the LEP Electroweak Working Group + and the SLD Heavy Flavou

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

EUROPEANORGANIZATIONFORNUCLEARRESEARCH

CERN-EP-2000-016January21,2000

ACombinationofPreliminaryElectroweakMeasurementsandConstraintsontheStandardModel

TheLEPCollaborations ALEPH,DELPHI,L3,OPAL,

theLEPElectroweakWorkingGroup

andtheSLDHeavyFlavourandElectroweakGroups

PreparedfromContributionsoftheLEPandSLDexperiments

tothe1999Summerconferences.

Abstract

ThisnotepresentsacombinationofpublishedandpreliminaryelectroweakresultsfromthefourLEPcollaborationsandtheSLDcollaborationwhichwerepreparedforthe1999summerconfer-ences.Averagesarederivedforhadronicandleptoniccrosssections,theleptonicforward-backward

cpartialwidthsandforward-backwardasymmetries,theτpolarisationasymmetries,theb

asymmetriesandtheq

TheLEPCollaborationseachtakeresponsibilityforthepreliminarydataoftheirownexperiment.

D.Abbaneo,J.Alcaraz,P.Antilogus,P.Bambade,A.Barczyk,T.Behnke,G.Bella,A.Blondel,S.Blyth,D.Bourilkov,D.G.Charlton,R.Clare,P.deJong,G.Duckeck,M.Elsing,F.Filthaut,D.Glenzinski,M.W.Gr¨unewald,A.Gurtu,J.B.Hansen,R.Hawkings,J.Holt,R.W.L.Jones,T.Kawamoto,R.G.Kellogg,N.Kjaer,M.Kobel,http://n¸con,W.Lohmann,A.Macchiolo,C.Mariotti,M.Martinez,G.Martinez,C.Matteuzzi,M.N.Minard,J.Mnich,K.M¨onig,P.Molnar,S.Olshevski,U.Parzefall,Ch.Paus,M.Pepe-Altarelli,B.Pietrzyk,G.Quast,D.Reid,P.Renton,H.Rick,J.M.Roney,E.Sanchez,C.Sbarra,R.Sekulin,D.Strom,R.Tenchini,F.Teubert,M.A.Thomson,J.Timmermans,M.Verzocchi,H.Wahlen,C.P.Ward,N.K.Watson,P.S.Wells.

J.Brau,N.deGroot,P.C.Rowson,M.Swartz,D.Su.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

1Introduction

ThefourLEPexperimentshavepreviouslypresented[1]parametersderivedfromtheZresonanceusingpublishedandpreliminaryresultsbasedondatarecordeduntiltheendof1995.Sincethenadditionalresultshavebecomeavailable.Toallowaquickassessment,aboxhighlightingtheupdatesisgivenatthebeginningofeachsection.Since1996LEPhasrunatenergiesabovetheW-pairproductionthreshold.In1998thedeliveredluminositywassigni cantlyhigherthaninpreviousyears,andthustheknowledgeofthepropertiesoftheWboson,especiallyitsmass,hasbeensigni cantlyimproved.TheseresultsaredenotedasLEP-IIresults.

TheLEP-Idata(1990-1995)consistofthehadronicandleptoniccrosssections,theleptonic

cpartialwidthsandforward-backwardasymmetries,theτpolarisationasymmetries,theb

forward-backwardasymmetriesandtheqbandc

fproductionatenergiesabovetheZ;

Section4τpolarisation;

Section5ALRmeasurementatSLD;Section6Heavy avouranalyses;

Section7Inclusivehadronicchargeasymmetry;

Section8Wbosonproperties,includingmW,branchingratios,WWproductioncrosssectionsand

triple-gauge-bosoncouplings;Section9ZZproductioncrosssections;

Section10Interpretationoftheresults,includingthecombinationofresultsfromLEP,SLD,neu-trinointeractionexperimentsandfromCDFandDØ;Section11Prospectsforthefuture.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

2ZLineshapeandLeptonForward-BackwardAsymmetries

Updateswithrespecttolastsummer:

Allexperimentshaveupdatedtheirresults.ALEPHhavepresented nalvalues.Manyrecenttheo-reticaldevelopmentshavebeenincludedintheresultsand ts.

2.1ResultsfromtheZPeakData

TheresultspresentedherearebasedonthefullLEP-Idataset.Thisincludesthedatatakenduring

√

theenergyscansin1990and1991intherange1|

s mZ|<1.8GeV)andthe

peakrunningin1994.ThetotalstatisticsandthesystematicerrorsontheindividualanalysesofthefourLEPcollaborationsaregiveninTables1and2.DetailsoftheindividualanalysescanbefoundinReferences4–7.

q

’90-’91’93prel.’95prel.

+

’92’94prel.

total

77

75

202

66

500

343127

81

1724

ALEPH

433

630

1310

735

370536

58

79

657

526

406658

293

DELPHI

697

646

1585

2572

L3416

OPAL733

2600LEP1660

Table1:LEPstatisticsinunitsof103eventsusedfortheanalysisoftheZlineshapeandleptonforward-backwardasymmetries.

FortheaveragingofresultstheLEPexperimentsprovideastandardsetof9parametersdescribingtheinformationcontainedinhadronicandleptoniccrosssectionsandleptonicforward-backwardasymmetries[2,10].Theseparametersareconvenientfor ttingandaveragingsincetheyhavesmallcorrelations.Theyare:

ThemassandtotalwidthoftheZboson,wherethede nitionisbasedontheBreit-Wignerdenominator(s m2Z+isΓZ/mZ)(s-dependentwidth)[11]. ThehadronicpolecrosssectionofZexchange:

σh≡

12π

Γ2Z

.(1)

HereΓeeandΓhadarethepartialwidthsoftheZfordecaysintoelectronsandhadrons.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

’93

Lexp.(a)σhadσµAµFB

0.067%

0.069%

0.16%

0.11%

0.18%0.0012

0.0005

0.0007

’95

prel.

0.080%0.073%

0.46%

0.11%

0.60%0.0026

0.0005

0.0020

’94

prel.

0.09%0.11%

0.52%

0.26%

0.60%0.0020

0.0005

0.0020

’93

prel.

0.086%0.042%

0.17%

0.32%

0.65%0.0025

0.0008

0.0032

’95

prel.

0.068%0.042%

0.17%

0.40%

0.49%0.001

0.0015

0.0012

’94

prel.

0.033%0.073%

0.16

0.10%

0.480.001

0.0003

0.0012

Table2:ExperimentalsystematicerrorsfortheanalysisoftheZlineshapeandleptonforward-backwardasymmetriesattheZpeak.TheerrorsquoteddonotincludethecommonuncertaintyduetotheLEPenergycalibration.Thetreatmentofcorrelationsbetweentheerrorsfordi erentyearsisdescribedinReferences4–7.

addition,thereisatheoreticalerrorforthecalculationofthesmallangleBhabhacrosssectionof0.054%[8]forOPALandacommon0.06%fortheotherthreeexperiments[9];theOPALerrorhasbeentreatedasafullycorrelatedcomponentofthecommon0.06%error.

(a)In

Theratios:

HereΓµµandΓττarethepartialwidthsoftheZforthedecaysZ→µ+µ andZ→τ+τ .Duetothelargemassoftheτlepton,asmalldi erenceof0.2%isexpectedbetweenthevaluesforReandRµ,andthevalueforRτ,evenundertheassumptionofleptonuniversality[12].

0,τ0,µ,e+ + + + Thepoleasymmetries,A0FB,AFBandAFB,fortheprocessesee→ee,ee→µµand

e+e →τ+τ .Intermsoftherealpartsofthee ectivevectorandaxial-vectorneutralcurrentcouplingsoffermions,gVfandgAf,thepoleasymmetriesareexpressedas

,fA0FB≡

Re≡Γhad/Γee,Rµ≡Γhad/ΓµµandRτ≡Γhad/Γττ.

(2)

3

2+g2gVfAf

.(4)

Theimaginarypartsofthevectorandaxial-vectorcouplingconstantsaswellasrealandimaginary

partsofthephotonvacuumpolarisationaretakenintoaccountexplicitlyinthe ttingformulaeandare xedtotheirStandardModelvalues.The ttingproceduretakesintoaccounte ectsofinitial-stateradiation[11]toO(α3)[13–15],aswellast-channelands-tinterferencecontributionsinthecaseofe+e nalstates.

Thesetof9parametersdoesnotdescribehadronandlepton-pairproductioncompletely,becauseitdoesnotincludetheinterferenceofthes-channelZexchangewiththes-channelγexchange.Fortheresultspresentedinthissectionandusedintherestofthenote,theγ-exchangecontributionsandthehadronicγZinterferencetermsare xedtotheirStandardModelvalues.TheleptonicγZinterferencetermsareexpressedintermsofthee ectivecouplings.

Thefoursetsof9parametersprovidedbytheLEPexperimentsarepresentedinTable3.Thecovariancematrixoftheseparametersisconstructed[10,16]fromthecovariancematricesoftheindividualLEPexperimentsandcommonsystematicerrors[16].ThecommonsystematicerrorsincludetheoreticalerrorsaswellaserrorsarisingfromtheuncertaintyintheLEPbeamenergy.Thebeamenergycontributes1.7MeVtomZand1.2MeVtoΓZ[17].Inaddition,theuncertaintyinthe

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

centre-of-massenergyspreadofabout1MeV[18]contributes0.2MeVtoΓZ.Thetheoreticalerroroncalculationsofthesmall-angleBhabhacrosssectionis0.054%[8]forOPALand0.06%[9]forall

0.QEDradiation,dominatedotherexperiments,andresultsinthelargestsystematicuncertaintyonσh

byphotonradiationfromtheinitialstateelectrons,contributesanestimatedcommonuncertaintyof

0andof±0.5MeVonmandΓ,wherethelatteroneisdominatedbytheuncertaintyin±0.02%onσhZZ

fermionpairradiation.Thecontributionoft-channeldiagramsandthes-tinterferenceinZ→e+e leadstoanadditionaltheoreticaluncertaintyestimatedtobe±0.11%onReandto±0.0013on,eA0FB,whichare 100%correlated.Uncertaintiesfromthemodel-independentparameterisationoftheenergydependenceofthecrosssectionarealmostnegligible,ifthede nitionsofReference[19]areapplied.ThroughunavoidableStandardModelremnants,dominatedbytheneedto xtheγ-Zinterferencecontributionintheq

mZ(GeV)

0(nb)σh

ALEPH

91.1886±0.003141.558±0.057

DELPHI2.4870±0.0041

L3

91.1893±0.003041.536±0.055

OPAL2.4941±0.004120.905±0.085

20.88±0.12

20.800±0.056

20.84±0.13

0.0184±0.0034

0.0165±0.0025

0.0170±0.0028

0.0260±0.00470.0106±0.005820.860±0.097

Rµ

,eA0FB,τA0FB

20.834±0.0910.0154±0.0023

χ2/d.o.f.

mZ(GeV)

ΓZ(GeV)0(nb)σhReRµRτ

,eA0FB

,µA0FB

,τA0FB

AverageValue

91.1872±0.00212.4944±0.002441.544±0.03720.803±0.04920.786±0.03320.764±0.0450.0145±0.00240.0167±0.00130.0188±0.0017

Table4:AveragelineshapeandasymmetryparametersfromthedataofthefourLEPexperimentsgiveninTable3,withouttheassumptionofleptonuniversality.Theχ2/d.o.f.oftheaverageis32/27.Ifleptonuniversalityisassumed,thesetof9parametersgivenaboveisreducedtoasetof5parameters.R isde nedasR ≡Γhad/Γ ,whereΓ referstothepartialZwidthforthedecayintoapairofmasslesschargedleptons.ThedataofeachofthefourLEPexperimentsareconsistentwithleptonuniversality(thedi erenceinχ2overthedi erenceind.o.f.withandwithouttheassumptionofleptonuniversalityis4/4,5/4,5/4and2/4forALEPH,DELPHI,L3andOPAL,respectively).

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

0,RandA0, fortheindividualLEPexperiments,assumingTable6givesthe veparametersmZ,ΓZ,σh FB

leptonuniversality.Tables7and8givethecombinedresultandthecorrespondingcorrelationmatrix.Figure1shows,foreachleptonspeciesandforthecombinationassumingleptonuniversality,the

,

resulting68%probabilitycontoursintheR -A0FBplane.ForcompletenessthepartialdecaywidthsoftheZbosonarelistedinTable9,althoughitshouldbenotedthattheyaremorecorrelatedthantheratiosgiveninTables4and5.

mZΓZ0σhReRµRτ

,eA0FB

,µA0FB

,τA0FB

mZ

1.000 0.008 0.0500.0730.0010.002 0.0150.0460.034ΓZ 0.0081.000 0.284 0.0060.0080.000 0.0020.002 0.003

0σh

0.050 0.2841.0000.1090.1370.1000.0080.0010.007

Re0.073 0.0060.1091.0000.0700.044 0.3560.0230.016Rµ0.0010.0080.1370.0701.0000.0720.0050.0060.004Rτ0.0020.0000.1000.0440.0721.0000.003 0.0030.010

,eA0FB 0.015 0.0020.008 0.3560.0050.0031.000 0.026 0.020,µA0FB0.0460.0020.0010.0230.006 0.003 0.0261.0000.045,τA0FB0.034 0.0030.0070.0160.0040.010 0.0200.0451.000

Table5:ThecorrelationmatrixforthesetofparametersgiveninTable4.

91.1862±0.0029

ΓZ(GeV)R

2.4951±0.0043

41.580±0.069

20.726±0.039173/180

0.0186±0.0019184/172

20.810±0.061165/1702.5017±0.0041

91.1847±0.002941.508±0.0540.0142±0.0017160/206

Table6:Lineshapeandasymmetryparametersfrom5-parameter tstothedataofthefourLEPexperiments,assumingleptonuniversality.R isde nedasR ≡Γhad/Γ ,whereΓ referstothepartialZwidthforthedecayintoapairofmasslesschargedleptons.

Parameter

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

mZΓZ0σhR , A0FB

mZ

1.000 0.008 0.0510.0310.053ΓZ 0.0081.000 0.2840.002 0.002

0σh

0.051 0.2841.0000.1930.010

R 0.0310.0020.1931.000 0.054

, A0FB0.053 0.0020.010 0.0541.000

Table8:ThecorrelationmatrixforthesetofparametersgiveninTable7.

WithoutLeptonUniversalityΓee(MeV)83.90±0.12Γµµ(MeV)83.96±0.18Γττ(MeV)84.05±0.22WithLeptonUniversalityΓ (MeV)83.959±0.089Γhad(MeV)1743.9±2.0Γinv(MeV)498.8±1.5

Table9:PartialdecaywidthsoftheZboson,derivedfromtheresultsofthe9-parameter(Tables4

and5)andthe5-parameter(Tables7and8) ts.Inthecaseofleptonuniversality,Γ referstothepartialZwidthforthedecayintoapairofmasslesschargedleptons.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

0.022

0.018

0,lfb

A

0.014

0.01Rl

,

Figure1:Contoursof68%probabilityintheR -A0FBplane.Forbettercomparisontheresultsfortheτleptonarecorrectedtocorrespondtothemasslesscase.TheStandardModelpredictionformZ=91.1871GeV,mt=174.3GeV,mH=300GeV,andαs(m2Z)=0.119isalsoshown.ThelineswitharrowscorrespondtothevariationoftheStandardModelpredictionwhenmt,mHandαs(m2Z)

2arevariedintheintervalsmt=174.3±5.1GeV,mH=300+700 205GeV,andαs(mZ)=0.119±0.002,

respectively.Thearrowspointinthedirectionofincreasingvaluesofmt,mHandαs.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

3Fermion-pairproductionatLEP2energies

Updateswithrespecttolastsummer:Thisisanewsection.

LEPhasoperatedatenergieswellabovetheZresonancesinceautumn1995.Duringthistimedatahavebeencollectedatcentre-of-massenergiesof130.2and136.2GeV(in1995and1997),161.3and172.1GeV(in1996),182.7GeV(in1997)and188.6GeV(in1998).InthissectionthecombinationoftheLEPresultsone+e →f

s′ofthe

nalstatefermion-pair.Becauseofthepresence oftheZresonance,alargefractionoftheeventsproducedviaans=channelprocesswillhave

(s′).Theeventswithhighe ectivecenter-of-massenergyareparticularlyinterestingastheyprobethehard-scatteringprocessesatthesehighenergies.

Wecombinedirectlythemeasureddataintermsofcrosssections(forq

fSignal

Therearedi erencesbetweentheLEPexperimentsinthemethodsusedtodetermine

√

s′hassomesubtletieswhicharediscussedinmoredetailinReference20.Therefore

itwasnecessarytochooseacommonde nitionofthef

s′istakentobethemassofthes-channelpropagator,withthef

s′/s>0.85.ISR-FSRphotoninterferenceissubtractedtorenderthe

propagatormassunambiguous.

√

De nition2:Fordileptonevents,

s′/s>0.85.WhencalculatingthecontributiontothehadroniccrosssectionduetoISR-FSRinterference,sincethepropagatormassisill-de ned,itisreplacedbythebareq

s′/sandthatthesecondarypairhasamassbelow70GeV.Thesignal

de nitionsusedbytheindividualLEPexperimentscanbefoundinReference20.De nition1corre-spondstothatusedbyL3andOPAL,whereasDe nition2representsacompromisebetweenthoseofALEPHandDELPHI.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

3.2Inputf

q,

andcrosssectionsandoftheandasymmetriesat183and189GeVaccordingtotheirownsignalde nition.Theresultsgivenbytheexperimentsarebasedonnumbersintheirpublications[21],althoughsomeappliedsmallcorrectionstothese.µ+µ

τ+τ

µ+µ

τ+τ

Thetotaluncertaintyoneachmeasurementisbrokendowninto vesubcomponents.Fortheresultsof nalstateXfromexperimentYataparticularcentre-of-massenergy,theseare:

1)Thestatisticaluncertaintyplusuncorrelatedsystematicuncertainties,combinedinquadrature.2)Thesystematicuncertaintyforthe nalstateXwhichisfullycorrelatedbetweenenergypointsforthatexperiment.3)ThesystematicuncertaintyforexperimentYwhichisfullycorrelatedbetweendi erent nalstatesforthisenergypoint.4)Thesystematicuncertaintyforthe nalstateXwhichisfullycorrelatedbetweenenergypointsandbetweendi erentexperiments.5)Thesystematicuncertaintywhichisfullycorrelatedbetweenenergypointsandbetweendi erentexperimentsforall nalstates.Notethatcrosssectionmeasurementsarealwaysconsideredtobeuncorrelatedwithasymmetrymea-surements.

Itshouldbestressedthatthebreakdownoftheerrorsinthisformisa rstattempttodosoandthat,assuch,itshouldbeconsideredaspreliminary.

3.3AveragingMethodforf

fanalysis,canbefoundinthewebpagesofthe

LEP-IIMonteCarloWorkshop[25].Thecorrectionsappliedtothedata√typicallycorrespondtoadding/removingISR-FSRphotoninterference,changingthede nitionof

s′oronthepolarangleacceptance.Themaximum

discrepanciesseenbetweenZFITTER,TOPAZ0andKKforthesizeofthecorrectionsare0.2%forthehadroniccrosssections,0.7%fordileptoncrosssectionsand0.003fortheleptonicasymmetries.Thesearetakenaspreliminaryestimatesofthetheoreticaluncertaintyonthecorrectionprocedure[26].AmoreexhaustiveevaluationofthetheoreticaluncertaintiesiscurrentlyunderwaywithintheframeworkoftheLEP-IIMonteCarloWorkshop.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

Thereare40inputmeasurements,comprising2centre-of-massenergiestimes4experimentstimes3crosssectionsplus2asymmetries.The40×40errormatrixEonthesemeasurementsisconstructed,suchthatitselementi,jisgivenby

Eij=

k=1

krepresentsthewherethesumextendsoverthe veerrorcontributionsdescribedinSection3.2.σi

kisequalto1iferroruncertaintyonmeasurementiduetoerrorsourcek(1≤k≤5).ThefactorCij

kcorrelatesmeasurementsiandjandequalszeroifitdoesnot.

5

kkkCijσiσj,

Theχ2whichmustbeminimizedtoobtaintheaveragesisthen

χ2=(V A)TE 1(V A),

whereVisavectorcontainingthe40correctedinputmeasurements,andAisavectorcontainingthe

desiredaveragescorrespondingtoeachofthesemeasurements.The40elementsofvectorAconsistoftenindependentnumbers(theaverages)repeatedfourtimes.

3.4Resultsoff

qcrosssectionsat183and189GeV.The

combinederrorsaredominatedbythestatisticalanduncorrelatedexperimentalsystematics.Forexample,forthe189GeVhadroniccrosssectionthepartoftheerrorarisingfromthecorrelatedcomponentsisaboutone-thirdofthetotalerror.

Figure2showstheLEPaveragedcrosssectionsandasymmetries,respectively,(basedonDe ni-tion1),asafunctionofcentre-of-massenergy,togetherwiththeSMpredictions.

ThereisgoodagreementbetweentheSMexpectationsandthemeasurementsoftheindividualexperimentsandthecombinedaverages.Thereisnoevidenceine+e →f

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

cmsenergy

σ(q

σ(µ+µ )AFB

188.6GeV

(µ+µ )

3.44±0.14pb

SMprediction24.20pb

0.14pb

3.45pb

0.547±0.034

0.576

22.38±0.25pb

3.207pb

3.135±0.102pb

0.569

0.597±0.027

0.018 0.10pb 0.048pb0.018

q)σ(τ+τ )AFB(τ+τ )

Table10:Preliminarycombined183and189GeVLEPresultsfore+e →f

quantityσ(q

σ(q

0.180.010.010.000.001.000.010.010.000.000.010.080.000.000.000.011.000.000.000.000.010.000.090.000.000.010.001.000.000.000.000.000.000.040.000.000.000.001.000.040.000.000.000.000.030.000.000.000.041.00

Table11:Thecorrelationmatrixoftheaveragedresults.

fore+e →µ+µ ande+e →τ+τ havebeenusedtoplacelimitsoncontactinteractionsbetweenleptons.Followingreference[28]theseinteractionsareparameterisedbyane ectiveLagrangianLe ,addedtotheStandardModelLagrangianoftheform

Le =

g2

eiγµei

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

cross-section / pb

45403530252015105010

86420-2-4-6-8-10asymmetry

50

+-

-

10.90.80.70.60.50.40.30.20.1020151050-5-10-15

ee→ ff LEP (preliminary)

√s′/s>0.85

e+e-→µ+µ-e+e-→τ+τ-

+-

-

(data-SM)/SM (%)

(data-SM)/SM (%)

-20

√s / GeV

180182184186188190192194196

√s / GeV

198200

Figure2:PreliminarycombinedLEPresultsonthecrosssectionsandforward-backwardasymmetries

asafunctionofcmsenergy.TheexpectationsoftheSMarealsoshown.Thelowerplotsshowthedi erencesbetweenthedataandtheSM,dividedbytheSMprediction.

valuesof extractedforeachmodelwereallcompatiblewiththeStandardModelexpectation =0,atthetwostandarddeviationlevel.Theseerrorson aretypicallyafactoroftwosmallerthanthoseobtainedfromasingleLEPexperimentwiththesamedataset.The ttedvaluesof wereconvertedinto95%con dencelevellowerlimitsonΛ,andareshowninTable12.

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

e+e →µ+µ (TeV 2)

LLRRVVAA

8.88.414.012.0

Λ (TeV)

Model

.009

0.002+0 0.010

.010

0.002+0 0.011

.004

0.003+0 0.004

.005

0.004+0 0.005

Λ+(TeV)

7.3

7.010.310.9

e+e → + (TeV 2)

LLRRVVAA

10.09.516.213.6

Λ (TeV)

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

4TheτPolarisation

Updateswithrespecttolastsummer:DELPHIhaveupdatedtheirresults.

ThelongitudinalτpolarisationPτofτpairsproducedinZdecaysisde nedas

Pτ

≡

σR σL

s=mZ,isgivenby

Pτ(cosθ)=

Aτ(1+cos2θ)+2Aecosθ

sdependenceoftheτpolarisation,whichisimportantbecausetheo -peakdataare

includedintheeventsamplesforallexperiments.WhenaveragedoverallproductionanglesPτisameasurementofAτ.Asafunctionofcosθ,Pτ(cosθ)providesnearlyindependentdeterminationsofbothAτandAe,thusallowingatestoftheuniversalityofthecouplingsoftheZtoeandτ.EachexperimentmakesseparatePτmeasurementsusingthe veτdecaymodeseνν,πν,ρνanda1ν[30–33].Theρνandπνarethemostsensitivechannels,contributingweightsofabout40%eachintheaverage.DELPHIandL3havealsousedaninclusivehadronicanalysis.Thecombinationismadeusingtheresultsfromeachexperimentalreadyaveragedovertheτdecaymodes.

4.1Results

Tables13and14showthemostrecentresultsforAτandAeobtainedbythefourLEPcollabora-tions[30–33]http://monsystematicerrorsarisefromuncertaintiesinthedecayradiationintheπνandρνchannels,andinthemodellingofthea1decays[2].Theseerrorsneedfurtherinvestigationandmightneedtobetakenintoaccountforthe nalresults(seeReference32).ForthecurrentcombinationthesystematicerrorsonAτandAearetreatedasuncorrelatedbetweentheexperiments.ThestatisticalcorrelationbetweentheextractedvaluesofAτandAeissmall(≤5%),andisneglected.

TheaveragevaluesforAτandAe:

Aτ

=0.1425±0.0044

(8)(9)

Ae=0.1483±0.0051,

arecompatible,inagreementwithleptonuniversality.Assuminge-τuniversality,thevaluesforAτandAecanbecombined.ThiscombinationisperformedneglectinganypossiblecommonsystematicerrorbetweenAτandAewithinagivenexperiment,astheseerrorsarealsoestimatedtobesmall.ThecombinedresultofAτandAeis:

A =0.1450±0.0033.

(10)

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 1999 summer conferences. Averages are derived for hadronic and leptonic cross sections,

ExperimentALEPHDELPHIL3OPALLEPAverage

(90(90(90(90

----95),95),95),94),

prel.prel. nal nal

Aτ

0.1452±0.0052±0.00320.1359±0.0079±0.00550.1476±0.0088±0.00620.134±0.009±0.010

0.1425±0.0044

Table13:LEPresultsforAτ.Theχ2/d.o.f.fortheaverageis1.3/3.The rsterrorisstatisticalandthesecondsystematic.IntheLEPaverage,statisticalandsystematicerrorsarecombinedinquadrature.Thesystematiccomponentoftheerroris±0.0026.

ExperimentALEPHDELPHIL3OPALLEPAverage

(90(90(90(90

----95),95),95),94),

prel.prel. nal nal

Ae

0.1505±0.0069±0.00100.1382±0.0116±0.00050.1678±0.0127±0.00300.129±0.014±0.005

0.1483±0.0051

Table14:LEPresultsforAe.Theχ2/d.o.f.fortheaverageis4.8/3.The rsterrorisstatisticalandthesecondsystematic.IntheLEPaverage,statisticalandsystematicerrorsarecombinedinquadrature.Thesystematiccomponentoftheerroris±0.0009.