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Measurement of spin correlation between top and antitop quarks produced in p(p)over-bar collisions at root s=1.96 TeV

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

spin

correlation

between

top

and

antitop

quarks

produced

in

p

p collisions

¯

at

s

=

1

.

96 TeV

D0

Collaboration

1

V.M. Abazov

af

,

B. Abbott

bp

,

B.S. Acharya

z

,

M. Adams

au

,

T. Adams

as

,

J.P. Agnew

ap

,

G.D. Alexeev

af

,

G. Alkhazov

aj

,

A. Alton

be

,

2

,

A. Askew

as

,

S. Atkins

bc

,

K. Augsten

g

,

V. Aushev

am

,

Y. Aushev

am

,

C. Avila

e

,

F. Badaud

j

,

L. Bagby

at

,

B. Baldin

at

,

D.V. Bandurin

bw

,

S. Banerjee

z

,

E. Barberis

bd

,

P. Baringer

bb

,

J.F. Bartlett

at

,

U. Bassler

o

,

V. Bazterra

au

,

A. Bean

bb

,

M. Begalli

b

,

L. Bellantoni

at

,

S.B. Beri

x

,

G. Bernardi

n

,

R. Bernhard

t

,

I. Bertram

an

,

M. Besançon

o

,

R. Beuselinck

ao

,

P.C. Bhat

at

,

S. Bhatia

bg

,

V. Bhatnagar

x

,

G. Blazey

av

,

S. Blessing

as

,

K. Bloom

bh

,

A. Boehnlein

at

,

D. Boline

bm

,

E.E. Boos

ah

,

G. Borissov

an

,

M. Borysova

am

,

13

,

A. Brandt

bt

,

O. Brandt

u

,

R. Brock

bf

,

A. Bross

at

,

D. Brown

n

,

X.B. Bu

at

,

M. Buehler

at

,

V. Buescher

v

,

V. Bunichev

ah

,

S. Burdin

an

,

3

,

C.P. Buszello

al

,

E. Camacho-Pérez

ac

,

B.C.K. Casey

at

,

H. Castilla-Valdez

ac

,

S. Caughron

bf

,

S. Chakrabarti

bm

,

K.M. Chan

az

,

A. Chandra

bv

,

E. Chapon

o

,

G. Chen

bb

,

S.W. Cho

ab

,

S. Choi

ab

,

B. Choudhary

y

,

S. Cihangir

at

,

D. Claes

bh

,

J. Clutter

bb

,

M. Cooke

at

,

12

,

W.E. Cooper

at

,

M. Corcoran

bv

,

F. Couderc

o

,

M.-C. Cousinou

l

,

J. Cuth

v

,

D. Cutts

bs

,

A. Das

bu

,

G. Davies

ao

,

S.J. de Jong

ad

,

ae

,

E. De La Cruz-Burelo

ac

,

F. Déliot

o

,

R. Demina

bl

,

D. Denisov

at

,

S.P. Denisov

ai

,

S. Desai

at

,

C. Deterre

ap

,

4

,

K. DeVaughan

bh

,

H.T. Diehl

at

,

M. Diesburg

at

,

P.F. Ding

ap

,

A. Dominguez

bh

,

A. Dubey

y

,

L.V. Dudko

ah

,

A. Duperrin

l

,

S. Dutt

x

,

M. Eads

av

,

D. Edmunds

bf

,

J. Ellison

ar

,

V.D. Elvira

at

,

Y. Enari

n

,

H. Evans

ax

,

A. Evdokimov

au

,

V.N. Evdokimov

ai

,

A. Fauré

o

,

L. Feng

av

,

T. Ferbel

bl

,

F. Fiedler

v

,

F. Filthaut

ad

,

ae

,

W. Fisher

bf

,

H.E. Fisk

at

,

M. Fortner

av

,

H. Fox

an

,

J. Franc

g

,

S. Fuess

at

,

P.H. Garbincius

at

,

A. Garcia-Bellido

bl

,

J.A. García-González

ac

,

V. Gavrilov

ag

,

W. Geng

l

,

bf

,

C.E. Gerber

au

,

Y. Gershtein

bi

,

G. Ginther

at

,

O. Gogota

am

,

G. Golovanov

af

,

P.D. Grannis

bm

,

S. Greder

p

,

H. Greenlee

at

,

G. Grenier

q

,

r

,

Ph. Gris

j

,

J.-F. Grivaz

m

,

A. Grohsjean

o

,

4

,

S. Grünendahl

at

,

M.W. Grünewald

aa

,

T. Guillemin

m

,

G. Gutierrez

at

,

P. Gutierrez

bp

,

J. Haley

bq

,

L. Han

d

,

K. Harder

ap

,

A. Harel

bl

,

J.M. Hauptman

ba

,

J. Hays

ao

,

T. Head

ap

,

T. Hebbeker

s

,

D. Hedin

av

,

H. Hegab

bq

,

A.P. Heinson

ar

,

U. Heintz

bs

,

C. Hensel

a

,

I. Heredia-De La Cruz

ac

,

5

,

K. Herner

at

,

G. Hesketh

ap

,

7

,

M.D. Hildreth

az

,

R. Hirosky

bw

,

T. Hoang

as

,

J.D. Hobbs

bm

,

B. Hoeneisen

i

,

J. Hogan

bv

,

M. Hohlfeld

v

,

J.L. Holzbauer

bg

,

I. Howley

bt

,

Z. Hubacek

g

,

o

,

V. Hynek

g

,

I. Iashvili

bk

,

Y. Ilchenko

bu

,

R. Illingworth

at

,

A.S. Ito

at

,

S. Jabeen

at

,

14

,

M. Jaffré

m

,

A. Jayasinghe

bp

,

M.S. Jeong

ab

,

R. Jesik

ao

,

P. Jiang

d

,

,

K. Johns

aq

,

E. Johnson

bf

,

M. Johnson

at

,

A. Jonckheere

at

,

P. Jonsson

ao

,

J. Joshi

ar

,

A.W. Jung

at

,

16

,

A. Juste

ak

,

E. Kajfasz

l

,

O. Karacheban

am

,

D. Karmanov

ah

,

I. Katsanos

bh

,

M. Kaur

x

,

R. Kehoe

bu

,

S. Kermiche

l

,

N. Khalatyan

at

,

A. Khanov

bq

,

A. Kharchilava

bk

,

Y.N. Kharzheev

af

,

I. Kiselevich

ag

,

J.M. Kohli

x

,

A.V. Kozelov

ai

,

J. Kraus

bg

,

A. Kumar

bk

,

A. Kupco

h

,

T. Kurˇca

q

,

r

,

V.A. Kuzmin

ah

,

S. Lammers

ax

,

P. Lebrun

q

,

r

,

H.S. Lee

ab

,

S.W. Lee

ba

,

W.M. Lee

at

,

X. Lei

aq

,

J. Lellouch

n

,

D. Li

n

,

H. Li

bw

,

L. Li

ar

,

Q.Z. Li

at

,

J.K. Lim

ab

,

D. Lincoln

at

,

J. Linnemann

bf

,

V.V. Lipaev

ai

,

R. Lipton

at

,

H. Liu

bu

,

Y. Liu

d

,

A. Lobodenko

aj

,

M. Lokajicek

h

,

http://dx.doi.org/10.1016/j.physletb.2016.03.053

0370-2693/©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

(2)

R. Lopes de Sa

at

,

R. Luna-Garcia

ac

,

8

,

A.L. Lyon

at

,

A.K.A. Maciel

a

,

R. Madar

t

,

R. Magaña-Villalba

ac

,

S. Malik

bh

,

V.L. Malyshev

af

,

J. Mansour

u

,

J. Martínez-Ortega

ac

,

R. McCarthy

bm

,

C.L. McGivern

ap

,

M.M. Meijer

ad

,

ae

,

A. Melnitchouk

at

,

D. Menezes

av

,

P.G. Mercadante

c

,

M. Merkin

ah

,

A. Meyer

s

,

J. Meyer

u

,

10

,

F. Miconi

p

,

N.K. Mondal

z

,

M. Mulhearn

bw

,

E. Nagy

l

,

M. Narain

bs

,

R. Nayyar

aq

,

H.A. Neal

be

,

J.P. Negret

e

,

P. Neustroev

aj

,

H.T. Nguyen

bw

,

T. Nunnemann

w

,

J. Orduna

bv

,

N. Osman

l

,

J. Osta

az

,

A. Pal

bt

,

N. Parashar

ay

,

V. Parihar

bs

,

S.K. Park

ab

,

R. Partridge

bs

,

6

,

N. Parua

ax

,

A. Patwa

bn

,

11

,

B. Penning

ao

,

M. Perfilov

ah

,

Y. Peters

ap

,

K. Petridis

ap

,

G. Petrillo

bl

,

P. Pétroff

m

,

M.-A. Pleier

bn

,

V.M. Podstavkov

at

,

A.V. Popov

ai

,

M. Prewitt

bv

,

D. Price

ap

,

N. Prokopenko

ai

,

J. Qian

be

,

A. Quadt

u

,

B. Quinn

bg

,

P.N. Ratoff

an

,

I. Razumov

ai

,

I. Ripp-Baudot

p

,

F. Rizatdinova

bq

,

M. Rominsky

at

,

A. Ross

an

,

C. Royon

h

,

P. Rubinov

at

,

R. Ruchti

az

,

G. Sajot

k

,

A. Sánchez-Hernández

ac

,

M.P. Sanders

w

,

A.S. Santos

a

,

9

,

G. Savage

at

,

M. Savitskyi

am

,

L. Sawyer

bc

,

T. Scanlon

ao

,

R.D. Schamberger

bm

,

Y. Scheglov

aj

,

H. Schellman

aw

,

br

,

M. Schott

v

,

C. Schwanenberger

ap

,

R. Schwienhorst

bf

,

J. Sekaric

bb

,

H. Severini

bp

,

E. Shabalina

u

,

V. Shary

o

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S. Shaw

ap

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A.A. Shchukin

ai

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V. Simak

g

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P. Skubic

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P. Slattery

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D. Smirnov

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G.R. Snow

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J. Snow

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S. Snyder

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S. Söldner-Rembold

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L. Sonnenschein

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K. Soustruznik

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J. Stark

k

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N. Stefaniuk

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D.A. Stoyanova

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M. Strauss

bp

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L. Suter

ap

,

P. Svoisky

bw

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M. Titov

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V.V. Tokmenin

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Y.-T. Tsai

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D. Tsybychev

bm

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B. Tuchming

o

,

C. Tully

bj

,

L. Uvarov

aj

,

S. Uvarov

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,

S. Uzunyan

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R. Van Kooten

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W.M. van Leeuwen

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bd

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n

aLAFEX,CentroBrasileirodePesquisasFísicas,RiodeJaneiro,Brazil bUniversidadedoEstadodoRiodeJaneiro,RiodeJaneiro,Brazil cUniversidadeFederaldoABC,SantoAndré,Brazil

dUniversityofScienceandTechnologyofChina,Hefei,People’sRepublicofChina eUniversidaddelosAndes,Bogotá,Colombia

fCharlesUniversity,FacultyofMathematicsandPhysics,CenterforParticlePhysics,Prague,CzechRepublic gCzechTechnicalUniversityinPrague,Prague,CzechRepublic

hInstituteofPhysics,AcademyofSciencesoftheCzechRepublic,Prague,CzechRepublic iUniversidadSanFranciscodeQuito,Quito,Ecuador

jLPC,UniversitéBlaisePascal,CNRS/IN2P3,Clermont,France

kLPSC,UniversitéJosephFourierGrenoble1,CNRS/IN2P3,InstitutNationalPolytechniquedeGrenoble,Grenoble,France lCPPM,Aix-MarseilleUniversité,CNRS/IN2P3,Marseille,France

mLAL,Univ.Paris-Sud,CNRS/IN2P3,UniversitéParis-Saclay,Orsay,France nLPNHE,UniversitésParisVIandVII,CNRS/IN2P3,Paris,France oCEA,Irfu,SPP,Saclay,France

pIPHC,UniversitédeStrasbourg,CNRS/IN2P3,Strasbourg,France qIPNL,UniversitéLyon1,CNRS/IN2P3,Villeurbanne,France rUniversitédeLyon,Lyon,France

sIII.PhysikalischesInstitutA,RWTHAachenUniversity,Aachen,Germany tPhysikalischesInstitut,UniversitätFreiburg,Freiburg,Germany

uII.PhysikalischesInstitut,Georg-August-UniversitätGöttingen,Göttingen,Germany vInstitutfürPhysik,UniversitätMainz,Mainz,Germany

wLudwig-Maximilians-UniversitätMünchen,München,Germany xPanjabUniversity,Chandigarh,India

yDelhiUniversity,Delhi,India

zTataInstituteofFundamentalResearch,Mumbai,India aaUniversityCollegeDublin,Dublin,Ireland

abKoreaDetectorLaboratory,KoreaUniversity,Seoul,RepublicofKorea acCINVESTAV,MexicoCity,Mexico

adNikhef,SciencePark,Amsterdam,TheNetherlands aeRadboudUniversityNijmegen,Nijmegen,TheNetherlands afJointInstituteforNuclearResearch,Dubna,Russia

agInstituteforTheoreticalandExperimentalPhysics,Moscow,Russia ahMoscowStateUniversity,Moscow,Russia

aiInstituteforHighEnergyPhysics,Protvino,Russia ajPetersburgNuclearPhysicsInstitute,St.Petersburg,Russia

(3)

alUppsalaUniversity,Uppsala,Sweden

amTarasShevchenkoNationalUniversityofKyiv,Kiev,Ukraine anLancasterUniversity,LancasterLA14YB,UnitedKingdom aoImperialCollegeLondon,LondonSW72AZ,UnitedKingdom apTheUniversityofManchester,ManchesterM139PL,UnitedKingdom aqUniversityofArizona,Tucson,AZ 85721,USA

arUniversityofCaliforniaRiverside,Riverside,CA 92521,USA asFloridaStateUniversity,Tallahassee,FL 32306,USA atFermiNationalAcceleratorLaboratory,Batavia,IL 60510,USA auUniversityofIllinoisatChicago,Chicago,IL 60607,USA avNorthernIllinoisUniversity,DeKalb,IL 60115,USA awNorthwesternUniversity,Evanston,IL 60208,USA axIndianaUniversity,Bloomington,IN 47405,USA ayPurdueUniversityCalumet,Hammond,IN 46323,USA azUniversityofNotreDame,NotreDame,IN 46556,USA baIowaStateUniversity,Ames,IA 50011,USA bbUniversityofKansas,Lawrence,KS 66045,USA bcLouisianaTechUniversity,Ruston,LA 71272,USA bdNortheasternUniversity,Boston,MA 02115,USA be

UniversityofMichigan,AnnArbor,MI 48109,USA

bfMichiganStateUniversity,EastLansing,MI 48824,USA bgUniversityofMississippi,University,MS 38677,USA bhUniversityofNebraska,Lincoln,NE 68588,USA biRutgersUniversity,Piscataway,NJ 08855,USA bjPrincetonUniversity,Princeton,NJ 08544,USA bkStateUniversityofNewYork,Buffalo,NY 14260,USA blUniversityofRochester,Rochester,NY 14627,USA bmStateUniversityofNewYork,StonyBrook,NY 11794,USA bnBrookhavenNationalLaboratory,Upton,NY 11973,USA boLangstonUniversity,Langston,OK 73050,USA bpUniversityofOklahoma,Norman,OK 73019,USA bqOklahomaStateUniversity,Stillwater,OK 74078,USA brOregonStateUniversity,Corvallis,OR 97331,USA bsBrownUniversity,Providence,RI 02912,USA btUniversityofTexas,Arlington,TX 76019,USA buSouthernMethodistUniversity,Dallas,TX 75275,USA bvRiceUniversity,Houston,TX 77005,USA

bwUniversityofVirginia,Charlottesville,VA 22904,USA bxUniversityofWashington,Seattle,WA 98195,USA

a

r

t

i

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l

e

i

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f

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a

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s

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Articlehistory:

Received31December2015

Receivedinrevisedform24February2016 Accepted18March2016

Availableonline25March2016 Editor:M.Doser

Wepresentameasurementofthecorrelationbetweenthespinsoft andt quarks¯ producedinproton– antiprotoncollisionsattheTevatronCollideratacenter-of-massenergyof1.96 TeV.Weapplyamatrix elementtechniquetodileptonandsingle-lepton+jetsfinalstatesindataaccumulatedwiththeD0 de-tectorthat correspondtoanintegratedluminosity of9.7 fb−1.Themeasuredvalue ofthecorrelation coefficientintheoff-diagonalbasis, Ooff=0.89±0.22(stat+syst),isinagreementwiththestandard

modelprediction,andrepresentsevidenceforatop–antitopquarkspincorrelationdifferencefromzero atalevelof4.2standarddeviations.

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

E-mailaddress:Viatcheslav.Sharyy@cea.fr(V. Shary). 1 withvisitorsfrom:

2 AugustanaCollege,SiouxFalls,SD,USA. 3 TheUniversityofLiverpool,Liverpool,UK. 4 DESY,Hamburg,Germany.

5 CONACyT,MexicoCity,Mexico. 6 SLAC,MenloPark,CA,USA.

7 UniversityCollegeLondon,London,UK.

8 CentrodeInvestigacionenComputacionIPN,MexicoCity,Mexico. 9 UniversidadeEstadualPaulista,SãoPaulo,Brazil.

10 Karlsruher Institut für Technologie (KIT) Steinbuch Centre for Computing (SCC),D-76128Karlsruhe,Germany.

11 OfficeofScience,U.S.DepartmentofEnergy,Washington,D.C.20585,USA. 12 AmericanAssociationfortheAdvancementofScience,Washington,D.C.20005, USA.

13 KievInstituteforNuclearResearch,Kiev,Ukraine. 14 UniversityofMaryland,CollegePark,MD20742,USA.

15 EuropeanOrganization forNuclearResearch(CERN),Geneva,Switzerland. 16 PurdueUniversity,WestLafayette,IN47907,USA.

Deceased.

1. Introduction

The topquark is theheaviest elementary particleinthe stan-dard model (SM) [1–4]. Despite the fact that the top quark de-cays weakly, its large mass leads to a very short lifetime of

5

·

10−25s [5–7].It decaysto a W bosonandab quarkbefore hadronizing,aprocess thathasa characteristictime of1

/

QCD

(

200 MeV

)

−1 equivalent to

τ

had

3

.

3

·

10−24s, where



QCD is

the fundamental scale of quantum chromodynamics (QCD). The topquarklifetimeisalsosmallerthanthespin-decorrelationtime from spin–spin interactions with the light quarks generated in the fragmentationprocess [8],

τ

spin

mt

/

2QCD

≈ (

0

.

2 MeV

)

−1

3

·

10−21s [9].The topquark thusprovidesa uniqueopportunity

tomeasurespin-relatedphenomenainthequarksectorby exploit-ingkinematicpropertiesofitsdecayproducts.

Inproton–antiproton (pp)

¯

collisions, thedominantprocess for producingtopquarksisthroughtop–antitop( tt )

¯

quarkpairs.This QCDprocessyieldsunpolarizedt and

¯

t quarks,butleavesthespins

(4)

oft and

¯

t correlated.Aspincorrelationobservablecanbedefined as[10]

Oab

= 

4

(

St

· ˆ

a

)(

S¯t

· ˆ

b

)

 =

σ

(

↑↑) +

σ

(

↓↓) −

σ

(

↑↓) −

σ

(

↓↑)

σ

(

↑↑) +

σ

(

↓↓) +

σ

(

↑↓) +

σ

(

↓↑)

,

where S is a spin operator, a,

ˆ

b are

ˆ

the spin quantization axes for the top quark (a)

ˆ

and the antitop quark (b),

ˆ



refers to an expectation value,

σ

is the t

¯

t production cross section, andthe arrows refer to the spin states of the t and

¯

t quarks relative to thea and

ˆ

b axes.

ˆ

The strengthofthe correlationdependsonthe

tt production

¯

mechanism[11–13].In pp collisions

¯

ata center-of-mass energyof 1.96 TeV, the correlation of spinsis predictedto be Ooff

=

0

.

80+00..0102 [10] in the off-diagonal spin basis, the

ba-sis in which the strength of the spin correlation is maximal at the Tevatron [12]. The most significant contribution is from the quark–antiquarkannihilationprocess (qq

¯

t

¯

t)witha spin corre-lationstrengthof

0

.

99,whilethe gluon–gluon(gg) fusion pro-cess(gg

t

¯

t)hasanticorrelatedspinswithatypical strengthof

≈ −

0

.

36 atnext-to-leadingorder(NLO)inQCD[10,14,15]. Contri-butions to t

¯

t productionfrom beyondthe SM can have different dynamicsthataffectthestrengthofthett spin

¯

correlation.

Evidence for t

¯

t spin correlations based on a matrix element technique [16], was presented by the D0 collaboration. Earlier lower precision measurements used a template method [17,18]. Spincorrelationeffectshavealsobeenmeasuredinproton–proton (pp) collisions by two LHC collaborations, ATLAS and CMS, at a center-of-massenergyof7 TeV[19–22]andat8 TeV[23,24].The mainmechanismfort

¯

t productionattheLHCisthegg fusion pro-cess.ThespincorrelationattheLHCarisesmainlyfromthefusion of like-helicity gluons [25]. The differences between pp and pp

¯

incidentchannels,thedifferentsourcesofspincorrelation(quark– antiquarkannihilationversuslike-helicitygg fusion),andtheir dif-ferentcollision energies,make themeasurements of thestrength of the spin correlation at both the Tevatron and LHC interesting andcomplementary.

In this letter, we present an updated measurement of the tt

¯

spin correlation strength in pp collisions

¯

at

s

=

1

.

96 TeV. The measurement uses the statistics accumulated during 2001–2011 data taking period of the Fermilab Tevatron Collider, which cor-respondstoanintegratedluminosityof9

.

7 fb−1,whichisalmost twotimesmorethaninourpreviouspublication[16].

2. Detector,eventselectionandsimulation,background

The D0 detector is described in Refs. [26–32]. It has a cen-traltracking systemconsistingofa siliconmicrostrip trackerand a central fiber tracker, both located within an

2 T supercon-ductingsolenoidalmagnet.Thecentraltrackingsystemisdesigned tooptimizetrackingandvertexingatdetectorpseudorapiditiesof

|

η

det

|

<

2

.

5.1 The liquid-argonsamplingcalorimeterhasa central

sectioncovering pseudorapidities

|

η

det

|

upto

1

.

1,andtwo end

calorimeters that extend coverage to

|

η

det

|

4

.

2, with all three

housed in separate cryostats. A outer muon system, with pseu-dorapidity coverage of

|

η

det

|

<

2, consists of a layer of tracking

detectors andscintillation trigger counters in front of 1

.

8 T iron toroids,followedbytwosimilarlayersafterthetoroids.

WithintheSM, the top quark decayswithalmost 100% prob-abilityinto a W bosonanda b quark.We alsoincludetwo final

1 Thepseudorapidityisdefinedasη= −ln[tan(θ/2)],whereθisthepolarangle ofthereconstructedparticleoriginatingfromthe pp collision¯ vertex,relativetothe protonbeamdirection.Detectorpseudorapidityηdetisdefinedrelativetothecenter ofthedetector.

states:thedileptonfinalstate(



),wherebothW bosonsdecayto leptons,andthelepton

+

jetsfinalstate(



+

jets),whereoneofthe

W bosonsdecaysintoapairofquarksandonedecaystoalepton and a neutrino. The

+

jets and



final states contain, respec-tively,oneortwoisolatedchargedleptons.Inbothfinalstateswe consideronlyelectronsandmuons,includingthosefrom

τ

-lepton decay, W

τ ν

τ

→ 

νν

τ . We also require the presence of two b quarkjets,twolight-quarkjetsfromW decay(in



+

jets),anda significantmissingtransversemomentum(

/

pT)duetotheescaping neutrinos.

We usethefollowingselection criteria.Inthe



channels, we require two isolated leptons with pT

>

15 GeV, both originating fromthesamepp interaction

¯

vertex.The

+

jets channelsrequire one isolatedleptonwith pT

>

20 GeV.Weconsiderelectronsand muons identified using the standard D0 criteria [33,34], in the pseudorapidityrangeof

|

η

det

|

<

2

.

0 formuons,and

|

η

det

|

<

1

.

1 for

electrons.Inthe



channels,weconsiderinadditionforward elec-tronsintherangeof1

.

5

<

|

η

det

|

<

2

.

5.Jetsarereconstructedand

identified from energydeposition in the calorimeterusing an it-erativemidpointconealgorithm[35]ofradius



( φ)

2

+ (

η

)

2

=

0

.

5.Theirenergiesarecorrectedusingthejetenergyscale(JES) al-gorithm [36].All



channelsalsorequirethepresenceofatleast two jets with pT

>

20 GeV and

|

η

det

|

<

2

.

5. Forthe

+

jets final

state, atleastfourjetsmust be identifiedwiththe same pT and

η

detcutoffs,butwiththeleadingjetrequiredtohavepT

>

40 GeV. When a muon track is found within a jet cone, the JES calcu-lation takes that muon momentum into account, assuming that themuonoriginatesfromthesemileptonicdecayofaheavy-flavor hadron belonging to the jet. To identify b quark jets, we use a multivariate b quarkjet identificationdiscriminantthat combines informationfromtheimpactparametersofthetracksandvariables thatcharacterizethepresenceandpropertiesofsecondaryvertices withinthejet[37].Werequirethatatleastonejetisidentifiedas a b quark jet in the



channels, and at least two such jets in the



+

jets channels.Toimprovesignalpurity,additionalselections basedontheglobaleventtopologyareapplied [38,39]ineach fi-nalstate.Adetaileddescriptionofeventselectioncanbefoundin Ref.[38]forthe



andinRef.[39]forthe



+

jets finalstates.

To simulatet

¯

t eventswe use the next-to-leading(NLO) order MonteCarlo(MC)QCDgeneratormc@nlo(version 3.4)[40,41], in-terfacedto herwig (version 6.510) [42]forpartonshoweringand hadronization. The CTEQ6M parton distribution functions (PDF)

[43,44] are usedto generateeventsata top quark massofmt

=

172

.

5 GeV. We use two samples, one including spin correlation effects, and the other without correlation. The generated events are processed through a geant3-based[45] simulationof theD0 detector.Tosimulateeffectsfromadditionaloverlapping pp inter-

¯

actions, “zero bias” events taken fromcollider data with an un-biassedtriggerbasedsolelyonbeambunchcrossingsareoverlaid onthesimulatedevents.Simulatedeventsarethenprocessedwith thesamereconstructionprogramasdata.

Inthe



channels, themainsources ofbackgroundareDrell– Yanproduction,qq

¯

Z

/

γ

→ 

,dibosonW W ,W Z ,Z Z

produc-tion, and instrumental background.The instrumental background arisesmainly frommultijetand

(

W

→ 

ν

)+

jetsevents,inwhich one jet in W

+

jets or two jets in multijet events are misidenti-fied as electrons, or where muonsor electrons originating from semileptonicdecayofheavy-flavor hadronsappeartobe isolated. The instrumental backgroundis determined fromdata,while the other backgrounds are estimated using MC simulations. For the



+

jets channel, in addition to the Drell–Yan and diboson pro-duction, the contribution from W

+

jets production is estimated from MC simulation, but normalized to data. Electroweak single top quark productionandtt dilepton

¯

final statesare also consid-ered as background.The Drell–Yanand

(

W

→ 

ν

)+

jets samples

(5)

Table 1

Numbersofexpectedevents,andnumbersofeventsfoundindata.

Z/γ Instrumental Diboson t¯t Total Data

13.2 16.4 3.7 303.4 336.7 347

ee 12.2 1.8 1.9 102.4 118.3 105

μμ 9.8 0.0 1.7 85.0 96.5 93

W+jets Multijet Other

e+jets 22.7 23.1 15.3 427.4 488.6 534

μ+jets 24.1 3.5 11.6 341.4 380.6 440

aregenerated with theleading order (LO) matrixelement gener-ator alpgen (version v2.11) [46], interfaced to pythia [47] (ver-sion 6.409, D0 modified tune A [48]) for parton showering and hadronization. Diboson events are generated with pythia. More detailsaboutbackgroundestimationcanbefoundinRefs.[38,39].

Table 1showsthenumberofexpectedeventsforeachbackground source and for the signal, and the number of selected events in data. The number of the expected tt events

¯

is normalized to the NLO cross section of 7

.

45+00..4867pb [49]. The observed num-ber ofeventsin the



+

jets channelis higherthan the expected, mainlyduetoanexcessinthe

μ

+

jetschannel.Theexpectedand observed number of events are consistent when the systematic uncertainties,partiallycorrelatedbetweenthe

+

jets and



chan-nels,are takeninto account.These uncertainties areof theorder of 10%. The most important contributions are the integrated lu-minosity,b-quark jet modeling,uncertainties on thet

¯

t modeling

anduncertaintyintheheavyflavor NLO K -factorsofthe W

+

jets backgroundinthe



+

jets channel.

3. Measurementtechniqueandresults

Ourmeasurementusesthesamematrixelement(ME)approach as Refs. [16,50], adapted to the spin correlation measurement. Thismethod consistsofcalculating thespin correlation discrimi-nant[51]

R

(

x

)

=

Ptt¯

(

x

,

SM

)

Pt¯t

(

x

,

SM

)

+

Pt¯t

(

x

,

null

)

,

(1)

where Pt¯t

(

x

,

H )

is aper-event probability forhypothesis

H

for the vector of the reconstructed object parameters x. Hypothesis

H =

SM assumesthet

¯

t spincorrelationstrengthpredictedbythe SM,and

H =

null assumesuncorrelatedspins.Theseprobabilities arecalculatedfromtheintegral

Ptt¯

(

x

,

H

)

=

1

σ

obs



fPDF

(

q1

)

fPDF

(

q2

)

×

(

2

π

)

4

|

M

(

y

,

H

)

|

2 q1q2s W

(

x

,

y

)

d



6dq1dq2

.

(2)

Here,q1 and q2 represent the respectivefractions of proton and

antiproton momentum carried by the initial state partons, fPDF

representsthepartondistributionfunctions,s isthesquare ofthe

pp center-of-mass

¯

energy,andy referstopartonicfinalstate four-momentaoftheparticles.Thedetectortransferfunctions,W

(

x

,

y

)

, correspondtotheprobabilitytoreconstructfour-momenta y asx, d



6representsthesix-bodyphasespace,and

σ

obs istheobserved tt production

¯

cross section, calculated using

M (H =

null

)

, tak-inginto account theefficiency oftheselection. The same

σ

obs is

usedfor

H =

null and

H =

SM hypotheses, becausethe differ-enceinobserved cross-sectionsis small, at theorder ofpercent, andaffectsonly theseparationpowerofthediscriminant R.This calculation uses the LO matrix element

M (

y

,

H )

for the pro-cesses qq

¯

t

¯

t

W+Wbb

¯

→ 

±

ν

qqbb or

¯



+



ν

ν

¯

bb,

¯

calcu-latedaccordingtothespin correlationhypothesis

H

.Thematrix

Fig. 1. Distribution of the spin correlation discriminant R in data and for the mc@nlot¯t predictionwithbackground,showingthemergedresultsfromand +jets events.Thelowerplotrepresentsthedifferencebetweendataand simula-tionwithSMspincorrelationandwithoutspincorrelation.Theerrorbars corre-spondtostatisticaluncertainties.

element

M

is averaged over the colors and spins of the initial partons,andsummedoverthe finalcolors andspins. Forthe hy-pothesis

H =

null,wesetthespincorrelationparttozero[11,12]. In the calculation, we assume perfect measurements of the lep-tonandjetdirections,andperfectmeasurementofelectronenergy, whichreducesthenumberofdimensionsthat requireintegration. Theprobabilityisobtainedbyintegratingovertheremaining kine-matic variables.In the



final state,we use thetop andantitop quark masses, W+ and W− boson masses, pT oftwo jets, 1

/

pT foranymuonsand pT and

φ

ofthett system

¯

asintegration vari-ables.Inthe

+

jets finalstate,thevariablesarethetopandantitop quark masses, the mass of the W boson decaying to qq

¯

, pT of thed-typequarkjet,pzoftheleptonicallydecayingtopquarkand 1

/

pT ofamuon.Giventheinabilitytoknowtheflavorofthetwo quarksfromtheW bosondecay,orwhichb-taggedjetoriginates fromthedecayofthetoporanti-topquark,allpossiblejet-parton assignments areconsideredand Pt¯t iscalculatedasthesumover alltheprobabilities.

The distributions in the discriminant R of Eq. (1) are calcu-lated forsimulated t

¯

t events withSM spin correlation andwith uncorrelatedspins.Theseandtheexpectedcontributionsfromthe backgroundeventsareused astemplates tofitthe R distribution

in data through a binned maximum-likelihood fit with two free parameters:thet

¯

t productioncrosssection

σ

t¯t,andthemeasured fractionofeventswiththeSMspincorrelationstrength, f .

This fit of the distributions in the



and



+

jets channels is performedsimultaneously,withtheexpectednumberofeventsni ineachbini givenby

ni

=

σ

tt¯ 7

.

45 pb



f nSMi

+ (

1

f

)

ninull



+

nibckg

,

(3) whereni

SM andninull arethe numberofevents inbini based on

the mc@nlo prediction, with andwithout spin correlations, and

nibckg is the expected numberof background events in the same bin. We use a non-uniform bin width and require a sufficiently large number ofevents foreach binin order to avoidbins with zeroevents,asthey couldbiasthefitresult.Theexactnumberof bins andtheir sizewere optimized togive the smallestexpected statisticaluncertainty inthe caseof theSM spin correlation.We usethe samenumberandwidths ofthebins forthe



+

jets and



channelssoastokeepthebinoptimizationprocedurerelatively simple.Thefityields f

=

1

.

16

±

0

.

21

(

stat

)

.The R distributionfor the combined



and



+

jets channelsis showninFig. 1.We es-timatethesignificanceofthenon-zerospincorrelationhypothesis

(6)

Table 2

Systematicuncertainties(absolutevalues)onthespincorrelationstrengthOmeas

off .

Source Uncertainty in Omeas

off

Modeling of signal ±0.135

PDF ±0.027

Statistical fluctuations in MC ±0.026 Identification and reconstruction ±0.032

Background contribution ±0.019

Total ±0.15

usingtheFeldmanandCousinsfrequentistprocedure[52], assum-ing that the parameter f is inthe range

[

0

,

1

]

,even though the measuredvalueobtainedinthefitisoutsideoftherange

[

0

,

1

]

.

Totranslate the f valuetothespin correlationstrengthinthe off-diagonal basis Ooff, we must consider the value of the spin

correlation strength inthe simulation OMCoff. We choose toobtain this value in the simulated



samples from the expected value ofk1k2OMCoff

= −

9



cos

θ

1

·

cos

θ

2



[14], where

θ

1 and

θ

2 represent

anglesbetweenthe respectivedirectionofa positivelyand nega-tivelychargedlepton andthe spinquantizationaxesinthet and

¯

t rest frame. The parameters k1 andk2 are the spin

analyzing-powercoefficientsofthetopquark(equalto1forleptonsatLOin QCD)[53].Withmc@nlo,thevaluecalculatedfortheparton-level distributions before any selections is found to equal Omc@nlo

off

=

0

.

766 in the off-diagonal basis. The measured spin correlation strengthfor



+

jets and



channelsistherefore

Omeasoff

=

Omc@nlooff

·

f

=

0

.

89

±

0

.

16

(

stat

) ,

inagreementwiththeNLOQCDcalculation Ooff

=

0

.

80+00..0102 [10].

Foreventsinthe

+

jets channel,theresultis Ooff+jets

=

1

.

02

±

0

.

24

(

stat

) ,

andfor



channeltheresultis Ooff

=

0

.

80

±

0

.

22

(

stat

) .

We can reinterpret the measured fraction f as the related measurement of the spin correlation observable Ospin

= 

43

(

St

·

St¯

)



[10]. This observable characterizes the distribution in the opening angle,

ϕ

, between the directions of the two leptons in dileptoneventsorbetweentheleptonandtheup-typequarkfrom theW decayin



+

jets events,wherethedirectionsaredefinedin thet and

¯

t restframe:

1

σ

d

σ

d cos

ϕ

=

1 2

(

1

k1k2Ospincos

ϕ

).

(4)

Thepredictionfromthemc@nlosimulationisgivenbythe expec-tationvaluek1k2Omc@nlospin

= −

3



cos

ϕ



atthepartonlevel,without

anyselections, andfound to be Omc@nlospin

=

0

.

20. The value mea-suredfromdataistherefore

Omeasspin

=

Omc@nlospin

·

f

=

0

.

23

±

0

.

04

(

stat

),

consistent with the NLO QCD calculation of Ospin

=

0

.

218

±

0

.

002[10].

4. Systematicuncertainties

The estimatedsystematicuncertainties are summarizedin Ta-ble 2. These are obtainedby replacingthe nominal tt and

¯

back-groundresultswithmodifiedtemplates,refittingthedataand de-terminingthenewfraction f .

We consider several sources ofuncertainties in the modeling of thesignal. Theseinclude initial-stateand final-state radiation,

thesimulationofhadronizationandunderlyingevents,theeffects ofhigher-ordercorrections,color-reconnectionanduncertaintyon thetopquarkmass.Thedetailsofthecorresponding samplesand parametersarediscussedinRefs.[1,2].

ForthePDFuncertainty,wechangethe20CTEQ6eigenvectors independently and add the resulting uncertainties in quadrature. In modelingboth theestimatedsignal andPDF uncertainties, the eventsampleshave differentfractionalcontributions from gg

fu-sion and qq annihilation,

¯

and thereforedifferent spin-correlation strengths.Wetakethisintoaccountbynormalizingthemeasured fraction to the spin-correlation strength of the sample OMCoff, in a way similar to that usedfor the nominalmeasurement O off

=

f

·

OMCoff.

The statisticaluncertainty inMC templates is estimatedusing the ensemble testing technique. The new ensembles are created through arandomgeneration ofa newnumberofeventsineach bin of the MC template assuming a Gaussian distribution in the numberofeventsinthebin.Thesamedistributionindataisfitted withthe modified templates andthe dispersion inthefit results over1000ensemblesisusedasanestimationofthestatistical un-certaintyintheMCtemplates.

Theuncertaintyonidentificationandreconstructioneffects in-cludes uncertainties on lepton, jet and b tagging identification efficiencies,jet energyresolutionandscalecorrections, trigger ef-ficiencies, andthe luminosity.The uncertaintyinthe background contributions includes all uncertainties that affect the signal-to-backgroundratiothatarenotcontainedinthepreviouscategories. These uncertainties includeuncertainties intheoretical cross sec-tionsforbackgrounds,uncertaintyinZ boson pT distribution,and uncertaintiesininstrumentalbackgroundcontributions.

The total absolutesystematic uncertaintyon the spin correla-tionobservable Omeasoff ,calculatedasaquadraticsumoverall indi-vidualsources,is0

.

15,asshowninTable 2.

5. Spincorrelationandthe tt production

¯

mechanism

The strength of the tt spin

¯

correlation in the SM is strongly dependent on thet

¯

t productionmechanism. The spin correlation measurement thus provides a way of measuring the fraction of events produced via gg fusion, fgg [13].The fgg fraction is not well defined at orders higher than LO QCD. The difficulty arises fromthefactthatthecrosssectionsforthegq

ttq and

¯

gq

¯

tt

¯

q

¯

processes at LO, as well as gg and qq production

¯

at NLO, con-tain a singularitywhenthefinal state quark iscollinearwiththe quarkintheinitialstate.Thismakestheintegrationoverthephase spacedivergent[15,54,55].Inpractice,thissingularityisabsorbed intothedefinitionofthePDF,butthefinal resultsdependonthe schemeused forregularization.FortheNLO PDF, theMS scheme is usuallypreferred. The gq and gq contribution

¯

atNLO isofthe orderofafewpercent[10,14,15],andconsideringthattheoverall spin correlation strengthis

80%, we neglectthesesmaller con-tributions,anddetermine fgg fromtherelation

O

= (

1

fgg

)

Oqq¯

+

fggOgg

.

Assuming Oqq¯

1,thegluonfractionbecomes fgg

1

O

1

Ogg

,

where O is the measured value of the total spin correlation strength,andOgg istheSM valueofthespincorrelationstrength forgg events.

The NLO calculation in the off-diagonal basis using the CT10 PDF yields Ogg

= −

0

.

36

±

0

.

02[10,14,15].The systematic uncer-tainty on the observable O can be translated to the uncertainty

(7)

onthegluonfractionthatincludesanadditionalcontributionfrom thetheoreticaluncertaintyonOgg.Intheabsenceofnon-SM con-tributions,thefractionoft

¯

t eventsproducedthroughgluonfusion becomes

fgg

=

0

.

08

±

0

.

12

(

stat

)

±

0

.

11

(

syst

)

=

0

.

08

±

0

.

16

(

stat

+

syst

) ,

inagreementwiththeNLOpredictionof fgg

=

0

.

135[10,14,15]. 6. Summary

Wehavepresentedanupdatedmeasurementoftt spin

¯

correla-tionswiththeD0detectorforanintegratedluminosityof9

.

7 fb−1. Theresultofthe measurementofthestrengthofthet

¯

t spin cor-relationintheoff-diagonalbasisis

Ooff

=

0

.

89

±

0

.

16

(

stat

)

±

0

.

15

(

syst

)

=

0

.

89

±

0

.

22

(

stat

+

syst

).

Thisresultisin agreementwiththe NLO QCD calculation Ooff

=

0

.

80+00..0102 [10]andsupersedesthatreportedinRef.[16].Usingthe Feldman and Cousins approach for interval setting [52], and as-suminguncorrelatedtt spins,

¯

weestimate a probability (p-value) of2

.

5

×

10−5 forobtaining a spincorrelation largerthanthe

ob-servedvalue. Thiscorresponds toevidenceforspin correlationin

tt events

¯

atasignificanceof4

.

2 standarddeviations.

Inthe absenceof non-SMcontributions, we usethe spin cor-relationstrengthmeasurementto constrainthefractionofevents producedthroughgluonfusionatNLOQCDandobtain

fgg

=

0

.

08

±

0

.

16

(

stat

+

syst

) ,

ingoodagreementwithSMprediction. Acknowledgments

Wethankthe staffsatFermilab andcollaborating institutions, and acknowledge support from the Department of Energy and NationalScience Foundation (United States ofAmerica); Alterna-tive Energies and Atomic Energy Commission andNational Cen-terfor Scientific Research/ NationalInstitute ofNuclear and Par-ticle Physics (France); Ministry of Education and Science of the RussianFederation, NationalResearchCenter“KurchatovInstitute” of the Russian Federation, and Russian Foundation for Basic Re-search (Russia);National Council forthe Developmentof Science andTechnology andCarlos ChagasFilho Foundation for the Sup-port of Research in the State of Rio de Janeiro (Brazil); Depart-mentofAtomicEnergyandDepartmentofScienceandTechnology (India);AdministrativeDepartmentofScience,Technology and In-novation(Colombia); National Council of Science and Technology (Mexico); National Research Foundation of Korea (Korea); Foun-dation for Fundamental Research on Matter (The Netherlands); Science and Technology Facilities Council and The Royal Society (UnitedKingdom);MinistryofEducation,YouthandSports(Czech Republic);Bundesministeriumfür BildungundForschung(Federal Ministry of Education and Research) and Deutsche Forschungs-gemeinschaft (German Research Foundation) (Germany); Science FoundationIreland(Ireland);SwedishResearchCouncil (Sweden); ChinaAcademy ofSciences andNationalNaturalScience Founda-tion of China (China); and Ministry of Education and Science of Ukraine(Ukraine).

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Figure

Table 1 shows the number of expected events for each background source and for the signal, and the number of selected events in data

References

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