Measurement of the inclusive differential cross section for Z bosons as a function of transverse momentum in $\bar{p}p$ collisions at $\sqrt s$ = 1.8 TeV

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for Z bosons as a function of transverse momentum in ¯

pp

collisions at

√

s = 1.8 TeV

B. Abbott, M. Abolins, V. Abramov, B.S. Acharya, I. Adam, D.L. Adams, M.

Adams, S. Ahn, V. Akimov, G.A. Alves, et al.

To cite this version:

B. Abbott, M. Abolins, V. Abramov, B.S. Acharya, I. Adam, et al.. Measurement of the inclusive

differential cross section for Z bosons as a function of transverse momentum in ¯

pp collisions at

√

s =

F

Fermi National Accelerator Laboratory

FERMILAB-Pub-99/197-E

D0

Measurement of the Inclusive Differential Cross Section for Z

Bosons as a Function of Transverse Momentum in ¯pp Collisions at

p

s

= 1.8 TeV

B. Abbott et al.

The D0 Collaboration

Fermi National Accelerator Laboratory

P.O. Box 500, Batavia, Illinois 60510

August 1999

Submitted to Physical Review D

Disclaimer

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Distribution

Approved for public release; further dissemination unlimited.

Copyright Notication

Measurement of the inclusive dierential cross section for Z bosons as a

function of transverse momentum in pp collisions at

p s=1:8 TeV B.Abbott, 45 M.Abolins, 42 V.Abramov, 18 B.S.Acharya, 11 I.Adam, 44 D.L.Adams, 54 M.Adams, 28 S.Ahn, 27 V.Akimov, 16 G.A.Alves, 2 N.Amos, 41 E.W.Anderson, 34 M.M.Baarmand, 47 V.V.Babintsev, 18 L.Babukhadia, 20 A.Baden, 38 B.Baldin, 27 S.Banerjee, 11 J.Bantly, 51 E.Barberis, 21 P.Baringer, 35 J.F.Bartlett, 27 A. Belyaev, 17 S.B. Beri, 9 I.Bertram, 19 V.A.Bezzubov, 18 P.C.Bhat, 27 V. Bhatnagar, 9 M.Bhattacharjee, 47 G.Blazey, 29 S.Blessing, 25 P.Bloom, 22 A.Boehnlein, 27 N.I.Bojko, 18 F.Borcherding, 27 C.Boswell, 24 A.Brandt, 27 R. Breedon, 22 G.Briskin, 51 R.Brock, 42 A.Bross, 27 D.Buchholz, 30 V.S.Burtovoi, 18 J.M.Butler, 39 W. Carvalho, 2 D. Casey, 42 Z.Casilum, 47 H.Castilla-Valdez, 14 D. Chakraborty, 47 S.V.Chekulaev, 18 W. Chen, 47 S.Choi, 13 S.Chopra, 25 B.C.Choudhary, 24 J.H. Christenson, 27 M.Chung, 28 D. Claes, 43 A.R.Clark, 21 W.G.Cobau, 38 J.Cochran, 24 L.Coney, 32 W.E.Cooper, 27 D.Coppage, 35 C.Cretsinger, 46 D.Cullen-Vidal, 51 M.A.C.Cummings, 29 D.Cutts, 51 O.I.Dahl, 21 K.Davis, 20 K.De, 52 K.DelSignore, 41 M.Demarteau, 27 D. Denisov, 27 S.P.Denisov, 18 H.T. Diehl, 27 M.Diesburg, 27 G.DiLoreto, 42 P. Draper, 52 Y. Ducros, 8 L.V.Dudko, 17 S.R.Dugad, 11 A.Dyshkant, 18 D.Edmunds, 42 J.Ellison, 24 V.D.Elvira, 47 R.Engelmann, 47 S. Eno, 38 G.Eppley, 54 P.Ermolov, 17 O.V.Eroshin, 18 H.Evans, 44 V.N.Evdokimov, 18 T.Fahland, 23 M.K.Fatyga, 46 S. Feher, 27 D. Fein, 20 T.Ferbel, 46 H.E.Fisk, 27 Y.Fisyak, 48 E. Flattum, 27 G.E. Forden, 20 M.Fortner, 29 K.C.Frame, 42 S.Fuess, 27 E.Gallas, 27 A.N.Galyaev, 18 P.Gartung, 24 V.Gavrilov, 16 T.L.Geld, 42 R.J.GenikII, 42 K.Genser, 27 C.E.Gerber, 27 Y. Gershtein, 51 B.Gibbard, 48 B.Gobbi, 30 B.Gomez, 5 G.Gomez, 38 P.I.Goncharov, 18

3

UniversidadedoEstadodoRio deJaneiro,RiodeJaneiro,Brazil 4

InstituteofHighEnergyPhysics,Beijing,People'sRepublicof China 5

Universidadde losAndes,Bogota,Colombia 6

UniversidadSanFranciscodeQuito,Quito,Ecuador 7

InstitutdesSciencesNucleaires, IN2P3-CNRS,Universitede Grenoble 1,Grenoble,France 8

DAPNIA/ServicedePhysiquedesParticules, CEA,Saclay,France 9

PanjabUniversity,Chandigarh, India 10

DelhiUniversity, Delhi,India 11

TataInstituteofFundamentalResearch,Mumbai,India 12

KyungsungUniversity,Pusan,Korea 13

SeoulNational University,Seoul,Korea 14

CINVESTAV,MexicoCity,Mexico 15

Institute ofNuclearPhysics,Krakow,Poland 16

Institute forTheoreticalandExperimentalPhysics, Moscow,Russia 17

Moscow StateUniversity,Moscow,Russia 18

Institutefor HighEnergyPhysics,Protvino,Russia 19

Lancaster University,Lancaster, UnitedKingdom 20

UniversityofArizona,Tucson,Arizona85721 21

LawrenceBerkeley NationalLaboratoryandUniversityofCalifornia,Berkeley,California94720 22

UniversityofCalifornia,Davis,California95616 23

UniversityofCalifornia,Irvine,California92697 24

UniversityofCalifornia,Riverside,California92521 25

FloridaState University,Tallahassee,Florida32306 26

UniversityofHawaii,Honolulu, Hawaii96822 27

FermiNationalAccelerator Laboratory, Batavia,Illinois60510 28

UniversityofIllinoisatChicago,Chicago,Illinois60607 29

Northern IllinoisUniversity,DeKalb,Illinois60115 30

Northwestern University,Evanston,Illinois60208 31

IndianaUniversity,Bloomington,Indiana47405 32

Universityof Notre Dame,NotreDame, Indiana46556 33

PurdueUniversity,West Lafayette, Indiana47907 34

IowaStateUniversity,Ames,Iowa50011 35

Universityof Kansas,Lawrence,Kansas66045 36

KansasStateUniversity,Manhattan, Kansas66506 37

Louisiana TechUniversity, Ruston,Louisiana71272 38

UniversityofMaryland,CollegePark,Maryland20742 39

BostonUniversity,Boston, Massachusetts02215 40

NortheasternUniversity,Boston,Massachusetts 02115 41

UniversityofMichigan,AnnArbor,Michigan48109 42

MichiganState University,EastLansing,Michigan 48824 43

Universityof Nebraska,Lincoln,Nebraska68588 44

ColumbiaUniversity,NewYork, NewYork10027 45

NewYorkUniversity, NewYork,NewYork10003 46

Universityof Rochester, Rochester, NewYork14627 47

State UniversityofNewYork,StonyBrook,NewYork11794 48

BrookhavenNational Laboratory, Upton,NewYork11973 49

LangstonUniversity,Langston, Oklahoma73050 50

Universityof Oklahoma,Norman,Oklahoma73019 51

BrownUniversity,Providence,RhodeIsland02912 52

UniversityofTexas,Arlington,Texas76019 53

Texas A&MUniversity,CollegeStation,Texas77843 54

RiceUniversity,Houston,Texas77005

We present a measurement of the dierentialcross section as a functionof transverse

momentumoftheZ bosoninppcollisions at p

s=1:8TeVusingdatacollectedbytheD

experimentatthe FermilabTevatronCollider during1994{1996. Wendgoodagreement

between our data and the NNLO resummationprediction and extractvalues of the

non-perturbative parameters for the resummed prediction from a t to the dierential cross

I.INTRODUCTION

The study of the production properties of the

Z boson began in 1983 with its discovery by the

UA1 and UA2 collaborations at theCERN pp

col-lider [1,2]. Together with the discovery of the W

boson[3,4]earlier that year, theobservationof the

Zbosonprovidedadirectconrmationoftheunied

modeloftheweakandelectromagneticinteractions,

which, together with QCD, is nowcalled the

stan-dardmodel. Sinceitsdiscovery,manyofthe

intrin-sic properties of the Z boson have been examined

in greatdetailviae +

e collisions attheLEPe +

e

collideratCERN[5]. ThemassoftheZboson

mea-suredat LEPandthe SLCe +

e collideratSLAC,

known to better thanonepart in 10 4

[6], is oneof

themost preciselymeasuredparameters in particle

physics.

LEP experiments have focused on the intrinsic

properties of the Z boson, examining the

elec-troweak character of its production and decay in

e +

e collisions.AttheTevatron,wheretheZboson

is produced in pp collisions, its production

proper-tiesarepresumablycharacterizedbyQCD.Sincethe

electroweak properties of the Z boson are not

cor-relatedwiththestrongpropertiesofitsproduction,

theZ boson canthereforeserveasacleanprobeof

the strong interaction. Also, thelarge mass of the

Z boson assures a large energy scale (Q 2

 M

2 Z )

forprobingperturbativeQCDwithgoodreliability.

Themeasurementof thecrosssectionasafunction

of transverse momentum (d=dp T

) of the Z boson

providesasensitivetestofQCDathigh-Q 2

. Inthis

article,wedescribeameasurementofd=dp T

ofthe

Z bosonusingthee +

e decaysoftheZ [7].

In the parton model, at lowest order, Z bosons

areproducedinhead-oncollisionsofqqconstituents

ofthe proton andantiproton,and cannothaveany

transversemomentum. Consequently, thefact that

observed Z bosons have nite p T

is attributed to

gluon radiation from the colliding partons priorto

their annihilation into the Z boson. Gluon

radia-tionwithin thecoloreld of theproton or

antipro-tonincreasesinproportiontothetimeavailablefor

such annihilation, which is proportional to the

in-verse of the energyscale for the process (1=Q) [8].

Theradiatedgluonscarryawaytransverse

momen-tum from the annihilating quarks and momentum

conservation requires that this be observed in the

p T

oftheZ boson. Thus, oneexpects that the

ob-servedtransversemomentumdistributionofany

di-electronsystem(producedat ascaleQM ee

)will

broadenasafunction ofQ. This is,indeed, the

ef-fect observed. At M ee

 10 GeV, the typical p T

for Drell-Yanpairs[9] isabout1GeV[10]. ForW

bosonproduction(Q80 GeV), theaveragep T

is

about5GeV[11]. ForZ bosonproduction(Q91

GeV),theaveragep isabout6GeV[12].

In general, the dierential cross section for

pro-ducingthestateV isgivenby:

d 2  ij!V dp 2 T dy = X i;j Z dx i dx j f(x i )f(x j ) d 2 ^  ij!V dp 2 T dy (1) wherep T

and y arethe transverse momentum and

therapidity of the stateV; x i

and x j

are the

mo-mentumfractionsofthecollidingpartons;f(x i

)and

f(x j

) are the parton distribution functions (pdf's)

fortheincomingpartons;and^ ij!V

isthepartonic

cross section for production of the state V, in our

case, the Z boson. The subscripts i and j denote

thecontributingparton avors(i.e.,up,down,etc.)

andthesumisoverallsuch avors.

In standardperturbativeQCD(pQCD), one

cal-culates the partonic cross section by expanding in

powers of the strong coupling constant,  s

. This

procedure works well when p 2 T Q 2 . However, as p T

! 0, correction terms that are proportional to

 s ln(Q 2 =p 2 T

)becomesignicantforallvaluesof s

,

and the cross section diverges at small p T

.

Phys-ically, the failure of the calculation is due to the

presenceofcollinearandlow-p T

gluonsthatarenot

properly accounted for in the standard

perturba-tiveexpansion. This diÆcultyissurmountedby

re-orderingtheperturbativeseriesthroughatechnique

calledresummation[8,13{19].

In its nal form, the dierential cross section is

calculatedasaFouriertransforminimpact

param-eter,b,space: d 2  ij!V dp 2 T dy  Z 1 0 d 2 be i ~pT
~ b W(b;Q)+Y(b;Q) (2)

whereW(b;Q)containstheresultsofresummingthe

perturbative series, and Y(b;Q) adds back to the

calculation the pieces that are perturbative in  s

,

but arenotsingularatp T

=0[8].

Althoughtheresummationtechniqueextendsthe

applicabilityofpQCDtolowervaluesofp T

,amore

fundamental barrier is encountered when p T

ap-proaches  QCD

, and pQCD is expected to fail in

general. Inthis region, weexpect non-perturbative

aspectsofthestrongforce todominatethe

produc-tionofthevectorboson. ThisimpliesthatW(b;Q 2

)

inEq.2isundenedabovesomevalueofb=b max

.

Toextend the calculationto p T =0, the following substitutionismade: W(b;Q)!W(b  ;Q)e SNP(b;Q) (3) whereb  b= p 1+(b=b max ) 2

. Thiseectivelycuts

o the contribution of W(b;Q) near b max

, leaving

the dierential cross section dominated by S NP

,

where S NP

(b;Q) is called the non-perturbative

Su-dakov form factor. S NP

has the generic

S NP (b;Q)= h 1 (b;x i )+h 1 (b;x j )+h 2 (b)
ln( Q 2Qo ) (4) wherex i andx j

arethemomentumfractionsofthe

annihilating quarks; Q o is an arbitrarymomentum scale;andh 1 (b;x),h 2

(b)arephenomenological

func-tions to be determined from experiment [15,17,18].

Thefactthath 2

(b)lacksanydependenceonthe

mo-mentum fractions of the incoming partons has led

tospeculationthat itmaycontainsomedeeper

rel-evancetothegluonicstructureoftheproton[20].

Thecurrentunderstandingofthep T

distribution

for Z bosons uses xed-order perturbative

calcu-lations [leading-order(LO)ornext-to-leading-order

(NLO)] to describethe high-p T

region, and

resum-mation calculationsof the perturbative solutionto

describe the low-p T

region. The resummation

cal-culationfails atlarge-p T

(oftheorder50GeV)due

tolargetermsmissingfromthecalculationresulting

fromthep T

!0approximation. Anadhoc

\match-ing"criteriaisinvokedtodecidewhentoswitchfrom

the resummed calculationto the xed-order

calcu-lation,whichisconsideredtoberobustatlarge-p T

.

Additionally,aparameterizationofEq.4isinvoked

toaccountfornon-perturbativeeectsatthelowest

p T

values which are notcalculable in perturbative

QCD.

Inourmeasurementofthep T

distribution,we

re-stricttheinvariantmassofthedielectronsystemto

be approximately the mass of the Z boson, where

the Z resonance greatly dominates dielectron

pro-duction. Theremaining contribution isdue almost

entirelyto productionofe +

e pairsviathephoton

propagator (Drell-Yan process), which is coherent

and interferesquantum mechanicallywith Z boson

production. Other processes also contribute to

in-clusivedielectronproductioninppcollisions,e.g.,tt

anddibosonproduction,however,theseare

incoher-entwithZ boson productionand theiroverall rate

isnegligiblysmall.

Besides being of intrinsic interest in the study

of QCD,precise understanding ofZ boson

produc-tioninppcollisionshasimportantpracticalbenets

for other measurements with electrons in the nal

state. The phenomenology used to describe Z

bo-sonproductionisapplicabletoW,Z,andessentially

all Drell-Yantype processes. Inthe low-p T

region,

where the cross section is highest, uncertainties in

thephenomenologyofvectorbosonproductionhave

contributed to the uncertainty in themeasurement

of the mass of the W boson (M W

) [21,22].

Addi-tionally, diboson, top quark, and Higgs boson

pro-duction all have single and dielectron backgrounds

from W and Z boson productionthat willbemore

constrainedthroughaprecisemeasurementofZ

bo-sonproductionproperties.

Despitelarger statisticaluncertainties relativeto

W boson production (there are 10 times more

W !e thanZ!eeeventsproduced at s=1:8

TeV),theZ bosonprovidesabetter laboratoryfor

evaluating thephenomenologyof vectorboson

pro-duction. The measurement of the transverse

mo-mentumofthee +

e pair(p ee T

)doesnotsuer from

the same level of experimental imprecision as the

measurementofp e T

becausethelatter reliesonthe

determination of the total missing transverse

mo-mentumin thedetector(E / T

),whichhasinherently

highersystematicuncertainties. Thetypical

resolu-tioninp ee T

isabout1.5GeVcomparedwith4{5GeV

forp e T ,and thep ee T

resolution isapproximately at

asp ee T

increases,whereasitcontinuesto degradefor

p e T

.

Previous measurements of the dierential cross

sectionforZ !ee productionin pp collisionshave

been limitedprimarily by statistics. The UA2 [23]

collaboration analyzed 162 events, concluding that

therewasbasicagreementwithQCD,butthatmore

statistics were needed. In the 1988{89 run at the

Tevatron, CDF [12] analyzed 235 dielectron events

and103dimuonevents,makingsimilarconclusions.

Ourstudy isbasedonatotalofabout6400events.

We determine the p T

distribution for the Z boson

anduseourresultstoconstrainthenon-perturbative

Sudakovform factor. Wethenremovetheeectsof

detectorsmearingandobtainanormalized

dieren-tialcrosssectiond=dp T

.

WepresentabriefdescriptionoftheDdetector

in the next section. We then present the selection

procedure for our data sample. The selection

eÆ-ciency (Section IV), kinematic and ducial

accep-tances(Section V), contributingbackgrounds

(Sec-tion VI), t for non-perturbative parameters

(Sec-tionVIII),andthesmearingcorrection(SectionIX)

areall discussed in turn. These individual

compo-nents are combined (Section X)to obtainthe nal

dierentialcrosssection, whichiscompared to

pre-dictionsfromQCD.

II.EXPERIMENTALSETUP

The Ddetector consists of three major

subsys-tems: acentraldetector, acalorimeter(Fig.1),and

amuonspectrometer. It isdiscussed in detail

else-where[24].Wedescribebelowonlythefeaturesthat

aremostrelevantforthis measurement.

A.Conventions

We use aright-handed Cartesiancoordinate

sys-temwith thez-axisdened by thedirection of the

protonbeam,thex-axispointingradiallyoutofthe

Tevatronring,andthey-axispointingup. Avector

~

pisthendenedintermsofitsprojectionsonthese

in the Tevatron are unpolarized, all physical

pro-cessesareinvariantwithrespecttorotationsaround

thebeamdirection. Itisthereforeconvenienttouse

acylindrical coordinatesystem, in which the same

vectoris given by the magnitude of its component

transversetothebeamdirection,p T

,itsazimuth ,

and p z

. In pp collisions the center of mass frame

of the parton-partoncollisions is approximatelyat

rest in the plane transverseto the beam direction,

but has an unknown boost along the beam

direc-tionduetothedispersionofthepartonmomentum

fraction within theinteracting proton and

antipro-ton. Consequently,thetotal transversemomentum

vectorinanyevent(E / T

)mustbeclosetozero,and

canbe used to reject background from eventsthat

haveneutrinosinthenalstate. Wealsouse

spher-icalcoordinatesby replacingp z

with thecolatitude

orthepseudorapidity= lntan(=2). The

ori-gin of the coordinate systemis, in general, dened

as the reconstructed position of the pp interaction

for describing the interaction, and the geometrical

centerofthedetectorwhendescribingthedetector.

For convenience, weuse natural units (~ =c =1)

throughoutthispaper. Additionally,weuse\p T

"to

refertothetransversemomentumoftheZ bosonor

objectswhichmimictheZ,e.g.,backgroundevents

inwhichthemomentafortheobjectsconsideredto

formthefake-Zareaddedtogethertogenerateap T

value. Deviationswillbenotedwithanappropriate

superscript.

1m

D0 LIQUID ARGON CALORIMETER

CENTRAL

CALORIMETER

END CALORIMETER

Outer Hadronic

(Coarse)

Middle Hadronic

(Fine & Coarse)

Inner Hadronic

(Fine & Coarse)

Electromagnetic

Coarse Hadronic

Fine Hadronic

Electromagnetic

FIG.1. A cutaway view of the D calorimeterand

trackingsystem.

B.CentralDetector

The central detector is designed to measure the

texdriftchamber,atransitionradiationdetector,a

centraldriftchamber(CDC),andtwoforwarddrift

chambers(FDC).Thereisnocentralmagneticeld,

and D therefore cannot distinguish particles by

their electric charge, with the exception of muons

which penetrate the outer toroidal magnets.

Con-sequently, in the rest of this paper, the term

elec-tron will refer to either an electron or a positron.

TheCDCcoversthedetectorpseudorapidityregion

j det

j <1:0. It is adrift chamber with delay lines

that givethe hitcoordinatesalongthe beam

direc-tion(z)andtransversetothebeam(r,). TheFDC

coverstheregion1:4<j det

j<3:0.

C.Calorimeter

The sampling calorimetry is contained in three

cryostats, each primarily using uranium absorber

platesandliquidargonastheactivemedium. There

isacentralcalorimeter(CC)andtwoend

calorime-ters (EC). Each is segmented into electromagnetic

(EM) sections, a ne hadronic (FH) section, and

coarse hadronic (CH) sections, with increasingly

coarser sampling. Theentire calorimeter isdivided

intoabout5000pseudo-projectivetowers,each

cov-ering 0.10.1 in  . The EM section is

seg-mented into four layers which are 2, 2, 7, and 10

radiation lengths in depth respectively. The third

layer, in which electromagnetic showersreachtheir

maximum energy deposition, is further segmented

intocellscovering0.050.05in. Thehadronic

sections are segmentedinto four (CC) orve(EC)

layers. Theentirecalorimeteris7{9nuclear

interac-tionlengthsthick. Therearenoprojectivecracksin

thecalorimeter,anditprovideshermeticandnearly

uniformcoverageforparticleswithj det

j<4.

D.Trigger

Readout of thedetector iscontrolled bya

multi-leveltriggersystem. Thelowestlevelhardware

trig-gerconsistsoftwoarraysofscintillatorhodoscopes,

whichregisterhitswitha220pstimeresolutionand

are mountedinfrontof theECcryostats. Particles

from the breakupof theproton andtheantiproton

producehits in hodoscopesat opposite endsof the

CC,eachof which aretightlyclustered in time. At

the lowest trigger level, the detector has a 98.6%

acceptance for W/Z boson production. For events

thatcontainonlyasingleppinteraction,thelocation

oftheinteractionvertexcanbedeterminedfromthe

time dierence betweenthehits at thetwoends of

thedetectortoanaccuracyof3cm. Thisinteraction

vertexisusedinthelastlevelofthetrigger.

crossingwhenseveralpreselectedconditionsaremet.

This decisionis madewithin the3.5 stime

inter-valbetweenbeambunchcrossings. Thesignalsfrom

22arraysofcalorimetertowers(\triggertowers"),

covering0.20.2 in , areadded together

elec-tronicallyfortheEMsections(\EMtriggertowers")

aswellasforallsections,andshapedwithafastrise

timeforuseatthistriggerlevel. Anadditional

trig-ger processor can be invoked to execute simple

al-gorithmsonthelimitedinformationavailableatthe

timeoftheAND-ORnetwork.Thesealgorithmsuse

theenergydepositsineachofthecalorimetertrigger

towers.

Thenal software-based level of thetrigger

con-sistsofanarrayof48VAXstation 4000computers.

Atthislevel,completeeventinformationisavailable

andmoresophisticatedalgorithmsareusedtorene

thetriggerdecisions. Eventsareacceptedbasedon

certainpreprogrammedconditionsandarerecorded

foreventualoinereconstruction.

III. DATASELECTION

A.Trigger Filter Requirements

Werequirethetransverseenergy,E T

(Esin),of

one or more trigger towers to be greater than 10

GeV.ThetriggerprocessorcomputesanEM

trans-verse energyby combining theE T

of the EM

trig-ger tower (that exceeded somethreshold) with the

largestsignalintheadjacentEMtriggertowers,but

doingthisonlyiftheoriginalEMsignalhasatleast

85%oftheenergyoftheentiretriggertower

(includ-inghadroniclayers).

For the accepted trigger tower, a software

algo-rithm nds the most energetic of four sub-towers,

and sums the energy in a 33 array of

calorime-ter cells around it. It examines the longitudinal

showerprole bycheckingthe fraction of the total

energyfoundindierentEMlayers. Thetransverse

showershapeis characterizedbythepattern of

en-ergydepositioninthethirdEMlayer.Thedierence

betweenthe energiesin concentricregionscentered

onthemostenergetictowercovering0.250.25and

0.150.15 in  must be consistent with

expec-tationsforanelectronshower. Thetriggeralso

im-posesanisolationconditionrequiring

P i E i sin i p e T p e T <0:15 (5)

where the sum runs over all cells within a cone of

radius R = p
 2 +
 2

= 0:4 around the

elec-trondirectionandp e T

isthetransversemomentumof

theelectron,basedonitsenergyandthez-position

of the interaction vertex as measured by the

ho-The trigger requires two electrons which satisfy

the isolation requirement, each with E T

>20 GeV.

Figure2showsthemeasureddetectioneÆciency of

theelectron lteras afunction of p e T

for a

thresh-old of 20 GeV. We determine this eÆciency using

Z boson data taken with a lower threshold value

(16 GeV). (The eÆciency corresponds to the

frac-tionofelectronsfoundatthehigherthreshold.) The

curve is a parameterization used in the simulation

describedinSectionIIID.

0

0.2

0.4

0.6

0.8

1

20

25

30

35

40

45

(GeV)

E

T

effi

ci

ency

cutoff

E

T

FIG.2. ElectrondetectioneÆciencyas afunctionof

electronET atthetriggerlevel. TheeÆciencyis

essen-tially ataboveournalE T

cutoof25GeV.

B.Fiducial and Kinematic Requirements

Eventspassingthelterrequirementareanalyzed

oinewhere theyare reconstructed with ner

pre-cision. The two highest-E T

electron candidates in

the event, both having E T

> 25 GeV, are used to

reconstruct the Z boson candidate. One electron

is requiredto be in the central region, j det

j< 1:1

(CC),andthesecond electronmaybeeitherin the

central orin the forward region, 1:5 <j det

j <2:5

(EC). This yields two topologies for the selected

events: CCCC,wherebothelectronsaredetectedin

thecentralregion,andCCEC,whereoneelectronis

detectedin thecentral regionand the other in the

forwardregion. In order to avoid areasof reduced

responsebetweenneighboringmodulesofthe

cen-tralcalorimeter,theofanyelectronisrequiredto

beat least0:052=32radiansawayfrom the

po-sitionofamoduleboundary. Finally,theeventsare

requiredtohave aninvariantmass nearthe known

valueoftheZ bosonmass,75<M ee

C. Electron Quality Criteria

To be acceptable candidates for Z production,

bothelectronsarerequiredtobeisolatedandto

sat-isfyoinecluster-shaperequirements. Additionally,

at least one of the electrons is required to have a

spatially matching trackassociatedwiththe

recon-structedcalorimetercluster.

Theisolationfraction isdenedas

f iso = E cone E core E core ; (6) whereE cone

istheenergyinaconeofradiusR=0:4

around the direction of the electron, summed over

theentiredepthofthecalorimeters,andE core

isthe

energyin acone ofR=0:2,summedoveronlythe

EMcalorimeter. Both electronsin thedata sample

arerequiredtohavef iso

<0:15.

Wetest how well theshapeof any cluster agrees

withthatexpectedforanelectromagneticshowerby

computingthequalityvariable 2 HM

forallcell

ener-giesusinga41-dimensionalcovariancematrixcalled

the H-matrix[25]. The covariancematrixis

deter-minedfromgeant-basedsimulations[26,27],which

were tuned to agreewith test beammeasurements.

Bothelectronsinthesamplearerequiredto havea

tightselectionof 2 HM

<100.

The quality of the spatial match between a

re-constructedtrackand anelectromagnetic clusteris

denedbythevariable

 2 = 
s Æs  2 + 
z Æz  2 ; (7)

where
sisthedistancebetweenthecentroidofthe

cluster in the third EM layerand theextrapolated

trajectoryofthetrackalongtheazimuthaldirection,

and
z istheanalogousdistanceinthez-direction.

ForECelectrons,z is replacedbyr, theradial

dis-tance from thecenter of thedetector. The

param-etersÆs=0:25cm, Æz =2:1 cm, andÆr=1:0cm,

aretheresolutionsin
s,
z,and
r,respectively.

At least one of the candidate electronsis required

to have <5for candidates with j det

j< 1:1 and

<10forcandidateswith1:5<j det

j<2:5.

Thetotal integratedluminosityof thedata

sam-ple is 111pb 1

. After applying theselection

crite-ria,6407eventsremain,with3594eventscontaining

bothelectronsinthecentralregionand2813events

containingoneelectroninthecentralregionandone

intheforwardregion. Figure3showsthemassand

p T

distributions (for 75 <M ee

< 105GeV) in the

naldatasample. Thereare157eventswithp T

>50

GeV,andtheeventwiththelargestp T hasp T =280 GeV.

0

250

500

750

1000

50

60

70

80

90

100

110

120

130

M

_ee

(GeV)

Events/GeV

(a)

1

10

10

2

10

3

0

50

100

150

200

250

300

p

_T

(GeV)

Events/GeV

(b)

FIG.3. (a)Massdistributionforallacceptedelectron

pairs, and (b)the pT distribution for those pairs with

75<M ee

<105GeV.

D.Resolutions and Modelingof theDetector

Both the acceptance and the resolution-smeared

theory are calculated using a simulation technique

originally developed for measuringthe mass of the

W boson[21] and inclusivecrosssectionsof theW

and Z bosons [28], with minor dierences arising

from small dierencesin theselection criteria. We

brie ysummarizethesimulationhere.

ThemassoftheZbosonisgeneratedaccordingto

an energy-dependent Breit-Wigner lineshape. The

p T

andrapidity(y)arechosenrandomlyfromgrids

created with the computer program legacy [19]

which calculates the Z boson cross section for a

given p T

, y, and Q. For calculating the grids, we

use a xed value for the mass of the Z boson of

91.184GeV.Wematch the low-p T

and high-p T

re-gions following the algorithm used in the program

resbos [19] to produce a grid of p T

and y values,

weightedbytheproductioncrosssection,calculated

to NNLO. The primary vertexdistribution for the

eventismodeledasaGaussianwithawidthof27cm

andameanof 0:6cm,correspondingtothewidth

andosetmeasuredin thedata. Thepositionsand

energies of the electrons are smeared according to

the measured resolutions and corrected for osets

inenergy scalecaused bytheunderlying eventand

recoilparticlesemitted intothe calorimetertowers.

Underlyingeventsaremodeledusingdatafrom

ran-dominelasticppcollisionswiththesameluminosity

proleas theZ sample.

The electron energy and angular resolutions are

eemass distribution at theZ resonance. The

frac-tional energy resolution can be parameterized as

a function of electron energy as
E=E = C 

S= p

E T

. Thesampling term,S, was obtainedfrom

measurements made in a calibration beam, and is

0.135 GeV

1=2

for theCCand 0.157GeV 1=2

for the

EC [29,30]. The constant term, C wasdetermined

specicallyforourselectioncriteria. IntheCC,the

valueisC=0:0140:002andintheECthevalueis

C =0:0 +0:01

0:00

. Theuncertaintyis dominatedby the

statisticsoftheZ !eesample. Theuncertaintyin

thepolar angleof theelectronsisparameterizedin

termsof the uncertaintyin thecenter-of-gravityof

the track used to determine the polar angle.

Fig-ure 4 compares electrons from Z boson data with

simulated results for distributions in electron E T

,

pseudorapidity,and.

Inadditiontothesmearingoftheelectronenergies

andpositions,certainspecicfeaturesofthe

exper-iment are also modeled in the simulation in order

tomorecloselyrepresentthedata. A

parameteriza-tionoftheriseineÆciency ofthetriggerasa

func-tionofelectronE T

isincluded,aswell asa

param-eterization of the tracking eÆciency as a function

of electronpseudorapidity. Both eÆciencies havea

negligibleeectontheshapeofthep T

distribution.

Details of the detector simulation can be found in

Refs.[31,32].

0

200

400

600

0

10

20

30

40

50

60

70

80

90 100

E

_T

(GeV)

0

250

500

750

1000

-4

-3

-2

-1

0

1

2

3

4

η

Arbitrary Units

0

200

400

0

1

2

3

4

5

6

φ

(radians)

FIG.4. ComparisonofelectronE T

,,and,fromZ

bosondata(crosses)toresultsofthedetectorsimulation

(dashed).

IV.EFFICIENCY

We determine the eÆciency of the event

selec-tioncriteriaasafunctionofthep T

oftheZ boson,

normalizingtheresult to the integrated totalcross

sectionforZ bosonproduction asmeasuredat D

( Z

B(Z !ee)=221pb)[28].

Of alltheselectioncriteria,theelectronisolation

requirementhasthelargestimpactontheobserved

p T

of the Z boson. Nearby jet activity spoils the

isolationof anelectron, causing itto fail the

selec-tioncriteria. The eect depends upon the detailed

kinematics of the event, in particular, the location

ofhadronicactivity(e.g.,associatedjetproduction)

andthep T

ofthevectorboson.

Twomethodshavebeenusedtodeterminethep T

-dependence of the electronidentication eÆciency.

In the rst method, the eect of jet activity near

anelectronshowerisparameterizedin termsofthe

component of the hadronic recoil energy (u)

pro-jectedontothevectorp e T

. Thisisdenotedasu jj

[33].

Therelationshipbetween~p e T

andu jj

isillustratedin

Fig.5. Weusedacombinationofsimulatedelectrons

andW bosondatatoobtaintheeÆciencyfor

identi-fyingelectronsasafunctionofu jj

. Electronshowers

weregeneratedusingthegeantdetector-simulation

program,andtheparametersforthesimulated

elec-trons (e.g., E T

, isolation,  2 HM

) agreed well with

those observed in W boson data [21]. The

agree-mentsuggeststhattheeectofhadronicactivityon

theelectron is well-modeled in thesimulation.

Al-thoughourparameterizationisobtainedusing

elec-tronsfrom W events, weapply itto electronsfrom

Zbosonevents(whichhaveverysimilarenergy

dis-tributions due to hadronicrecoil), because the

pa-rameterizationre ectstheeectofhadronicactivity

onhigh-p T

electrons,regardlessoftheoriginofthat

activity.

TheelectronidenticationeÆciencyasafunction

ofu jj isparameterizedas: (u k )=   if(u k <u o ) (1 s(u k u o )) if(u k >u o ) (8) where u o is the valueof u jj

at which the eÆciency

beginsto decreasewith u jj

, ands istherate of

de-crease. The values obtained from the best t are

are u o

= 3:850:55 GeV and s = 0:0130:001

GeV 1

. The parameter  re ects the overall

eÆ-ciency,which,aswehaveindicated,isobtainedfrom

a normalization to the overall selection eÆciency.

Thenal eventeÆciency asafunction of p T

ofthe

Z boson, shownin Fig. 6,is obtainedfrom the

de-tectorsimulation,bycomparingthep T

distribution

withandwithouttheu jj

correction. Thenalevent

eÆciencyisinsensitivetotheuseofdierent

param-eterizationsoftheu jj

FIG.5. Illustration of the relationship between the

transversemomentumoftheelectron, thevectorE T

of

the hadron recoil (u) in the calorimeter, and u jj

, the

projectionof the recoilonto the transversedirectionof

theelectron. Intheparticularexampleillustratedhere,

u jj

isnegative.

to obtain the u jj

parameterizationcan be found in

Ref.[21].

Inthe end, the u jj

parameterizationof theevent

identication eÆciency alone is unsatisfactory for

application to this measurement. In particular,

thatanalysisrequiredp W T

<30GeV,thereby

restrict-ing applicability to that region. To obtain a

rea-sonable parameterization of the electron

identica-tion eÆciency for all values of p T

, we extract the

Z bosonidentication eÆciency from events

gener-ated with herwig [34], smeared with the D

de-tector resolutions, and overlaid onto randomly

se-lected pp collisions (\zero-bias" events). The

eÆ-ciency asafunction ofp T

is denedby theratioof

thep T

distributionforeventswithresolution

smear-ing andkinematic, ducial and electronquality

re-quirements imposed, to that with only kinematic

and ducial requirements. Figure 6a compares the

eÆciencyasafunctionofp T

usingtheu jj

parmeteri-zationwiththatusingthedetector-smearedherwig

events. Thedistributions havebeen normalizedto

each other in the region p T

<30 GeV. Figure 6(b)

shows the ratio of the two normalized results for

p T

<30GeV.Theagreementoftheherwiganalysis

withtheu jj

analysisistakenasconrmation ofthe

validityoftheherwigresultforallp T

. (Themodel

fortheu jj

analysishasbeenshowntobereliablefor

p T

<30GeV.)

InnormalizingoureÆciencytothepreviously

de-terminedinclusiveZbosoneventselectioneÆciency,

we use the combined CCCC and CCEC eÆciency

of 0.76 [28]. We t the herwig result to a

lin-earfunction in the regionp T

<18 GeV, and a

con-stant in the region p T

>18 GeV, to obtain the p T

-dependent event selection eÆciency for all p T

val-ues. Theparameterizationis shown inFig. 7. The

p T

-dependence of the eÆciency, in absolute terms,

isgivenby=0:78 0:004p T ,forp T <18GeV,and 0.73forp T >18GeV.

We assume that the eÆciency above 100GeV is

thesameasintheregionof18{100GeV.Thisisthe

simplestassumptionwecanmakegiventhestatistics

ofthesimulation. TheeÆciency athigh-p T

cannot

begreaterthanatp T

=0,whichwouldcorrespond

toabouta1.5standarddeviationchangeinthecross

sectionin that region, andthis dierencewould be

re ectedintheuncertaintyontheextracted

dieren-tialcrosssection. WedonotexpecttheeÆciencyto

decreaseintheregionbeyond100GeV,becausethe

jetsinsucheventswilltendtobein thehemisphere

oppositetotheelectrons. Eventswithhighjet

mul-tiplicity may haveinstances in which the large-E T

jets balance most of the transverse momentum of

theevent,butsmaller-E T

jetscanoverlapwith one

oftheelectrons. However,becausetheelectronsare

veryenergetic, low energyjets are not likely to

af-fecttheeÆciencyoftheisolationcriteria. Weassign

estimateduncertaintieson theeÆciency of 3%in

thebinbelow18GeV,and5%intheregionabove

18GeV.

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0

20

40

60

80

100

p

_T

(GeV)

efficiency

(a)

0.9

0.95

1

1.05

1.1

0

5

10

15

20

25

30

p

_T

(GeV)

ratio

(b)

FIG.6. (a)Comparison oftheZ bosonselection

eÆ-ciencyasa functionofp T

as determinedusingherwig

(dashedcrosses),andasdeterminedusinga

parameter-ization of the single-electroneÆciency as a functionof

u jj

(solidcrosses). (b)Theratioofthe twomethodsin

0.6

0.66

0.72

0.78

0.84

0.9

0

20

40

60

80

100

p

_T

(GeV)

efficiency

FIG.7. FinaleventidenticationeÆciencyasa

func-tionof p T

,based onherwigevents;the lineis the

pa-rameterizationusedincalculatingthenalcrosssection.

V.ACCEPTANCE

Theparameterizeddetectorsimulationreferredto

inSectionIIIisusedtodeterminetheoverall

accep-tanceasafunctionofp T

oftheZboson. Theeects

of the triggerturn-on in E T

, the rapidity cut-os,

the  module boundaries in the central

calorime-ter, the pseudorapidity dependence of thetracking

eÆciency, and thenal E T

requirementsare all

in-cludedinthecalculationoftheacceptance. Figure8

showstherelativeeectsoftherequirementsonthe

electronE T

and pseudorapidity, and of the trigger

andtrackingeÆciency ontheacceptanceasa

func-tion of p T

. As can be seen, the strongest eects

come from the electron E T

and pseudorapidity

re-quirements. Thedip in relativeacceptance seenin

Fig. 8(a) for middle values of p T

results from one

of the electrons carrying most of the p T

of the Z

boson{one electron can have a relatively large E T

while the other has relatively small E T

. However,

asthep T

of theZ bosonincreasesbeyond45GeV,

thisasymmetryisnolongerallowed{bothelectrons

must haverelativelylargeE T

. Themonotonic rise

oftherelativeacceptancein Fig.8(b)is dueto the

increasing\centrality"oftheevent{asp T

increases,

therapidityoftheZ bosonisclosertozero. Ascan

beseenin Figs.8(c)and(d), theimposition of the

other selection criteriamerely changes the

normal-ization and doesnotaect the shape asafunction

ofp T

.

Themassrequirementonthedielectronpairshas

been ignored in the nal acceptance calculation.

Figure9comparesthep T

distributionfordielectron

pairswithinvariantmassnear that oftheZ boson

to those with invariant mass above and below the

nominal Z boson mass, and supports the

expecta-tionthat any p T

dependence on mass (near the Z

bosonmasspeak)is verysmall.

Figure10showstheacceptancefortheCCCCand

CCECeventtopologies,aswellasforthecombined

eventsample. Hereweseetheincreasedcentralityof

theeventsasafunctionofp T

,notingtheincreasing

acceptanceforthe CCCC events in contrastto the

decreasingacceptancefortheCCECevents. Thedip

andriseinFig.10(b)areduetocompetingeectsof

theelectronE T

andpseudorapidityrequirements.

Theeectofuncertaintiesintheenergyscaleand

resolution, the tracking resolution, and the trigger

eÆciency is assessed for each bin of p T

by

vary-ing the values of these parameters by their

mea-sured uncertainties. Figure 11 shows the nominal

acceptanceand those obtained by varying the

val-ues of the parameters. The largest dierences are

observed at high p T

. If we parameterize this

sys-tematic uncertainty as a linear function of p T , we obtain Æ acc = (0:01+0:0001p T ). This resulting

bandofuncertaintyisalsoshownin Fig.11.

Because wedeterminethe acceptancebin bybin

in p T

, we are relatively insensitive to the

underly-ingmodelforthep T

spectrumusedin thedetector

simulation. Nevertheless,wearesensitivetothe

as-sumedrapidity distribution of theZ boson in each

binofp T

. Theuncertaintyinthepredictedrapidity

oftheZ boson isexpectedto bedominatedbythe

uncertainty in the pdf's used for modeling Z

pro-duction. Theuncertaintyin acceptancedue to the

choice of pdf has been found to be 0:3% for the

inclusivemeasurementoftheZ bosoncrosssection

[28]. Thisconstrains the uncertaintyin thelow-p T

region,wherethecrosssectionislargest,to avalue

thatis farsmallerthanthe uncertaintyfrom

varia-tionsin the parameters of the model of the

detec-tor. Figure12showsthattherapiditydistributions

obtainedfrom thedetector simulationand fordata

agreeforbothlowandhigh valuesofp T

; we

there-foreignoreanyadditionaluncertaintyinthe

accep-tancedue to the modeling of therapidityof the Z

boson.

VI.BACKGROUNDS

Theprimarybackgroundtodielectronproduction

attheTevatronisfrommultiple-jetproductionfrom

QCDprocesses in which thejets havea large

elec-tromagnetic component (most of the energy is

de-positedintheEMsectionofthecalorimeter)orthey

aremismeasured in some way that causes them to

passthe electron selection criteria. There are also

0.2

0.4

0.6

0.8

1

1.2

0

100

200

300

(a)

p

_T

(GeV)

Relative Acceptance

_0.2

0.4

0.6

0.8

1

1.2

0

100

200

300

(b)

p

_T

(GeV)

0.2

0.4

0.6

0.8

1

1.2

0

100

200

300

(c)

p

_T

(GeV)

Relative Acceptance

_0.2

0.4

0.6

0.8

1

1.2

0

100

200

300

(d)

p

_T

(GeV)

FIG.8. Eect of requirementson(a) ET,(b), (c)

triggerE T

cut-o,and(d)trackingeÆciencyonthe

rel-ativeacceptanceasafunctionofp T .

0

0.04

0.08

0.12

0.16

0.2

0

10

20

30

40

50

60

p

_T

(GeV)

Arbitrary Units

10

-2

10

-1

1

10

50

75 100 125 150 175 200 225 250 275 300

p

_T

(GeV)

Arbitrary Units

FIG.9. Comparisonofthetransversemomentum

dis-tributionofdielectronpairswithmassveryclosetothe

nominal Z bosonmass, 90<Mee <92GeV(solid

cir-cles)to thoseinthemass regions 75<Mee <90GeV

(open circles) and 92<M ee

<105 GeV (closed

trian-gles).

0

0.14

0.28

0.42

0.56

0.7

0

100

200

300

(a)

p

_T

(GeV)

Acceptance

0

0.05

0.1

0.15

0.2

0.25

0

100

200

300

(b)

p

_T

(GeV)

0

0.14

0.28

0.42

0.56

0.7

0

50

100

150

200

250

300

(c)

p

_T

(GeV)

Acceptance

FIG.10. Final acceptanceasafunctionofpT for(a)

theCCCC, (b)CCECevent topologies, and(c)for the

combinedeventsample.

0.25

0.34

0.43

0.52

0.61

0.7

0

50

100

150

200

250

300

p

_T

(GeV)

Acceptance

Energy Resolution +

σ

Energy Resolution -

σ

Energy Scale +

σ

Energy Scale -

σ

Tracking Resolution +

σ

Tracking Resolution -

σ

FIG.11. Eectofuncertaintiesontheacceptancein

eachbinofp T

. Thebandcorrespondstoa

parameteriza-tionoftheuncertaintyasafunctionofpT,as discussed

0

0.9

1.8

2.7

3.6

4.5

-3

-2

-1

0

1

2

3

y

(a)

0

0.8

1.6

2.4

3.2

4

-3

-2

-1

0

1

2

3

y

Arbitrary Units

(b)

0

1.2

2.4

3.6

4.8

6

-3

-2

-1

0

1

2

3

y

(c)

FIG.12. ComparisonofZbosonrapidity(y)

distribu-tionforthedata(solid)andthesimulation(dashed)for

(a)allvaluesofp T ,(b)p T <20GeV,and(c)20<p T <50 GeV.

arenotfrom misidentication ofelectrons,but

cor-respond to otherprocessesthat dierfrom theone

we are trying to measure, e.g., Z !  +

 and tt

production. Such processes are irreducible due to

the fact that they havethe samenal event

signa-ture as the signal, and often havep T

dependences

that candierfrom theZ/ 

mediated production

oftheZ bosonandDrell-Yanpairs. Thesemustbe

determinedandaccountedforinanycomparisonof

datawiththeory.

Boththenormalizationandtheshapeofthe

mul-tijetbackgroundasafunctionofp T

aredetermined

from data. Three typesof backgroundshave been

studied to examine whether dierences in

produc-tion mechanism or detector resolution would

pro-duce a signicant variation in the background:

di-jet events (from multijet triggers), direct- events

(fromsinglephotontriggers), anddielectronevents

in which both electrons failed the quality criteria

(fromtheZ bosontrigger). Forthedijetevents,we

selected thetwo highest-E T

jets and reconstructed

the \Z boson" as if the jets were electrons.

Simi-larly,forthedirect- events,weselectedthe

highest-E T

photoncandidateandthehighest-E T

jetin the

event. Forthefailed-dielectronsample,weusedthe

two highest-E T

electron candidates whose cluster

shapevariable( 2 HM

)didnotmatch wellwiththat

ofanelectron. Forallthreebackgrounds,the

\elec-tron" objectswererequired tosatisfy thesameE T

and criteriaasthedatasample.

Figures13{16showtheinvariantmassandp T

dis-tributions for the background samples in both the

CCCC and CCEC event topologies. The

direct-photonandfailed-dielectroneventsagreeinthemass

and p

T

distributions. The Kolmogorov-Smirnov

probability (P KS

) forthe twomassdistributions is

0.78andbetweenthetwop T

distributionsitis0.97.

Thep T

distributionfromthedijetsamplealsoagrees

wellwiththedirect- andfailed-dielectronsamples,

withP KS

=0:51andP KS

=0:57,respectively. The

dijet mass distribution does notagree as well,

giv-ing P KS

= 0:005 when comparing to the direct-

sampleandP KS

=0:1whencomparingtothe

failed-dielectronsample. Thedierenceislikelyduetothe

poorer jet-energy resolution compared to the

elec-tronenergyresolution. Thisdierence intheshape

of theinvariantmass is included in thesystematic

uncertainty on the background normalization, and

isasmalleect (seeSection VIA).

0

50

100

150

50

100

150

(a)

Arbitrary Units

50

100

150

(b)

50

100

150

(c)

Mass(GeV)

0

50

100

150

40

60

80

100

120

140

Mass(GeV)

Arbitrary Units

(d)

jj Data

γ

j Data

Failed ee Data

FIG. 13. Invariant mass distributions for the three

typesofQCDmultijetbackgroundsamplesintheCCCC

topology: (a)dijetdatasample, (b)direct- data

sam-ple,(c)failed-dielectrondatasample. Weshowthe

dis-tributionsforall threedatasamplesin(d).

A.Multijet BackgroundLevel

Because the mass distribution for the multijet

backgroundsamplesdependsoneventtopology,the

levelofthemultijetbackgroundisdetermined

sepa-ratelyforCCCC and CCECdielectronevents.

Us-ingthisbackground, andthecontributionfrom the

Z boson, we can obtain the relative background

fraction through a maximum-likelihood t for the

amountofbackgroundandsignalinthedata.

Weusethepythiaeventgenerator[35]toproduce

Con-0

20

40

60

80

50

100

150

(a)

Arbitrary Units

50

100

150

(b)

50

100

150

(c)

Mass(GeV)

0

20

40

60

40

60

80

100

120

140

Mass(GeV)

Arbitrary Units

(d)

_{jj Data}

γ

j Data

Failed ee Data

FIG.14. Invariant mass distributions for the three

typesofQCDmultijetbackgroundsamplesintheCCEC

topology: (a)dijetdatasample, (b)direct- data

sam-ple,(c)failed-dielectrondatasample. Weshowthe

dis-tributionsforallthreedatasamplesin(d).

0

20

40

60

80

0

5

10

15

20

25

30

35

40

45

50

p

_T

(GeV)

Arbitrary Units

jj Data

γ

j Data

Failed ee Data

10

-3

10

-2

10

-1

1

10

0

50

100

150

200

250

300

p

_T

(GeV)

Arbitrary Units

FIG.15. Comparisonofshapesoftransverse

momen-tumdistributionsforthethreemultijetbackground

sam-plesfortheCCCCeventtopology.

0

20

40

60

80

0

5

10

15

20

25

30

35

40

45

50

p

_T

(GeV)

Arbitrary Units

jj Data

γ

j Data

Failed ee Data

10

-3

10

-2

10

-1

1

10

10

2

0

50

100

150

200

250

300

p

_T

(GeV)

Arbitrary Units

FIG.16. Comparisonofshapesoftransverse

momen-tumdistributionsforthethreemultijetbackground

sam-plesfortheCCECeventtopology.

tributions from both Z boson and Drell-Yan

pro-ductionand their quantum-mechanicalinterference

areincludedinthecalculation. Thegenerated

four-momenta are smeared using the detector

simula-tion described previously. We obtain the amount

of multijet background in the data by performing

abinnedmaximum-likelihood t to thesumof the

signal(pythia)andbackground:

N data (m i )=c 1 N pythia (m i )+c 2 N background (m i ) (9) where c 1 and c 2

are the normalization factors for

the signal and background contributions,

respec-tively, andm i

is theithmassbin. Thet was

per-formed in the dielectron invariant mass window of

60<M ee

<120GeV.Figure17showsthebesttto

thedielectroninvariantmass,separately forCCCC

andCCEC topologiesusing the direct- sample as

the background. Using the other two background

samplesyieldssimilarresults. Thenalvalueforthe

fractionofmultijetbackgroundinthedata,f back

,is

dened by normalizing the t parameterc 1

to the

number of events observed in the mass window of

N 75 105 (sample)= 75<mi<105 N sample (m i ): (12)

We usethe direct- sample for thecentral value

ofthelevelofmultijetbackground,andusethe

sta-tistical uncertainty from that t. We also assign

asystematicuncertaintyassociatedwithourchoice

of mass window used in the t and for dierences

in the backgroundmodels. We assign asystematic

uncertainty to the background normalization that

correspondstohalfofthemaximumdierencefrom

thecentralvalueinthedeterminedbackground

frac-tions. Thebackgroundvaluesforeachtopologyand

the resulting uncertainties are summarized in T

a-bleI.

Combiningtheuncertaintiesinquadrature,we

ob-tainabackgroundfractionof(2:450:50)%forthe

CCCC topology and (7:091:00)%for the CCEC

topology. Weightingthebackgroundfractionsbythe

relativenumberofeventsineachtopology,weobtain

atotalmultijet backgroundlevelof(4.440.89)%.

10

-1

1

10

10

2

50

60

70

80

90

100

110

120

130

M(GeV)

Events/2 GeV

10

-1

1

10

10

2

50

60

70

80

90

100

110

120

130

M(GeV)

Events/2 GeV

FIG.17. Comparisonofthedielectroninvariantmass

distribution(closedcircles)andthebackground(dashed

line) to the t to pythia Z/ 

and background(solid

line)for(a)CCCCand(b)CCECtopologies.

B.pT-Dependenceofthe MultijetBackground

The direct- sample is used to determine the

shapeofthebackgrounddistributionforseveral

rea-sons. First,thissample hasthegreatestnumberof

events. Second, we expect the direct- data

sam-ple to provideagood approximationof the

combi-nationof backgrounds from dijet and true direct-

production because abouthalf of thedirect-

sam-BackgroundModel CCCC CCEC

direct- (2:450:41%) (7:090:87%) 55<Mee <125 (2:100:36%) (7:520:83%) 65<M ee <115 (2:740:51%) (6:840:96%) dijets (1:980:35%) (6:370:80%) faileddielectrons (2:100:37%) (6:220:78%) modeluncertainty 0.24% 0.44% windowuncertainty 0.17% 0.22%

TABLEI. Background fractions inthe two primary

eventtopologies. Thevaluesintherstverowsinclude

onlystatistical uncertaintiesforeachmethod. The

sys-tematicuncertaintiesobtainedbyconsideringvariations

inthebackgroundselectionandttingcriteriaareshown

inthelast tworows.

Parameter p T <8GeV p T >8GeV  0:310:02 0:10140:0015 a 0:0010:002 0:080:03 b 0:650:18 0:1360:004

TABLE II. Values of the parameters obtained from

thettothedirect- background.

theapproximatebalanceofdijetanddirect- events

expectedfrom QCDsources. Third,sinceeventsin

thedirect- oftencontainatleastonegood

electron-like object, detailed dierences between choosing

electron-likeobjectsandjetobjectsfor

reconstruct-ingthe\Z"bosonaresmallerhere.

Thenal shapeofthebackgroundis obtainedby

combiningtheCCCCandCCECsamples,weighted

bytherelativecontributionstothebackground. To

facilitatelater analysis,the shape is parameterized

as a function of p T

using the following functional

forms: a(p T +b) 2 e pT if (p T <8GeV) a( 1 p T ) 2 +be pT if (p T >8GeV) (13)

Thefunctionisnormalizedtobeaprobability

dis-tribution,thatistheproductofthefunctionandthe

totalnumberofbackgroundeventsresultsinthe

dif-ferential background in each bin of p T

. Figure 18

shows the resultsof thet to the background and

TableII showsthevaluesofthetparameters.

C.OtherSourcesofDielectron Signal

AlthoughZ !eeandQCDmultijet eventsmake