Search for the Higgs boson in events with isolated photons at LEP 2

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Transcript of Search for the Higgs boson in events with isolated photons at LEP 2

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN�EP������

�� April ����

Search for the Higgs boson in events

with isolated photons at LEP II

DELPHI Collaboration

Abstract

A search for the Higgs boson in �nal states with one� two or three isolatedphotons has been performed based on data taken at LEP II by the DELPHIdetector The data analysed correspond to a total integrated luminosity of ��pb�� at centre�of�mass energies of GeV ��� pb���� �� GeV � � pb��� and �� GeV ���� pb��� No evidence for the processes e�e� � H� with H � b�bor �� and e�e� � Hq�q with H � �� was observed Model�independentlimits on ��e�e� � H�� �BR�H � b�b�� ��e�e� � Hq�q��BR�H � ��� and��e�e� � H���BR�H � ��� are set� as well as model�dependent limits onHiggs boson anomalous couplings to vector bosons

�Submitted to Physics Letters B�

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�Department of Physics and Astronomy� Iowa State University� Ames IA ������� USA�Physics Department� Univ� Instelling Antwerpen� Universiteitsplein �� BE� �� Wilrijk� Belgiumand IIHE� ULB�VUB� Pleinlaan � BE�� Brussels� Belgiumand Facult�e des Sciences� Univ� de l�Etat Mons� Av� Maistriau ��� BE�� Mons� Belgium�Physics Laboratory� University of Athens� Solonos Str� ��� GR���� Athens� Greece�Department of Physics� University of Bergen� All�egaten � NO�� Bergen� Norway�Dipartimento di Fisica� Universit�a di Bologna and INFN� Via Irnerio ��� IT��� � Bologna� Italy�Centro Brasileiro de Pesquisas F��sicas� rua Xavier Sigaud �� BR� � Rio de Janeiro� Braziland Depto� de F��sica� Pont� Univ� Cat�olica� C�P� ���� BR� �� Rio de Janeiro� Braziland Inst� de F��sica� Univ� Estadual do Rio de Janeiro� rua S�ao Francisco Xavier �� Rio de Janeiro� Brazil�Comenius University� Faculty of Mathematics and Physics� Mlynska Dolina� SK��� � Bratislava� SlovakiaColl�ege de France� Lab� de Physique Corpusculaire� IN P��CNRS� FR�� �� Paris Cedex � FranceCERN� CH�� �� Geneva �� Switzerland��Institut de Recherches Subatomiques� IN P� � CNRS�ULP � BP � FR����� Strasbourg Cedex� France��Institute of Nuclear Physics� N�C�S�R� Demokritos� P�O� Box � �� GR���� Athens� Greece��FZU� Inst� of Phys� of the C�A�S� High Energy Physics Division� Na Slovance � CZ��� �� Praha �� Czech Republic��Dipartimento di Fisica� Universit�a di Genova and INFN� Via Dodecaneso ��� IT������ Genova� Italy��Institut des Sciences Nucl�eaires� IN P��CNRS� Universit�e de Grenoble �� FR��� � Grenoble Cedex� France��Helsinki Institute of Physics� HIP� P�O� Box �� FI��� Helsinki� Finland��Joint Institute for Nuclear Research� Dubna� Head Post O�ce� P�O� Box ��� RU��� Moscow� Russian Federation��Institut f�ur Experimentelle Kernphysik� Universit�at Karlsruhe� Postfach ���� DE���� � Karlsruhe� Germany�Institute of Nuclear Physics and University of Mining and Metalurgy� Ul� Kawiory �a� PL�� Krakow� Poland�Universit�e de Paris�Sud� Lab� de l�Acc�el�erateur Lin�eaire� IN P��CNRS� B�at� � FR���� Orsay Cedex� France��School of Physics and Chemistry� University of Lancaster� Lancaster LA� �YB� UK��LIP� IST� FCUL � Av� Elias Garcia� ����o� PT�� Lisboa Codex� Portugal��Department of Physics� University of Liverpool� P�O� Box ���� Liverpool L�� �BX� UK��LPNHE� IN P��CNRS� Univ� Paris VI et VII� Tour �� �RdC�� � place Jussieu� FR�� Paris Cedex � France��Department of Physics� University of Lund� S�olvegatan ��� SE� � �� Lund� Sweden��Universit�e Claude Bernard de Lyon� IPNL� IN P��CNRS� FR���� Villeurbanne Cedex� France��Univ� d�Aix � Marseille II � CPP� IN P��CNRS� FR��� �� Marseille Cedex �� France��Dipartimento di Fisica� Universit�a di Milano and INFN� Via Celoria ��� IT� ��� Milan� Italy�Niels Bohr Institute� Blegdamsvej ��� DK� � Copenhagen �� Denmark�NC� Nuclear Centre of MFF� Charles University� Areal MFF� V Holesovickach � CZ��� � Praha �� Czech Republic��NIKHEF� Postbus ���� � NL��� DB Amsterdam� The Netherlands��National Technical University� Physics Department� Zografou Campus� GR����� Athens� Greece��Physics Department� University of Oslo� Blindern� NO�� Oslo �� Norway��Dpto� Fisica� Univ� Oviedo� Avda� Calvo Sotelo s�n� ES���� Oviedo� Spain��Department of Physics� University of Oxford� Keble Road� Oxford OX� �RH� UK��Dipartimento di Fisica� Universit�a di Padova and INFN� Via Marzolo �� IT����� Padua� Italy��Rutherford Appleton Laboratory� Chilton� Didcot OX�� OQX� UK��Dipartimento di Fisica� Universit�a di Roma II and INFN� Tor Vergata� IT���� Rome� Italy�Dipartimento di Fisica� Universit�a di Roma III and INFN� Via della Vasca Navale ��� IT���� Rome� Italy�DAPNIA�Service de Physique des Particules� CEA�Saclay� FR������ Gif�sur�Yvette Cedex� France��Instituto de Fisica de Cantabria �CSIC�UC�� Avda� los Castros s�n� ES���� Santander� Spain��Dipartimento di Fisica� Universit�a degli Studi di Roma La Sapienza� Piazzale Aldo Moro � IT��� Rome� Italy��Inst� for High Energy Physics� Serpukov P�O� Box �� Protvino� �Moscow Region�� Russian Federation��J� Stefan Institute� Jamova ��� SI�� Ljubljana� Slovenia and Laboratory for Astroparticle Physics�

Nova Gorica Polytechnic� Kostanjeviska ��a� SI� Nova Gorica� Slovenia�and Department of Physics� University of Ljubljana� SI�� Ljubljana� Slovenia

��Fysikum� Stockholm University� Box ���� SE���� � Stockholm� Sweden��Dipartimento di Fisica Sperimentale� Universit�a di Torino and INFN� Via P� Giuria �� IT��� Turin� Italy��Dipartimento di Fisica� Universit�a di Trieste and INFN� Via A� Valerio � IT���� � Trieste� Italy

and Istituto di Fisica� Universit�a di Udine� IT���� Udine� Italy��Univ� Federal do Rio de Janeiro� C�P� �� � Cidade Univ�� Ilha do Fund�ao BR� ������ Rio de Janeiro� Brazil�Department of Radiation Sciences� University of Uppsala� P�O� Box �� SE��� � Uppsala� Sweden�IFIC� Valencia�CSIC� and D�F�A�M�N�� U� de Valencia� Avda� Dr� Moliner � ES���� Burjassot �Valencia�� Spain��Institut f�ur Hochenergiephysik� �Osterr� Akad� d� Wissensch�� Nikolsdorfergasse ��� AT�� Vienna� Austria��Inst� Nuclear Studies and University of Warsaw� Ul� Hoza ��� PL���� Warsaw� Poland��Fachbereich Physik� University of Wuppertal� Postfach � � �� DE�� �� Wuppertal� Germany��On leave of absence from IHEP Serpukhov��Now at University of Florida

� Introduction

The Standard Model �SM� has been successful in describing the interactions betweenthe gauge bosons and the fermions Direct tests of the self�interactions of the electroweakgauge bosons are being carried out at LEP II and the Tevatron and no deviations fromthe SM have been observed so far In the symmetry breaking sector the picture is quitedi�erent There is no direct experimental evidence for the couplings of the gauge bosonsto the Higgs boson and extensions of the symmetry breaking sector of the SM are stillpossible These extensions can be described in terms of an e�ective Lagrangian density�which could give rise to anomalous H�� and HZ� couplings � �In the SM the HZ� and H�� vertices do not exist The Z���� �H� and H� �� pro�

cesses must involve charged particle loops and therefore the corresponding cross�sectionsare tiny For example� in the SM the total cross�section for e�e� � H� at LEP II energiesvaries from �� to ��� fb for the Higgs boson�s mass in the range �� � MH � �� GeV�c

������ and the branching ratio BR�H� ��� is of order ��� ��� The presence of new par�ticles in the loops �as predicted� for instance� in the Minimal Supersymmetric StandardModel� would not increase the strength of the couplings by more than a factor of three���� On the other hand� the existence of anomalous HZ� and H�� couplings in theframework of the Standard Model symmetry group could result in the enhancement ofthe e�e� � H� cross�section and of the H � �� decay rate by two or three orders ofmagnitude � ���� thus allowing these processes to be detectable at LEP IIA search for a Higgs boson in �nal states with one� two or three isolated pho�

tons has been performed on the data taken at LEP II by the DELPHI detectorMore precisely� the topologies investigated correspond to the processes e�e� � H�with H � b�b or �� and to the process e�e� � Hq�q with H � �� The num�ber of candidates found are compatible with the background expectation Model�independent limits on ��e�e� � H�� �BR�H � b�b�� ��e�e� � Hq�q��BR�H � ���and ��e�e� � H�� �BR�H � ��� are set Although these processes are highly sup�pressed in the SM� they can be used to search for anomalous couplings of the Higgsboson to photons and to the Z � ��� This study was also carried outThe data were taken at centre�of�mass energies of GeV� �� GeV� and �� GeV

with integrated luminosities of �� pb��� � pb�� and ��� pb�� respectively The ef�fects of experimental resolution� both on the signals and on backgrounds� were stud�ied by generating Monte Carlo events for the possible signals and for the SM pro�cesses and passing them through the full DELPHI simulation chain Other limits on��e�e� � Hq�q��BR�H � ��� from a LEP experiment can be found in ��� A detaileddescription of the DELPHI detector and its performance can be found elsewhere ��� ��

� Production and decay of the Higgs boson

The Standard Model �SM� predicts the existence of one neutral Higgs boson H � �which is searched for at LEP Direct Higgs boson production in e�e� collisions is possible��gure �a��� but since the coupling of the Higgs boson to the fermions is proportionalto their squared masses � ��� this process has a very small cross�section Therefore� atLEP the Higgs boson has been mainly sought through the process e�e� � HZ� In theStandard Model for Higgs boson masses� MH � up to �� GeV�c � ��� the main H decayprocess is through b�b Several possible channels of Z� decay have been analysed and lowerlimits for MH have been set by the LEP collaborations � ��

Although suppressed in the framework of the SM� �nal states with one� two or threephotons have been proposed as possible clear signatures for the discovery of the Higgsboson ����� These �nal states can occur through�

e�e� � H� � b�b� � �

e�e� � Hq�q� ��q�q ���

e�e� � H� � ���� ���

In � � and ��� a mono�energetic photon recoils against the Higgs boson� giving riseto a resonance in the photon spectrum� albeit with a combinatorial background in ���The main background to process � � is Z� � q�q� In ��� the polar angle distributions ofthe two photons are mainly isotropic� while the main background consists of double ISRphotons in q�q events which have a forward peaked distribution Selection criteria on thepolar angle can thus be applied to separate the signal from the background Final statesfrom ��� are characterised by three energetic photons The QED background to thisprocess has at least one forward soft photon� which again provides a good discriminationbetween signal and backgroundWithin the Standard Model� reactions � �� ��� and ��� occur through W or charged

fermions loops The amplitude is dominated by the W loop contribution ��� and isnegligible for LEP energies and luminosities � ��� �� � A possible enhancement of theproduction and decay rates of the Higgs boson can be originated by anomalous couplingsof the Higgs boson to the vector bosons These interactions can be expressed in terms ofe�ective energy�dimension�six operators included in the interaction Lagrangian density� ��

Leff ��X

i��

fi� Oi� ���

where the Oi are the operators which represent the anomalous couplings� � is the typicalenergy scale of the interaction and fi are the constants which de�ne the strength of eachterm One of the anomalous operators in equation ��� contributes via the renormalizationof the Higgs wave function� giving rise to a common rescaling of all Higgs production anddecay rates � � � this constant factor was set to one The other six operators give rise tothe anomalous couplings H��� HZ�� HZZ and HWW� which can be written in the unitarygauge as � ����

LHV Veff � g

mW

� � � s �fBB � fWW � fBW �

�HA��A

�� ��m

W

g

f���c

HZ�Z�

�c fW � s fB

�c Z��Z

����H�� s�fBB � c�fWW � s c fBW�c

HZ��Z��

�s�fW � fB�

�cA��Z

����H� �s��s fBB � �c fWW � �c � s �fBW �

�cHA��Z

��

�fW��W�

��W�� �W�

��W������H� � fWWHW

���W

��� � � ���

where g � e �s � �m WGF �

p�� s�c��sin�cos�W � GF is the Fermi coupling constant�

mW the W boson�s mass� W the weak mixing angle and X�� � ��X� � ��X� withX � A�Z�W � the photon� Z and W �elds respectively

The most remarkable feature of the e�ective Lagrangian is the existence of direct HZ�and H�� couplings� resulting in possible large deviations from the SM cross�sections ofthe studied processes The production of the Higgs boson associated with photons wouldthen increase and H � ��� which has a very small branching ratio in the SM� might evenbecome the dominant decay A large enhancement of the Z�� H� decay width wouldmean that the fi

�� coe�cients were of the order � � �� TeV � On the other hand� the introduction of Leff ��� as an extension to the SM Lagrangian

will also contribute to other processes besides the Higgs boson interactions� namely togauge boson self�interactions � � Therefore� some of the fi

�� coe�cients are already boundby precise measurements of the SM parameters The coe�cient f��� would contribute to achange of the Z mass and fBW would change theW ��B mixing and are thus bound by lowenergy experiments with typical values of O��� � TeV � � � �� The coe�cients fB andfW contribute to the Trilinear Gauge boson Couplings �TGC�� but these measurementsstill allow values of O� �� TeV � � The remaining coe�cients have no tight restrictionsTherefore� in what follows� the f��� and fBW coe�cients will be taken as zero� and onlyfB� fW � fBB and fWW will be consideredThe Higgs boson production and decay processes where anomalous HZ�� HZZ and H��

couplings are present at tree level� giving �nal states with one� two or three photons aredisplayed in �gures �b� to �e� However� process �e� will not be taken into account inthe present analyses� since it is negligible in most of the parameter space when comparedto process �c�Possible signals for processes � �� ��� and ��� were simulated using the PYTHIA gen�

erator � �� Events were generated at a set of possible Higgs boson masses� ranging from� to �� GeV�c The interpretation of the results requires the computation of the cross�sections as a

function of the anomalous couplings� fi�� � as well as of MH �Higgs boson mass� TheCompHEP package was used for this calculation � �� All the new interactions wereincorporated in the generator by the use of the LanHEP code ���� In a scenario wherethe anomalous contributions to the cross�section are important� the Higgs boson widthdepends on the fi values and must be supplied to CompHEP The computation of theHiggs boson width was taken from � � and �� � and includes the interference between theSM model contribution and the new anomalous diagrams In theMH range studied �from� to �� GeV�c �� decays of the Higgs boson into ZZ� or WW� are important � � andtheir contribution was taken into account �� � The Higgs boson width increases for highervalues of the Higgs mass and for increasing absolute values of the anomalous couplingsIt ranges from a few MeV up to hundreds of MeV� never reaching the experimentalMH

resolution for the range of Higgs masses and couplings consideredThe main background to processes � � and ��� are Z � q�q with initial and �nal state

radiation For process ��� the main background is the QED process e�e� � ��� Allthe other relevant SM processes were also consideredBhabha events were generated with the Berends�Hollik and Kleiss generator ����� while

e�e� � Z� events were generated with PYTHIA � �� PYTHIA was also used for thefollowing processes� e�e� � WW � e�e� �We� e�e� � ZZ� and e�e� � Zee In allfour�fermion channels� studies with the EXCALIBUR generator ���� were also performedThe two�photon ������ physics events were generated according to the TWOGAM ����generator for quark channels and to the Berends� Daverveldt and Kleiss generator ����for the Quark Parton Model giving hadrons Compton events were generated accordingto ���� and e�e� � ��� events according to ����

� Event selection

Charged particles were considered only if they had momentum greater than � GeV�cand impact parameters in the transverse plane and in the beam direction below � cm and � cm� respectively Energy depositions in the calorimeters unassociated to chargedparticle tracks were required to be above � GeVNeutral clusters were classi�ed as isolated photons if the total energy inside a double

cone centered around the cluster with half angles of �� and ��� was less than GeV andif there were no charged particles above ��� GeV�c inside the inner cone The energy ofthe isolated photons was then reevaluated as the sum of the energies of all the particlesinside the inner coneThe �nal state topologies under study are characterized by the presence of jets and

photons and the absence of isolated leptons Therefore� the identi�cation of isolatedcharged particles is of importance for vetoing isolated leptons The algorithm used toidentify isolated charged particles demanded that inside a double cone centered on thetrack� with internal and external half angles of �� and ���� the total charged energy wasless than GeV and the total neutral energy was less than � GeV The energy of theparticle was rede�ned as the sum of the energies of all the charged and neutral particlesinside the inner cone and required to be greater than � GeVFor the topology with three photons� no charged tracks were allowed in the event �no

converted photons were recovered�� the visible energy in the polar angle region between��� and �� was required to be above ��

ps� and the minimum energy of each photon

was required to be � GeV Whenever more than � GeV of hadronic energy was associatedto a photon� at least �� of it had to be in the �rst layer of the Hadronic Calorimeter�HCAL�Hadronic topologies �b�b� and q�q���� required that at least six charged tracks were

present as well as one or two electromagnetic clusters with energy greater than � GeVand visible energy in the polar angle region between ��� and �� above ���

ps� including

at least one charged particle with an energy greater than � GeV No isolated chargedparticles were allowed A protection against fake photons was set by requiring less than GeV in the HCAL and no High Density Projection Chamber �HPC� layer with morethan �� of the photon electromagnetic energy Alternatively an energy deposition inthe hadronic calorimeter was allowed if at least �� was in the �rst layerAll selected charged particles and neutrals not associated to photons were forced to

be clustered into jets using the DURHAM jet algorithm ���� The algorithm was appliedthree times� requiring a de�ned number of jets� Njets � � �� � The values of the resolutionvariable at each transition� ycut�Njets���Njets�� characterize the event topologyThe hadronic �nal states searched for are well de�ned � jet topologies Therefore�

events with a clear monojet or � jet signature were excluded by constraining the resolutionvariables ycut� ��� to be greater than ���� and ycut��� � to be smaller than �� Eventswith � jets �and photons� were preselected if the jets had polar angle in the range ��� � �� and momentum greater than GeV�cThe analyses were optimized for each topology and selection levels were established

Selection level corresponds to adding topological requirements to the above set of se�lection criteria After selection level � speci�c selection criteria were applied to thepreselected samples corresponding to selection level � Selection level � is exclusively forthe b�b� topology and consists of tagging the b quarksThese selection criteria are described in subsections � � �� and �� for the b�b�� q�q��

and ��� �nal states respectively The comparison between the number of events found

in data and the Monte Carlo expectation for the various topologies and for the di�erentselection levels is displayed in table The average signal selection e�ciency correspond�ing to the last selection level for each searched topology is displayed in table � for thethree centre�of�mass energy values

selection levelps�GeV � topology � �

b�b� � � ����� �� �� ��� � ��� � q�q�� �� � �� � � ������� �

��� �� ��� � ����� � �

b�b� �� � ����� �� ����� � �� � �� q�q�� � � �� � � � ����� �

��� � ���� � ����� � �

b�b� � � �� ���� � � � ��� � ������ �� q�q�� �� ������ � ��� � �

��� �� �� ���� ������� �

Table � Number of events passing the sets of cuts corresponding to the selection levelsdescribed in the text for each topology and centre�of�mass energy The MC predictednumbers of events and their statistical errors� are displayed within parentheses Selectionlevel � applies only to the b�b� topology

ps�GeV� �� ��

topology b�b� q�q�� ��� b�b� q�q�� ��� b�b� q�q�� ���� �� �� �� �� �� �� �� � ��

Table �� Average signal selection e�ciencies at the �nal selection level for the threesearched topologies and for the di�erent centre�of�mass energy values

An important contribution to the signal selection e�ciencies comes from the photonreconstruction e�ciency The ����� QED simulation was used to perform a systematicstudy of the e�ciency of the isolated photon reconstruction algorithm described previ�ously This e�ciency was found to be �� in the barrel region �polar angle between��� and ���� of DELPHI and �� in the part of the forward region considered in theanalyses �polar angle between ��� and ��� or between ��� and ����The presence of matter in front of the electromagnetic calorimeters is a source of a

non�negligible photon conversion rate The probability that a photon would convert inthe tracking detectors and be reconstructed was evaluated for the polar angle regionsconsidered in the analyses This was done using both a �� sample selected from the ��GeV data and the respective ����� QED full simulation Within statistics� a reasonableagreement between data and simulation was found The systematic uncertainty due tothe material description in the simulation was found to be negligible compared to thatfrom data statistics

��� Events with one photon and two jets

Selection criteria were implemented to identify events with two jets and only oneisolated photon Candidates were required to have the isolated photon with polar anglebetween �� and ��� �level �After these cuts the following selection criteria were applied to the data

� photon angle to the nearest jet direction� greater than ���!� photon momentum greater than �� GeV�c!� photon polar angle between ��� and ���In order to improve momentum and energy resolution� a three body kinematic �t ����

imposing total energy and momentum conservation was performed on the selected eventsOnly events with a � per degree of freedom lower than � were accepted �level ��! thejet�jet e�ective mass resolution was then � GeV�c Figure ��a� shows the jet�jet invariant mass distribution at �� GeV after the kinematic

�t The peak of the radiative return to the Z is reconstructed with a good resolutionThe mass distribution of a simulated signal at �� GeV�c is also shownThe main decay channel for the Higgs boson in the studied mass range is through b�b

In order to reduce the q�q� background� event "avour tagging was performed based onthe identi�cation of the �nal state quark The b�tagging probability is shown in �gure��b� for the �� GeV data� for the expected background and for a simulated Higgs signalof �� GeV�c Events with a high probability of containing a b quark �b�tag variable�as de�ned in references � �� and ����� lower than ��� � were accepted �level �� Thee�ciency for this b�tagging selection was �� and the purity of the data sample wasestimated to be �

��� Events with two photons and two jets

Selection criteria were used to identify events with two jets and two isolated photons�level � A four body kinematic �t ���� was performed on the selected sample imposingtotal energy and momentum conservation Only events with � per degree of freedom lessthan � were accepted corresponding to a mass resolution of � GeV for the Higgs signalThe �� and jet�jet invariant mass distributions after this �t at

ps � �� GeV are

displayed in �gure � The corresponding reconstructed mass spectrum for a �� GeV�c

Higgs boson signal is also shown After the �t the following cuts were imposed �level ���

� �tted photon polar angles between ��� and �� !� angle between photons greater than ���

��� Events with three photons

Selection criteria were implemented to identify events with three isolated photonsEach of the photon candidates was required to ful�ll the following criteria�

� There could not be any Vertex Detector �VD� track element pointing to the photonwithin �� ��� in azimuthal angle in the barrel �forward� region of DELPHI �a VDtrack element was de�ned as at least two hits in di�erent VD layers aligned withinan azimuthal angle interval of ����

� If the photon candidate was located inside the FEMC �Forward ElectroMagneticCalorimeter��

� Its polar angle had to be greater than ��� and less than ��� or greater than ���

and less than ���!� Its associated hadronic energy had to be less than � of its total depositedenergy

� If the photon candidate was inside the HPC then �� Its polar angle had to be greater than ��� and less than ��� or greater than ���

and less than ���!� If its azimuthal angle lay outside the inter�modular divisions �� there had to beat least three HPC layers with more than � of the total electromagnetic energyof the photon candidate

The preselected ��� sample�level � consisted of events with at least two photons ful�llingthe above criteria Moreover� the two most energetic photons had to have energies above � of the collision energy and to be separated by more than ���The preselected samples correspond to a broad selection of ����� QED events A

dedicated analysis of this process including the � �� and �� GeV data sets can befound in �� �The second level of the event selection consisted in demanding a third photon �within

the above conditions� with energy above of the collision energy The energies can berescaled by imposing energy and momentum conservation and using the measured polarand azimuthal angles The compatibility of the momenta calculated from the angleswith the measured momenta was quanti�ed on a � basis After the event selection� athree�body kinematic �t ���� was applied to the data sample and all selected events werefound to be compatible with a � � � The invariant masses of the photon pairs werereevaluated using the �tted energy values The mass resolution for the Higgs signal afterthe kinematic �t was found to be GeV�c

� Results

From the results in table � according to the SM� no evidence for unexpected phe�nomena has been found Model�independent limits at �� Con�dence Level �CL� onthe cross�sections were derived for the di�erent topologies studied at the centre�of�massenergies of GeV� �� GeV and �� GeV The limits were obtained using a Poisson dis�tribution with background ���� and taking into account the mass resolution informationfor each topologyThe �� CL upper limits on ��e�e� � H���BR�H � b�b�� ��e�e� � Hq�q� �

BR�H � ��� and ��e�e� � H�� �BR�H � ��� are displayed in �gure � �a�� �b� and�c� respectively The limits obtained depend on the e�ciency for the detection of the �nalstate particles For Higgs boson masses above the kinematic limit� the cross�sections cor�respond to the production of a virtual Higgs boson For this reason the signal e�ciencydoes not drop to zero at threshold Nevertheless� when the model�independent limits areconverted into a speci�ed model� limits obtained for masses above the threshold will be

�mod������ � ���� ���� for more details see ���!

�The �� parameter was de�ned as �� � �

Pi����

�pcalci

�pmeas

i

�i

��

pmeasi are the measured momenta or energies and

pcalci

are the momenta calculated from the kinematic constraints� �i� is de�ned in reference � ! for the three photontopology�

much weaker since the Higgs production cross�section would have to be very large for itsvirtual states to be seenLimits on the anomalous couplings were computed for a centre�of�mass energy of

�� GeV They were set assuming three di�erent scenarios�In the �rst scenario each fi parameter was considered independently by setting all

the others to zero Limits on each fi�� parameter were set as a function of the Higgsboson�s mass ��gure �� The ��� analysis contributes to set exclusion limits on the valuesof jfBB�� j and jfWW �� j for Higgs boson masses up to �� GeV�c The q�q�� analysisleads to tighter limits on fBB for massesMH up to �� GeV�c The b�b� cross�section hasa weak dependence on fBB and fWW and the analysis of this process does not improvethe limits on these two parametersWhen fBB and fWW are zero� H � �� has a negligible rate so the ��� and q�q��

processes do not contribute to set limits on other parameters In this case H � b�b is thedominant decay and limits on fB and fW may be obtained for MH up to �� GeV�c

��gures � �c� and �d��Also shown in �gure � �c� are the limits obtained on the anomalous TGC parameters

by the direct measurements of WW production ���� �dashed�dotted horizontal lines� Asmentioned in section �� fB�� and fW�� contribute also to the TGCs� and the resultingconstraints from the b�b� analysis give indirect limits on the deviations from the SMtrilinear gauge boson couplings vertices The anomalous WW� and WWZ dipole likecouplings and the WWZ charge like couplings are de�ned as�

#k �M

W

�fB � fW �

� � #kZ �

M W

�fB� tan W � fW �

� � #gZ� �

M Z

fW�

��

In the case in which only fB is di�erent from zero� #k is proportional to fB�� and#gZ� is zero� assumptions used in the TGC direct limit for #k In this case the limitobtained with the b�b� analysis improves the direct limit of massesMH up to �� GeV�c In the second scenario� all fi except fBB and fWW �which directly contribute to the

decay H � ��� were assumed to be negligible In this scenario� the derived �� CLcross�section upper limits were used to exclude regions in the fWW vs fBB plane Thecontour plots of the limits obtained from the b�b�� q�q�� and ��� analyses are displayedin �gure for MH � �� GeV�c and MH � �� GeV�c For MH � �� GeV�c �each �nal state contributes to exclude particular regions in the fWW vs fBB plane ForMH � �� GeV�c the limits derived using the ��� �nal state are clearly stronger thanthose from the hadronic �nal states analysisIn the third scenario the simplest assumption was made All fi�s have a strength of

the same order and are set to fi � F The q�q�� cross�section shows a clear asymmetrybetween positive and negative values of F�� � due to the interference between the anoma�lous and standard HZZ coupling ��gure �c�� For the other �nal states there is no suchinterference� as in the SM there is no tree�level vertex for the Higgs boson productionwith a photon For the b�b� the dependence on the F�� parameter is weaker since theanomalous coupling is only present in the production vertex In this scenario� limits onF�� as a function of the Higgs boson mass were derived ��gure �� Stronger constraintson F�� come from the three�photon analysis results� and are of the order � �� TeV�

for MH � �� GeV�c The q�q�� results improve the ��� limit if MH � �� GeV�c fornegative values of F If F is positive� the interference between anomalous and SM HZZ

couplings is destructive� therefore the limit obtained is not as strong The q�q�� cross�section decreases above MH � �� GeV�c � which corresponds to the kinematic limit forHZ production In the mass region analysed� the b�b� �nal state does not improve thelimits

� Summary

DELPHI data corresponding to integrated luminosities of ��� pb��� � pb�� and�� pb�� at the centre�of�mass energies of �� GeV� �� GeV and GeV respectivelyhave been analysed and a search for the Higgs boson in �nal states b�b�� q�q�� and ���performed No evidence of unexpected phenomena has been found Model�independentupper limits on the cross�sections of these processes were derived at �� CL as a functionof the Higgs mass The cross�section upper limits have been used to derive limits oncontributions from operators which could give rise to anomalous Higgs to gauge bosoncouplings and trilinear gauge boson couplings

Acknowledgements

We would like to thank JCRom$ao for very interesting and long discussions�SFNovaes for his cooperation in cross checking our results and VIlyin for his assis�tance in the use of the CompHEP and LanHEP packagesWe are greatly indebted to our technical collaborators� to the members of the CERN�SLDivision for the excellent performance of the LEP collider� and to the funding agenciesfor their support in building and operating the DELPHI detectorWe acknowledge in particular the support ofAustrian Federal Ministry of Science and Tra�cs� GZ �����III��a����FNRS�FWO� Belgium�FINEP� CNPq� CAPES� FUJB and FAPERJ� Brazil�Czech Ministry of Industry and Trade� GA CR ���������� and GA AVCR A � ��� �Danish Natural Research Council�Commission of the European Communities �DG XII��Direction des Sciences de la Mati%ere� CEA� France�Bundesministerium f&ur Bildung� Wissenschaft� Forschung und Technologie� Germany�General Secretariat for Research and Technology� Greece�National Science Foundation �NWO� and Foundation for Research on Matter �FOM��The Netherlands�Norwegian Research Council�State Committee for Scienti�c Research� Poland� �P��B�� �� �P��B��� andSPUB�P��� ������JNICT�Junta Nacional de Investiga'c$ao Cient()�ca e Tecnol(ogica� Portugal�Vedecka grantova agentura MS SR� Slovakia� Nr ���� ��� ���Ministry of Science and Technology of the Republic of Slovenia�CICYT� Spain� AEN�� and AEN�� � �The Swedish Natural Science Research Council�Particle Physics and Astronomy Research Council� UK�Department of Energy� USA� DE�FG�����ER��� �

��

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Figure �� �� CL limits on F�� as a function of the Higgs boson mass� from the �� GeV analysis The dotted line corresponds to the ��� and the dashed line to theq�q�� analysis