses which were not simulated. In most cases this was done using one polynomial or if neces- sary two polynomials, one to describe the slow rise, and a second to handle the kinematic cut-off, which can be much more abrupt. For the cases where two signal masses must be allowed, a two-dimensional parameterization was used. The shapes of the PDFs were derived using histograms which are taken from the simulated events. In the case of two-dimensional PDFs these distributions were smoothed using a two-dimensional kernel, which consists of a Gaussian distribution with a small component of a longer tail [26]. The global covariance of the distribution was used to determine the relative scale factors of the two axes. The width of the kernel varied from point to point, such that the statistical error on the estimated background processes was constant at 20%. Finally multiplicative correction factors (each a one-dimensional distribution for one of the two dimensions of the PDF) were derived such that when projected ontoeither axisthePDFhasthesamedistributionaswouldhave beenobserved if it had been projected onto the axis first and then smoothed. This makes better use of the simulation statistics if there are features which are essentially one-dimensional, such as mass peaks. The error parameter fixed to 20% was an important choice. It was set by dividing the background simulation into two subsamples, generating a PDF with one and using the other to test for over-training by calculating the CL obtained from simulation b of background events. This should be 0.5 if the results are not to be biased, and a value of 20% for the error gave the closest approximation to 0.5 in all channels. Examples of smoothed two-dimensional PDFs are given in Fig. 3. 7 The signal simulations were made at fixed Higgs boson masses, but in order to test a continuous range of masses, interpolation software [27] was used to create signal PDFs at arbitrarymasses. Inthelast year ofoperation,LEP energywasvariedcontinuously while simulations were made at fixed beam energies. The same interpolation software was used to create signal and background PDFs at the correct centre-of-mass energies [1]. The interpolation was done by linearly interpolating the cumulative distributions taking as a parameter the signal mass or the centre-of-mass energy. The procedure has been tested over ranges up to 40 GeV/c2 in mass while the actual shifts in the simulations were up to 0.3 GeV in √s, and 5 GeV/c2 in mass for the hZ signals overall, but less than 0.5 GeV/c2 for Higgs boson masses between 113.5 and 116.5 GeV/c2. For the hA channels, the actual shifts were 5 GeV/c2 in either mass for Higgs boson masses between 80 and 95 GeV/c2 and up to 20 GeV/c2 elsewhere. Comparisons of simulated and interpolated distributions for a given mass were made in all channels and showed good agreement. 3.3 The case of non-independent channels When combining the results in all channels to derive confidence levels, only inde- pendent channels must be included, which requires some special treatment for a few non-independent cases. a) different signals - one analysis with mass hypothesis-independentselections analysis √s (GeV) signals added ref. ffh four-b 91 (bb¯h bb¯bb¯),(bb¯A bb¯bb¯), (hA bb¯bb¯) [21] ffh bb¯τ+τ− 91 (bb¯h → bb¯τ+τ−), (bb¯→A bb¯τ+τ−)→, (hA bb¯τ+τ−) [21] ffh four-τ 91 (τ+τ−→h τ+τ−τ+τ−),→(τ+τ−A τ+τ−τ→+τ−) [21] → → νν¯qq¯ 161-172 (h qq¯) (Z νν¯), (h AA) (Z νν¯) [17] τ+τ−qq¯ 189-208 (h → τ+τ−)→(Z qq¯), (→h qq¯) (Z→ τ+τ−), (hA τ+τ−qq¯) [19,20,1] → → → → → hZ four-jet 161-183 (h qq¯) (Z qq¯), (h AA) (Z qq¯) [17,18] hZ four-jet 192-208 (h → qq¯) (Z→ qq¯), (h→AA) (Z→ qq¯), (hA bb¯bb¯) [20,1] hA four-jet 161-172 (hA→ bb¯bb¯)→, (h AA→) A → → [17] hA four-jet 192-208 (hA → bb¯bb¯), (h→ qq¯) (Z qq¯) [20,1] four-b 189-208 (h →AA)A, (h →AA)Z, (h→A bb¯bb¯) [21] → → → b) different analyses - one final state final state √s (GeV) competing analyses ref. four-jet 91 bb¯bb¯, bb¯c¯c [14] multi-jet 91 three and four-jet analyses [21] νν¯qq¯ 192-208 low mass and high mass hZ analyses [1] 189-208 low mass and high mass flavour-blindanalyses [22] 189-208 hZ and flavour-blindanalyses [19,20,1,22] llqq¯,l=e,µ 189-208 hZ and flavour-blindanalyses [19,20,1,22] four-jet 192-208 low mass and high mass hZ analyses [1] 189-208 low mass and high mass hZ flavour-blindanalyses [22] 189-208 three and four-jet hA flavour-blindanalyses [22] 189-208 cscs and WAWA analyses [23] 189-208 hZ, hA, four-b, flavour-blind,c¯s¯cs and W∗AW∗A analyses [19,20,1,21–23] τν jet jet 189-208 csτντ and W∗Aτντ analyses [23] Table 2: a) list of signals from the two lightest Higgs bosons h and A treated by a single analysis: the signal expectations are combined (rates added, PDFs summed with weights according to the rates) prior to the confidence level calculations. b) list of different analyses of the same final state: only one analysis is selected at each point in the scans, based on the best expected performance for exclusion. In this Table, h and A denote any neutral Higgs boson allowed to be produced in the indicated production processes.