Searhes at LEP2 Latest Results
M. Begalli
InstitutodeFsia,UniversidadedoEstadodoRiode Janeiro, UERJ
RuaSFranisoXavier,524/3023-D,20559-900, Rio deJaneiro,RJ,Brasil
(member oftheDELPHICollaboration)
Reeivedon30Marh,2001
Searhes for theHiggs bosonof theStandard Modeland supersymmetrimodels havebeen
per-formed by the four LEP experiments in the data olleted over almost 12 years (August/1989
untilNovember/2000)atentre-of-massenergiesvaryingfrom91.2 GeVto209GeV.Anexessof
andidatesfor theproesse +
e !Z
!Z 0
H 0
wasfoundforHiggsmassesnear114GeV.
I Introdution
TheLEP(LargeEletron Positron)aelerator,plaed
at CERN, the European Laboratory for Partile
Physis, has suesfully delivered e +
e olisions with
energiesupto209GeVforalmost12years.
TheLEP ollider'sinitial energywashosento be
around 91 GeV, sothat in these ollisions a Z 0
par-tile would be produed. The theory of fundamental
partiles alled theStandard Model hasbeen ritially
tested by studying the reationand deay of the Z 0
.
Thesestudiesstillontinue. TheZ 0
isveryshort-lived,
so its presene has to be inferred from its
disintegra-tion fragments, whih may vary from twoto nearly a
hundred. Sine the end of 1995, LEP has moved on
from theZ 0
and entered itsseond phase. Its energy
wasdoubledtoallowthestudyoftheprodutionofthe
Z 0
Z 0
pairsandofW +
W pairs,theharged
ounter-parts oftheZ 0
,thusopeninganewdomainof
investi-gationsandStandardModeltests aswellasthesearh
for newpartiles, partiularlythe Higgsboson and/or
supersymmetri partiles.
II The experiments
FourexperimentswereplaedintheLEPring,namely
ALEPH, DELPHI, L3 and OPAL. They are general
purpose experiments. They have a silion vertex
de-tetor apable to reonstrut the deay of short lived
partilesliketheonesformedbythebquarks,a
trak-inghamberinordertoreonstrutthetrajetoryofall
hargedpartilesproduedinthee +
e ollisions,
ele-tromagneti andhadronialorimeters tomeasure the
energyoftheeletrons,photonsandhadrons,andmuon
hambers. Detailsofeahexperimentan befoundin
[1℄. Fig.1showsapiture of theDELPHI experiment
SineAugust1989,whentheystartedthedata
tak-ing,until November2000, when LEPwasstopped, an
integratedluminosityof2:5fb 1
wasolleted.
Figure1. TheDELPHIexperimentatLEP.
Luminosityisaveryusefullnumberin highenergy
physis. The number of events produed in a ertain
proessisgivenby
N=L
whereN isthenumberofevents, istherosssetion
ofthegivenproess and Lis theluminosity. To
mea-suretheLuminosityawellknown proessisused: the
Bhabhasattering , e +
e ! e +
e . Calorimeters are
plaedveryforwardineahofthedetetorsinorderto
registerboththeeletron andthepositron from these
interations. Sinethemomentumoftheeletron(and
thepositron)ismuhhigherthanitsmassthe
dieren-tialrosssetionintheentre-of-masssystemis
alu-latedtaking intoaountmanyordersin perturbation
perLEPexperiment. Onehasto notiethat although
theluminosity ispratiallythesamefortheZ 0
mass
peakandforthedatatakenduring year2000,therst
onemeansamuhhighernumberofeventsinewewere
atapeakof therosssetionfortheproesse +
e .
Fromthesevaluesweareabletopreditthenumber
ofexpetedeventsforanyproesswewantto study.
III Searhes
The searhes at LEP experiments are performed in a
verybroadway. Wetry to look everywhere, onsider
all the models and investigate eah hannel and eah
utuation. Inorderto getthehighestavailable
num-berofevents(orluminosity)the4experimentsombine
the results, disuss all the anomalies found by an
ex-periment andross-hektheanalysis gettingahigher
hanetondanewpartileifitwasproduedatLEP.
Diret searhesaredoneintheframeworkofa
spe-i model (supersymmetry or harged Higgs, for
ex-ample)lookingfortheexpetedsignal. Exessesinany
nalstatetopologyarealsostudiedsinetheywill
trig-ger new models. Indiret searhes take the Standard
Modelasthenullhypothesisandseeifthereare
devia-tions.
Inthispaperwewillpresentthesearhforthe
Stan-dard Model Higgs and for the Higgses predited by
theMSSM(MinimalSuperSymmetriModel). All
re-sults are taken from the presentations at the LEPC
(LEP Commitee)[2℄, from the publiations of the 4
experiments[3℄andreferenestherein.
IV The Standard Model Higgs
The theory of the Standard Model, SU(2)U(1),
de-sribesatthepermillleveltheouplingsofquarksand
leptonsto,Z 0
, W
and(to lessauray)thetriple
gauge verties: the gauge symmetry is indeed exat.
Yet the partiles are note degenerate in mass i.e. the
symmetry is broken in the masses: the symmetry is
spontaneouslybrokenviatheHiggsmehanism.
Theexistene oftheHiggsboson iswellsupported
by thedata onradiativeorretion but, whih isthe
valueofitsmass?
PreisiontestsoftheStandardModelhavereently
been performed by LEP, SLD and the Tevatron, at
FERMILAB(USA).Inthedatatherewasnosigniant
evidene for departure from theStandard Model with
preisionof theorder of 0.1% ([5℄), asan be seen in
Fig. 2.Fig. 3showsthe 2
tfortheombinationofall
thoseresultsforaHiggs massvarying between10and
1000GeV/ 2
. Thetheoryunertaintyisshownaswell
astheresultsfortwodierentvaluesof
hadrons . The
mass value already exluded by the direted searhes
performedat LEPis113,5 GeV.Thet resultsgivea
lowerlimitfortheHiggsmassofm(H)=62 +53
GeV= 2
andanupperlimitofm(H)=170GeV= 2
at95%
Con-deneLevel.
TheHiggsboson anbeproduedat LEPvia
Hig-gsstrahlungombinedwith gaugebosonfusion. Fig. 4
showsthe diagrams for these proesses. The plot for
the Higgsprodution rosssetion asafuntion ofits
mass is given in Fig.5. It is lear that at LEP
ener-gies the Higgsstrahlung plays the major ontribution
sine our mass reah is 115 GeV/ 2
. For suh values
of masstheHiggspredominantlydeayinto bquarks,
BR (H 0
!b
b)85%. Theseond mostprobable
de-ayhannelis theBR (H 0
! +
)8%. Fordata
takenabove200GeVthehannelsH 0
!W +
W and
H 0
!gg were alsostudied.
Figure2. PreisiontestsoftheStandardModel.
Figure3.The 2
tforallthetestsintheStandardModel
foraHiggsmassvaryingbetween10and1000GeV/ 2
.
IftheHiggswasproduedviae +
e !Z
!H 0
Z 0
we expet to have 3 topologiesfor an event having a
4 jets: 2 jets oming from the Z 0
! qq deay
andtheother2fromtheHiggsdeayinapairof
bquarksin the event. Eah jet omes from the
hadronizationofeahofthequarks. Suh
topol-ogyisthemostprobableone,itours60%ofthe
time.
2jets and missing energy: themissing energyis
duetothedeayZ 0
!andthe2jetsfromthe
Higgsdeay. Theprobabilityhereis19%.
2jetsand2leptons: hereZ 0
!e +
e ; +
giv-ingaverylearsignature,theHiggsproduesthe
2jets. Unfortunatelyitis thelessprobablease,
only6%.
WhentheHiggsdeaysinapairof leptonsthe
topologiesremainsthesame,onlythejetsoming
fromitsdeayshaveverylowmultipliity(1,3or
5hargedtraks).
Many hannels an have the same topology as a
Higgsevent. Inordertoredue thebakground,whih
is some orders ofmagnitude higher than thesignal, a
set of uts wasapplied by eah experiment to the
re-onstrutedevents.
e +
e ! qq and e +
e ! Z 0
are the dominant
bakgroundbut easyto redueonewetakeinto
aountthehermetiityofthedetetors.
e +
e ! e +
e Z 0
and e +
e ! e
W
is
re-dued by analysing the missing momentum and
themissingenergyoftheevent.
speial are is needed with 4-fermion, e +
e !
Z 0
Z 0
and e +
e !Z 0
gg events, whereg stands
forgluon. Inthis ase, agood mass
reonstru-tionisneededbothfortheZ 0
andfortheHiggs.
e +
e ! W
+
W is an irreduible bakground
for thestudies of the harged Higgs prodution,
e +
e !H +
H .
e +
e ! Z
0
Z 0
is an irreduible bakground
for the Standard Model and the
supersymmet-ri Higgs searh, namely e +
e ! Z
0
H 0
and
e +
e !h 0
A 0
.
Figure 4. The diagrams for the prodution of the Higgs
bosonat LEP:Higgsstrahlungombinedwithgauge boson
Figure5.CrosssetionforHiggsbosonprodutionine +
e
ollisionsasafuntionofitsmass.
Figure 6. The dierent topologies of the events e +
e !
Z 0
H 0
.
Theb-taggingisthefundamentaltooltoreduethe
bakground. Combininga set of seletionuts, whih
inludesawellreonstrutedseondaryvertex
ompat-ible with the b-lifetime, it givesa veryaurate
iden-tiation of the b-deays. Fig. 7 shows the
distribu-tionsofthevariablesusedintheb-taggingbyDELPHI,
namelythelifetime,themassofthe seondaryvertex,
the fration of the harged energy, the missing
trans-verse momentum of the seondary vertex, the lepton
identiation and transverse momentum in ase of a
semi-leptonideayandthetrakrapidity. The
agree-mentobtainedbetweenreal data(RD)andtheMonte
Carlo(MC)is also shown. Fig. 10presentsalose-up
ofthevertexregionofadoubleb-taggedevent,aHiggs
andidate,foundbyL3.
Tolivewith the remaining bakgroundone has to
searh for an exess in the mass distribution for the
Higgsandidates. Fig. 8showsthereonstrutedHiggs
sele-They dier by asking a dierent value for the
rela-tionsignal/bakground(S/B).Sineitisimpossibleto
eliminateompletelythebakground,aneuralnetwork
and/or adisriminantlikelihood analysis wasused by
the4experimentsinordertogetabetteralulationof
theprobabilityofaneventtobesignalorbakground.
ThereforetherstplotinFig. 4wasdonebyrequiring
S=B = 0:3, the seond plot by requiring S=B = 1:0
and thethird S=B =2:0 at least. It means, an event
willneverbealledaHiggseventbut aandidatewith
highprobabilityto beaHiggs,ifthiswill bethease.
Oneansee that itis possibleto observeanexessof
thesignaloverthebakgroundifthemassoftheHiggs
bosonisoftheorderof115GeV/ 2
.
Figure7. Thedistributions ofthevariables usedinthe
b-taggingbyDELPHI.
Figure8. Distributionsofreonstrutedmass fortheloose
(S/B=0.3), medium (S/B=1.0) and tight (S/B=2.0)
sele-A. 2jetsand 2 leptonshannel
As it wassaid before, the topologywith 2 leptons
and 2 b-quarksis the leanestoneto be analysed. In
thisase, the2leptonsmustbewellidentied as
ele-tron, muon or tau, be well isolated from the jets (in
ordertoavoidthebakgroundfrome +
e !b
b()and
e +
e !()eventswherebothquarksdeay
semilep-tonialy), t a Z 0
mass and have2 jets tagged as b.
Speial are is taken for the ase with a pair of taus,
beause of the neutrinos originated in the tau lepton
deay. A good agreement between the data and the
expeted bakgroundwasfoundbythe4experiments,
showingnoevideneforaHiggsandidateinthis
topol-ogy.
B. 2jets and missingenergy hannel
Themainharateristisoftheseeventsisthe
miss-ingenergyoftheorderoftheZ 0
mass. Theb-jetsmust
be aoplanar, the missing momentum should never
pointtoarakinthedetetorandaspeialarewith
theZ 0
Z 0
produtionandthesymmetridouble
radia-tivereturn must be taken. In the double Z 0
produ-tiononeofthebosonsandeayin2neutrinosfakinga
andidateevent. Theproesse +
e !Z 0
isan
irre-duible bakground. DELPHIhas measuredthe ross
setionforitand,asanbeseenin Fig. 9,onlyfewof
thoseeventshavebothphotonsreonstruted. Inboth
asesagoodmeasurementofthetraksandof the
en-ergyinthealorimetersisneessaryin ordertoobtain
agood massreonstrution ofthe jets. A reoilt to
theZ 0
massisalwaysperformedinordertoutothe
Z 0
Z 0
events.
Figure9. Crosssetionsasafuntionoftheenterofmass
energymeasuredbyDELPHIfortheproesse +
e !Z 0
.
L3found1 andidateeventin this topologywhere
0.16bakgroundand 0.38signaleventswereexpeted.
bak-verylittlemissingmomentum,ompatiblewiththe
pro-dutionoftheHiggsandtheZ 0
nearlyatrest. The
visi-blemassis111GeV/ 2
. AssumingaZ 0
bosonreoiling
againsttheHiggs,thettedmassis114.4GeV/ 2
with
a resolution of3 GeV/ 2
. The event hasa high b-tag
value(probability). Onejethasaverylearseondary
vertex 7.3 mm from the primary, with a largevisible
mass.
Figure 10. The mostsigniant H 0
andidate foundby
C. 4jetshannel
Events are seleted outof thehadroni sample by
foringthem to have4jets and asking at least one of
them to beb-tagged. This already redues the qq(),
twophotoninterationandtheZ 0
bakground.
Us-ingthe DURHAM algorithm thejets areagain
reon-struted and the b-tagging is applyed giving a global
valuedened asthemaximumb-tag valuefor any
di-jet in the event, omputed as the sum of the
orre-spondingjetb-taggingvalues. ANeuralNetwork(NN)
ombiningdierentnumberofvariables(itdependson
theexperiment,DELPHI,forexample,uses13)isused
to further selet theevents. The rstvariable for the
NNisalwaystheglobalb-taggingvalueoftheevent.
Test of the kinematial ompatibility of the event
with the hypotheses of W +
W and Z
0
Z 0
pair-prodution are performed in either 4 or 5 jet
ong-urations. First,onstrained tsare used toderivethe
probabilitydensityfuntion measuringthe
ompatibil-ityoftheeventkinematis withtheprodutionoftwo
objetsofanymasses. Thistwo-dimensional
probabil-ity,theideogramprobabilityisthenfoldedwiththe
ex-petedmassdistributionforbothpair-prodution
pro-esses.
Furtherutsareperformedbyeahexperiment
de-pendingontheirpartiularanalysis. Thehoieofthe
Higgs dijet makes use of both the kinematial 5C-t
probabilitiesandtheb-tagginginformationintheevent.
Thelikelihoodpairingfuntion,
((1 P Z b P Z )P
j1 b P j2 b P j3 q P j4 q +P Z b ) P j 1 b P j 2 b P j 3 b P j 4 b +P Z ) P j 1 b P j 2 b P j 3 P j 4 )P
5C
3;4
isalulatedforeahofthesixpossibilitiestoombine
thejets j
1 ;j 2 ;j 3 ;j 4 with P ji b ;P j i ;P j i q
being the
prob-ability of getting the observed b-taggingvalue for the
jetj
i
whenoriginatingfrom ab, orlightquarks,
es-timatedfromsimulation. P Z
b
andP Z
arethehadroni
branhingratiosoftheZ 0
intob, quarksandP 5C
3;4 is
theprobabilityorrespondingtothekinematial5C-t
with the jets j
3 and j
4
assigned to the Z 0
.
Selet-ing the pairing ombination that maximizes this
fun-ion, the proportion of right mathings for the Higgs
di-jet, estimated in simulated signal events with 114
GeV/ 2
isabove 70%at thetight level, keeping alow
rate of wrong, ross-legged, pairings for Z 0
Z 0
bak-groundevents.
Three andidateswere foundbyALEPH. Therst
high purity andidate, shown in Fig.11, at a
entre-of-massenergyof 206.6GeVwasreonstrutedwitha
Higgsboson massof 110.0 GeV/ 2
. Threeof the four
jetsare wellb-tagged and theevent wasseleted as a
net-jetwithavalueof0.214isseletedasoneoftheHiggs
bosonjets. Theprobabilityforanyjetina4b eventto
havesuhalowb-taggingvalueis19%.
Figure11. Four-jetHiggs bosonandidatewithareonstrutedHiggs bosonmassof110.0 GeV/ 2
. Three ofthefourjets
arewellbtagged. Theeventisshownintheviewtransversetothebeamdiretionandinaloseupofthehargedpartiles
inthevertexregion.
Figure12. Four-jetHiggs bosonandidate withareonstrutedHiggs bosonmassof 112.9 GeV/ 2
. Allfour jetsare well
Figure 13. Four-jet Higgsboson andidatewitha reonstrutedHiggs bosonmass of112.9 GeV/ 2
. All fourjets arewell
btagged. Theeventis shownintheview transverse tothebeamdiretionand inaloseupofthehargedpartilesinthe
vertexregion.
As theeventis identied as a4b event,anyof the
sixpairingombinationsanbeonsideredin its
inter-pretation. ThepairingmostompatiblewiththeZ 0
Z 0
hypothesis,usingatinludingtheZ 0
bosonwidthand
massresolutions,giveslargettedZ 0
bosonmassesof
98.9GeV/ 2
and101.6GeV/ 2
.
Theseondhighpurityandidate,showninFig.12,
hasareonstrutedHiggsbosonmassof112.9GeV/ 2
.
All four jets in the event are well b-tagged with a
b-taggingneuralnetworksumof3.76. Themeasured
visi-bleenergyinthiseventis252GeV,whihismuhlarger
thanthatallowedbytheenergyresolutionofabout10
GeVforaneventwithaentre-of-massenergyof206.7
GeV. A 22 GeVeletromagneti showerwas deteted
in thesmallanglealorimeter(SICAL)in theplaneof
theaelerator. Asthereistoomuhreonstruted
en-ergy and the momentum imbalane is in the opposite
diretion to the22GeVenergy deposit,this showeris
most likely a beam-related partile, unrelated to the
rest of the event. Although the overlapping of suh
beam-relatedbakgroundis not frequent, the 22 GeV
of energy is onsistent with the observation in events
triggeredatrandombeamrossings.
Ifthislowangleenergydepositisremovedfromthe
event, the reonstruted Higgs boson mass inreases
from 112.9 GeV/ 2
to 114.5 GeV/ 2
. The neural
net-workforthiseventisstableandhangesfrom0.997to
0.998. As the reonstruted Higgs boson mass shifts
losetotheexess,thesignianeoftheexesswould
inreaseby0.2.
Even if the 22 GeV partile is removed from the
event, there is still an energy exess of 23.3 GeV
in-diating a mismeasurement of jet energy. Suh
mis-measurementis oftendueto fakeneutralhadrons,i.e.,
aharged partile. This auses double outing in the
omputation of the energy of the jet. Indeed, a
de-tailedinspetionofoneofthejetsshowsthata13GeV
neutralhadron is likely to havebeen misidentied. If
thisobjetisremovedfromthejetandtheHiggsboson
massreomputed,exluding atthe sametimethe low
angle (SICAL)objet, avalue of 114.2 GeV/ 2
is
ob-tained. The very small variationin the reonstruted
Higgsboson massours beausethettedmasses
de-pendmorestronglyonthemeasuredjetdiretionsthan
onthejetenergies.
As fortherstandidate, thebest bakground
ex-planationforthis eventis theZ 0
Z 0
hypothesiswitha
dierentjetpairing. TheZ 0
bosonmassesfromatfor
themostprobableZ 0
Z 0
pairinghoieare94.0GeV/ 2
and97.3GeV/ 2
.
The third high purityfour-jet andidate, shownin
Fig.13, at a entre-of-mass energy of 206.7 GeV/ 2
,
hasareonstrutedHiggsbosonmassof114.3GeV/ 2
.
BothoftheHiggsbosonjetsareverywellb-taggedwith
well measured displaed verties and neural network
values of 0.999. The 13.8 GeV/ missing momentum
in the event points to the middle of the Higgs boson
jetontaininganidentiedmuonomingfromthe
se-ondaryvertex,asshowninFig.13. Thisisastrong
in-diationthat,exeptfortheunmeasuredneutrinofrom
thesemileptonibquarkdeay,therest oftheeventis
wellmeasured. Thisisalsosupportedbythefatthat
the measuredinvariantmass of the two non b-tagged
jetsis 92.1 GeV/ 2
, onsistent with aZ 0
boson. The
measuredinvariantmass of the b-taggedjets and the
missingmomentumis114.4GeV/ 2
,whihrenders
un-likelytheZ 0
Z 0
thefourjets(37 o
),themostlikelybakground
explana-tionforthiseventistheb
bgghypothesis. Theminimum
jet-jetanglefortheb
bggbakgroundpeaksatlow
val-ueswith42%oftheeventshavingangleslessthan37 o
,
while 11%of the signalevents havesuh alow angle.
The twomeasured jet energies of the non b-jets, 43.5
GeVand49.0GeV,aretypial,however,forthedeay
ofaZ 0
bosonprodued nearlyatrest.
V Condene level estimation
ThemassisnottheonlyinformationwhihallowsHiggs
bosonprodutiontobedistinguishedfrombakground.
Additionalinformationistakenintoaountinthe
like-lihood ratio Q =L
s+b =L
b
, where L
b
is the likelihood
of the bakground hypothesis and L
s+b
is the
likeli-hoodwhenaspeiHiggsbosonsignalisaddedtothe
bakground. Thelikelihoodratiomeasuresthe
ompat-ibility oftheexperiment withapartiular signalmass
hypothesis. Thelikelihoodratiois traditionallyshown
intheform 2lnQbeauseiftherelationshipbetween
thelikelihood ratio and the 2
distributions,and also
due to the fat that when the logarithm is taken
in-dividual events ontribute as a sum of event weights
whihanbeexaminedindividually.
2lnQ=2ln exp
(s+b)
exp b
n
obs
Y
i=1 sf
s (
~
X
i )+bf
b (
~
X
i )
bf
b (
~
X
i )
2lnQ=2s 2 n
obs
X
i=1
ln(1+sf
s =bf
b )
heres stands forthe total number of signal and b for
bakground events expeted, f
s and f
b
are the
prob-ability densities that a signal or a bakground event
will befound inagivennal statewiththe setof
val-ues ~
X
i
whih inludes the reonstruted mass, the
b-tagging, the jet reonstrution algorithm, the missing
energy,theleptonpairseletionriteria,thequalityof
thetandsomeneuralnetworkanalysis(inaseitwas
used). Negletingthef
s
andthef
b
termsQissimply
the ratio of the Poisson probabilities to observe n
obs
events for the signal-plus-bakground hypotheses and
bakground-onlyhypotheses.
Noorrelation was foundexept betweenthe
neu-ralnetwork ALEPH analysis for the four-jets andthe
reonstrutedHiggsmassforboththebakgroundand
thesignaldistributions. The eetof this orrelations
was takenintoaount.
The ompatibility of an experiment with a given
hypothesis is determined from the expeted
distribu-tion of the likelihood ratio by alulating the
proba-bility of obtaining a likelihood ratio smaller than the
one observed. This probability, alled the ondene
level (CL), depends upon the hypothesized Higgs
bo-bakground-only hypotheses. If the hypothesis being
tested is true, then the distribution of possible
on-dene levels is equally distributed between 0 and 1,
with a median value of 0.5. A signal is expeted to
produeanexessrelativetotheexpetedbakground,
whihwouldappearasadipinthe1 CL
b
distribution,
where CL
b
istheondene levelfor the
bakground-onlyhypothesis.
A. Results
Fig.14givesthelog-likelihood,-2lnQ,asafuntion
of the Higgs mass. The blak region shows the 1
limitandthegrayregionthe2limitfortheexpeted
bakground. The urve (dotted) shows the expeted
signal+bakgrounddistributionforaHiggsmassof115
GeV/ 2
andthefullline theresultsobtainedfrom the
data.
Figure14. Thelog-likelihood,-2lnQ,as afuntionofthe
Higgs mass. Theblakregionshowsthe 1limit andthe
grayregionthe2limitfortheexpetedbakground. The
urve (dotted)shows theexpetedsignal+bakground
dis-tributionfor aHiggsmass of115GeV/ 2
andthefull line
theresultsobtainedfromthedata.
Fig.15showstheprobabilitydensityasafuntionof
log-likelihoodforeahexperiment,separately. The
ver-tial line showsthe valueof-2lnQ found in thedata,
the urve drawn in a full line the expeted
distribu-tionforthebakgroundandtheurveinabrokenline
theexpeteddistribution forthesignalofaHiggswith
mass 115 GeV/ 2
. As desribed before, ALEPH has
3 andidates, L3 has 1 andidate with a not so high
probability. OPALhasshownnoandidatewithahigh
probabilitybutombiningtheireventstheyalsoshowa
displaementofthedatainthediretionoftheexpeted
signal+bakgroundprobability distribution. DELPHI
hasno andidate. At theDELPHIolliding point the
beamshad an angle smaller than180 o
whih brought
an inertainty in the determination of the seondary
vertex of the b-deays. This unertainty was enough
exper-Figure 15. The probability density as a funtion of
log-likelihoodfortheeventsfoundbyeahofthe4experiments.
Thevertiallineshowsthevalueof-2lnQfoundinthedata,
the urvedrawninafull linetheexpeteddistributionfor
thebakgroundandtheurveinabrokenlinetheexpeted
distributionforthesignalofaHiggswithmass115GeV/ 2
.
Fig. 16 gives the same distributions for the
om-binedresultsofthe4experiments.
Fig. 17showsthe1 CL
b
distributionforthe
om-bineddatafromthe4LEPexperiments.
Figure 16. The probability density as a funtion of
log-likelihood for the ombined results of the 4 experiments.
The vertial line shows the value of -2 lnQ found in the
data, theurvedrawninafull line the expeted
distribu-tionfor thebakgroundand theurveinabrokenlinethe
expeted distributionfor the signal of a Higgs with mass
2
Figure17. 1-CL
b
as afuntionoftheHiggsmass. The
ex-peted 2, 3, and 4 limits are drawnin the gure. The
dashedlineinthe topshowstheexpetedbakground, the
urve(dotted)theexpetedsignal+bakgrounddistribution
foraHiggsmassof115GeV/ 2
andthefulllinetheresults
obtainedfromthedata.
It is learly seen that an exess of events was
ob-served, namely 2.9 away from the expeted
bak-ground. Althougit isnotenoughtolaimadisovery,
alimitfortheHiggs massat 95%CLanbesetat
m
H
>113:2GeV = 2
:
VI MSSM Neutral Higgs boson
Theanalysisis verysimilarto that doneforthe
Stan-dard Model Higgs, exept that now we searh for a
pair of neutral Higgs boson, h and A. Two
han-nels have been studied, e +
e ! h
0
A 0
! b
bb
b and
e +
e !h 0
A 0
! +
b
b,themostprobableones. The
jetseletion and reonstrution is thesameasfor the
standardHiggs analysis. The nal disrimination
be-tweenbakgroundandsignalisbasedona
multidimen-sionalvariablewhihombineseightvariablesinluding
b-tagging,anti-QCDvariables and theprodution
an-gleoftheHiggsbosonandidates. Theomparison
be-tweenthedataandthebakgroundsimulationshowsa
smallexessofeventsinthedata,allwith3b-jetswell
identied but they are totally ompatible with Z 0
Z 0
events.
A tighter ut in the likelihood of the Standard
Model Higgsanalysis forthehannel e +
e ! +
is needed in order to selet the e +
e ! h
0
A 0
!
+
b
bandidates. Noandidatewasfoundwhile0.25
areexpetedfrom StandardModel bakground,
keep-ingareasonableeÆieny forthesignal.
Theresultsare ombinedwith the samestatistial
methodasitwasfortheStandardModelHiggs. Inthe
MSSM,attreelevel,theprodutionross-setionsand
the Higgs branhing frations depend on twofree
pa-rameters,tan andoneHiggsbosonmass,or,
alterna-tively,twoHiggsbosonmasses,in generalm
A andm
byradiativeorretionswhihintrodueadditional
pa-rameters: themassoftheeletroweaksale,M
susy ,the
ommonSU(2)gauginomassterm 1
attheeletroweak
sale, M
2
, and the ommon squark trilinear oupling
at the eletroweaksale, A. The interpretation of the
experimentalresultsdependsonthevaluesassumedfor
theseparametersandalsoontheorderofthealulated
radiativeorretions[6℄.
The results presented here rely on leading-order
two-loop alulations of the radiative orretions in
the renormalization group approah[7℄, with reent
modiations[8℄. The values adopted for the
param-eters are: 175GeV/ 2
for thetopmass, 1TeV/ 2
for
M
susy
,200GeV/ 2
forM
2
and-200GeV/ 2
for,the
Higgsmixing parameterinthesuperpotential. Forthe
mixinginthestopsetorthem max
h
senarioandno
mix-ing were onsidered. Then asan overthe MSSM
pa-rameterstan andm
A
,inthem
A
rangeof20GeV/ 2
-1TeV/ 2
,andtan between0.5and30. Ateahpoint
of the parameter spae, the hZ and hA ross-setions
andtheHiggsbranhingfrationswereomputedwith
theHZHAprogram[9℄(version3).
Theresultstranslateinto regionsof theMSSM
pa-rameterspaeexludedat95%ondenelevelormore.
The exludedregions are presented in the (m
h ;tan)
andinthe(m
A
;tan)planeinFigs. 18and19,therst
forthe maximalm
h
and theseond fortheno mixing
ase. The(m
A ;m
h
) planeis presentedin Fig. 20. As
ilustrated in the latter, there is a small region of the
parameter spae where the deay h ! AA opens, in
whihaseitsuplantstheh!b
bdeay. Thisexplains
theunexludedholeattan=0:5andm
a
40GeV/ 2
inthenomixing senario. A sanforlargevaluesof
wasalsodone. Theresults,obtainedbyusingall
avail-ableLEP2data,areshowninthe(m
h
;tan)planeand
in the(m
A
;tan) plane in Fig. 21. In this ase, the
BR(h 0
!b
b)!0dueto largelooporretionsandthe
proesse +
e !h 0
A 0
is suppressed.
Figure 18. Theexludedregions ofthe MSSM parameter
spaeexludedat95%ondenelevelormoreforthe
max-imalm
h ase.
Figure 19. Theexluded regions of theMSSM parameter
spae exludedat95% ondenelevelor morefor the no
mixingase.
Figure 20. Theexludedregions of the m
A ;m
h
plane
ex-ludedat95%ondenelevelormore.
Figure 21. Theexluded regions of theMSSM parameter
spaeexludedat95%ondenelevelormoreforthesan
overlargevaluesof.
Finally,these resultsestablish95%ondenelevel
lowerlimits onm
h and m
A
, for either assumption on
themixinginthestopsetorandforallvaluesoftan
above0.6:
m
h
>89:9GeV= 2
m
A
>90:5GeV= 2
1
TheU(1)andSU(3)gauginomasstermsattheeletroweaksale,M
1 andM
3
,areassumedtoberelatedtoM
2
throughtheGUT
relationsM =(5=3)tan 2
M andM =( =)sin 2
Furthermore, there are exluded ranges in tan
be-tween 0.5 and 2.3 in the no mixing ase and between
0.9and7.7inthem max
h
senarioasanbeseeninFigs.
18and19.
VII Charged Higgs bosons
IntheMSSMtheH
isonstrainedtobeheavierthan
the W
. The sensitivity of the urrent searhes are
limitedatm
H <m
W
thenanysignalofH +
H would
indiate newphysisbeyond theMSSMoranextreme
set ofparametervalues.
ThehargedHiggsaneitherdeayin squarksor
. The branhing ratios are unknown. Speial are
is needed withthe H +
H ! hannel beause4
neutrinos will be present in the event. Angular uts
and a good identiation for the tauswere used. For
theH +
H !ss hannelenergy-momentum
onser-vation and equal di-jet masses were required. For all
hannels, inluding the semi-leptoni H +
H ! s
anti-b-tagging, WW and QCD uts were applied
tak-ing into aount the polarization, the aoplanarity
and event shape variables, - and s-tagging, and the
polarangles(totakeintoaountthespinoftheHiggs
bosonsprodued).
TheLEPHiggsworkinggrouphasfoundno
india-tion that the WW wall wasbrokenfor anybranhing
ratio of the Higgs deay setting a mass limit at 95%
ondene level
m
H
>80:8GeV= 2
BR ()=0
m
H
>87:7GeV= 2
BR ()=1
m
H
>77:4GeV= 2
anyBR ()
Fig. 22 shows the limits obtained in the plane
BR(H
!)versusthehargedHiggsmass.
Figure22. TheupperlimitforthehargedHiggsmassasa
funtion oftheBR(H
!
)at95%ondene.
VIII Non fermioni Higgs
ou-pling h !
IntheStandardModel andin theTwoHiggs Doublet
ModelweanproduetheHiggsviathehannels
e +
e !h 0
A 0
!A
0
!b
b
e +
e !h 0
A 0
!h 0
h 0
Z 0
!
e +
e !h 0
A 0
!A 0
A 0
A 0
!b
bb
bb
b
e +
e !h 0
Z 0
The h 0
! hannel has been searhedby the 4
experiments. Alltheinformationfromthe
eletromag-netialorimeters wereusedaswellasthehermetiity
andtheb-tagging. Thereonstruted massforthe
pair has shown a good agreement with the expeted
bakground. TheupperlimitasafuntionoftheHiggs
massisgivenin Fig.23.
Figure23. TheupperlimitasafuntionoftheHiggs mass
at95%ondenelevelfortheh 0
! searh.
IX The invisible Higgs
TheHiggsbosondeaysintotheheaviestkinematially
aessible partiles. In the MSSM it an deay into
invisiblespartiles,likethelightestneutralino 0
h 0
! 0
1
0
1
Ifthe 0
is purelyphotinothenthisproessis
sup-pressedand
h 0
! 0
0
;
0
! 0
Z 0
Thenalstateisthenharaterizedby2leptonsor
2jetsfromtheZ 0
plusmissingenergyandmomentum.
Whenthe Z 0
deaysinto apair of quarks,the
analy-sisisthesameasfortheH 0
hannelbutherethere
wasnoneedoftheb-tag. Themainbakgroundsome
from e +
e !qq(), W
e
andW +
W for thease
Z 0
!` +
` .
ALEPH,DELPHI andOPALombined theirdata
andfoundnosignalputtingalimitof107.6GeV/ 2
for
theHiggsmassat95%ondenelevel.
X Conlusions
LEP has had a very suessful running over almost
12years,opperatingatenergiesmuhaboveitsdesign
value. If LEPwould havereahed 7GeVmorein the
entre-of-mass energy than what it hasdelivered, the
MSSM would havebeenoveredompletely, although
strong onstraintshave been put (also from the
om-binedanalysisofthe4experiments):
m(h 0
);m(A 0
)>90:5GeV= 2
0:9>tan>2:3
m(H
)>77:4GeV= 2
m(LSP)>48GeV= 2
m(
)>104GeV
TheresultspresentedherewereshownattheLEPC
meeting atCERN onNovember3,2000andalso
pub-lishedbythe4experiments,asgivenin thereferenes.
More data, or results, from other experiments, rather
thantheLEPones,willbeneededtodeterminewether
the observations reported hereare theresult of a
sta-tistialutuationortherstsignofdiretprodution
oftheHiggsboson.
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