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Direct Measurement of the Mass Difference between Top and Antitop Quarks

V. M. Abazov,37B. Abbott,75M. Abolins,65B. S. Acharya,30M. Adams,51T. Adams,49E. Aguilo,6M. Ahsan,59 G. D. Alexeev,37G. Alkhazov,41A. Alton,64,*G. Alverson,63G. A. Alves,2L. S. Ancu,36T. Andeen,53M. S. Anzelc,53

M. Aoki,50Y. Arnoud,14M. Arov,60M. Arthaud,18A. Askew,49,†B. A˚ sman,42O. Atramentov,49,†C. Avila,8 J. BackusMayes,82F. Badaud,13L. Bagby,50B. Baldin,50D. V. Bandurin,59S. Banerjee,30E. Barberis,63A.-F. Barfuss,15

P. Bargassa,80P. Baringer,58J. Barreto,2J. F. Bartlett,50U. Bassler,18D. Bauer,44S. Beale,6A. Bean,58M. Begalli,3 M. Begel,73C. Belanger-Champagne,42L. Bellantoni,50A. Bellavance,50J. A. Benitez,65S. B. Beri,28G. Bernardi,17 R. Bernhard,23I. Bertram,43M. Besanc¸on,18R. Beuselinck,44V. A. Bezzubov,40P. C. Bhat,50V. Bhatnagar,28G. Blazey,52 S. Blessing,49K. Bloom,67A. Boehnlein,50D. Boline,62T. A. Bolton,59E. E. Boos,39G. Borissov,43T. Bose,62A. Brandt,78

R. Brock,65G. Brooijmans,70A. Bross,50D. Brown,19X. B. Bu,7D. Buchholz,53M. Buehler,81V. Buescher,22 V. Bunichev,39S. Burdin,43,‡T. H. Burnett,82C. P. Buszello,44P. Calfayan,26B. Calpas,15S. Calvet,16J. Cammin,71

M. A. Carrasco-Lizarraga,34E. Carrera,49W. Carvalho,3B. C. K. Casey,50H. Castilla-Valdez,34S. Chakrabarti,72 D. Chakraborty,52K. M. Chan,55A. Chandra,48E. Cheu,46D. K. Cho,62S. Choi,33B. Choudhary,29T. Christoudias,44

S. Cihangir,50D. Claes,67J. Clutter,58M. Cooke,50W. E. Cooper,50M. Corcoran,80F. Couderc,18M.-C. Cousinou,15 S. Cre´pe´-Renaudin,14D. Cutts,77M. C´ wiok,31A. Das,46G. Davies,44K. De,78S. J. de Jong,36E. De La Cruz-Burelo,34

K. DeVaughan,67F. De´liot,18M. Demarteau,50R. Demina,71D. Denisov,50S. P. Denisov,40S. Desai,50H. T. Diehl,50 M. Diesburg,50A. Dominguez,67T. Dorland,82A. Dubey,29L. V. Dudko,39L. Duflot,16D. Duggan,49A. Duperrin,15 S. Dutt,28A. Dyshkant,52M. Eads,67D. Edmunds,65J. Ellison,48V. D. Elvira,50Y. Enari,77S. Eno,61M. Escalier,15 H. Evans,54A. Evdokimov,73V. N. Evdokimov,40G. Facini,63A. V. Ferapontov,59T. Ferbel,61,71F. Fiedler,25F. Filthaut,36

W. Fisher,50H. E. Fisk,50M. Fortner,52H. Fox,43S. Fu,50S. Fuess,50T. Gadfort,70C. F. Galea,36C. Garcia,71 A. Garcia-Bellido,71V. Gavrilov,38P. Gay,13W. Geist,19W. Geng,15,65C. E. Gerber,51Y. Gershtein,49,†D. Gillberg,6

G. Ginther,50,71B. Go´mez,8A. Goussiou,82P. D. Grannis,72S. Greder,19H. Greenlee,50Z. D. Greenwood,60 E. M. Gregores,4G. Grenier,20Ph. Gris,13J.-F. Grivaz,16A. Grohsjean,18S. Gru¨nendahl,50M. W. Gru¨newald,31F. Guo,72 J. Guo,72G. Gutierrez,50P. Gutierrez,75A. Haas,70P. Haefner,26S. Hagopian,49J. Haley,68I. Hall,65R. E. Hall,47L. Han,7

K. Harder,45A. Harel,71J. M. Hauptman,57J. Hays,44T. Hebbeker,21D. Hedin,52J. G. Hegeman,35A. P. Heinson,48 U. Heintz,62C. Hensel,24I. Heredia-De La Cruz,34K. Herner,64G. Hesketh,63M. D. Hildreth,55R. Hirosky,81T. Hoang,49 J. D. Hobbs,72B. Hoeneisen,12M. Hohlfeld,22S. Hossain,75P. Houben,35Y. Hu,72Z. Hubacek,10N. Huske,17V. Hynek,10 I. Iashvili,69R. Illingworth,50A. S. Ito,50S. Jabeen,62M. Jaffre´,16S. Jain,75K. Jakobs,23D. Jamin,15R. Jesik,44K. Johns,46

C. Johnson,70M. Johnson,50D. Johnston,67A. Jonckheere,50P. Jonsson,44A. Juste,50E. Kajfasz,15D. Karmanov,39 P. A. Kasper,50I. Katsanos,67V. Kaushik,78R. Kehoe,79S. Kermiche,15N. Khalatyan,50A. Khanov,76A. Kharchilava,69

Y. N. Kharzheev,37D. Khatidze,70T. J. Kim,32M. H. Kirby,53M. Kirsch,21B. Klima,50J. M. Kohli,28J.-P. Konrath,23 A. V. Kozelov,40J. Kraus,65T. Kuhl,25A. Kumar,69A. Kupco,11T. Kurcˇa,20V. A. Kuzmin,39J. Kvita,9F. Lacroix,13 D. Lam,55S. Lammers,54G. Landsberg,77P. Lebrun,20W. M. Lee,50A. Leflat,39J. Lellouch,17J. Li,78,‡‡L. Li,48Q. Z. Li,50

S. M. Lietti,5J. K. Lim,32D. Lincoln,50J. Linnemann,65V. V. Lipaev,40R. Lipton,50Y. Liu,7Z. Liu,6A. Lobodenko,41 M. Lokajicek,11P. Love,43H. J. Lubatti,82R. Luna-Garcia,34,xA. L. Lyon,50A. K. A. Maciel,2D. Mackin,80P. Ma¨ttig,27

R. Magan˜a-Villalba,34A. Magerkurth,64P. K. Mal,46H. B. Malbouisson,3S. Malik,67V. L. Malyshev,37Y. Maravin,59 B. Martin,14R. McCarthy,72C. L. McGivern,58M. M. Meijer,36A. Melnitchouk,66L. Mendoza,8D. Menezes,52 P. G. Mercadante,5M. Merkin,39K. W. Merritt,50A. Meyer,21J. Meyer,24J. Mitrevski,70N. K. Mondal,30R. W. Moore,6

T. Moulik,58G. S. Muanza,15M. Mulhearn,70O. Mundal,22L. Mundim,3E. Nagy,15M. Naimuddin,50M. Narain,77 H. A. Neal,64J. P. Negret,8P. Neustroev,41I. Nikolaev,71H. Nilsen,23H. Nogima,3S. F. Novaes,5T. Nunnemann,26

G. Obrant,41C. Ochando,16D. Onoprienko,59J. Orduna,34N. Oshima,50N. Osman,44J. Osta,55R. Otec,10 G. J. Otero y Garzo´n,1M. Owen,45M. Padilla,48P. Padley,80M. Pangilinan,77N. Parashar,56S.-J. Park,24S. K. Park,32 J. Parsons,70R. Partridge,77N. Parua,54A. Patwa,73G. Pawloski,80B. Penning,23M. Perfilov,39K. Peters,45Y. Peters,45

P. Pe´troff,16R. Piegaia,1J. Piper,65M.-A. Pleier,22P. L. M. Podesta-Lerma,34,kV. M. Podstavkov,50Y. Pogorelov,55 M.-E. Pol,2P. Polozov,38A. V. Popov,40W. L. Prado da Silva,3S. Protopopescu,73J. Qian,64A. Quadt,24B. Quinn,66 A. Rakitine,43M. S. Rangel,16K. Ranjan,29P. N. Ratoff,43P. Renkel,79P. Rich,45M. Rijssenbeek,72I. Ripp-Baudot,19

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R. Schwienhorst,65J. Sekaric,49H. Severini,75E. Shabalina,24M. Shamim,59V. Shary,18A. A. Shchukin,40 R. K. Shivpuri,29V. Siccardi,19V. Simak,10V. Sirotenko,50P. Skubic,75P. Slattery,71D. Smirnov,55G. R. Snow,67

J. Snow,74S. Snyder,73S. So¨ldner-Rembold,45L. Sonnenschein,21A. Sopczak,43M. Sosebee,78K. Soustruznik,9 B. Spurlock,78J. Stark,14V. Stolin,38D. A. Stoyanova,40J. Strandberg,64M. A. Strang,69E. Strauss,72M. Strauss,75 R. Stro¨hmer,26D. Strom,53L. Stutte,50S. Sumowidagdo,49P. Svoisky,36M. Takahashi,45A. Tanasijczuk,1W. Taylor,6

B. Tiller,26M. Titov,18V. V. Tokmenin,37I. Torchiani,23D. Tsybychev,72B. Tuchming,18C. Tully,68P. M. Tuts,70 R. Unalan,65L. Uvarov,41S. Uvarov,41S. Uzunyan,52P. J. van den Berg,35R. Van Kooten,54W. M. van Leeuwen,35 N. Varelas,51E. W. Varnes,46I. A. Vasilyev,40P. Verdier,20L. S. Vertogradov,37M. Verzocchi,50D. Vilanova,18P. Vint,44

P. Vokac,10M. Voutilainen,67,{R. Wagner,68H. D. Wahl,49M. H. L. S. Wang,71J. Warchol,55G. Watts,82M. Wayne,55 G. Weber,25M. Weber,50,**L. Welty-Rieger,54A. Wenger,23,††M. Wetstein,61A. White,78D. Wicke,25 M. R. J. Williams,43G. W. Wilson,58S. J. Wimpenny,48M. Wobisch,60D. R. Wood,63T. R. Wyatt,45Y. Xie,77C. Xu,64

S. Yacoob,53R. Yamada,50W.-C. Yang,45T. Yasuda,50Y. A. Yatsunenko,37Z. Ye,50H. Yin,7K. Yip,73H. D. Yoo,77 S. W. Youn,53J. Yu,78C. Zeitnitz,27S. Zelitch,81T. Zhao,82B. Zhou,64J. Zhu,72M. Zielinski,71D. Zieminska,54

L. Zivkovic,70V. Zutshi,52and E. G. Zverev39

(D0 Collaboration)

1Universidad de Buenos Aires, Buenos Aires, Argentina 2

LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil

3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4

Universidade Federal do ABC, Santo Andre´, Brazil

5Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil 6University of Alberta, Edmonton, Alberta, Canada;

Simon Fraser University, Burnaby, British Columbia, Canada; York University, Toronto, Ontario, Canada

and McGill University, Montreal, Quebec, Canada

7University of Science and Technology of China, Hefei, People’s Republic of China 8

Universidad de los Andes, Bogota´, Colombia

9Center for Particle Physics, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 10

Czech Technical University in Prague, Prague, Czech Republic

11Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 12Universidad San Francisco de Quito, Quito, Ecuador

13

LPC, Universite´ Blaise Pascal, CNRS/IN2P3, Clermont, France

14LPSC, Universite´ Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France 15

CPPM, Aix-Marseille Universite´, CNRS/IN2P3, Marseille, France

16LAL, Universite´ Paris-Sud, IN2P3/CNRS, Orsay, France 17

LPNHE, IN2P3/CNRS, Universite´s Paris VI and VII, Paris, France

18CEA, Irfu, SPP, Saclay, France

19IPHC, Universite´ de Strasbourg, CNRS/IN2P3, Strasbourg, France

20IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite´ de Lyon, Lyon, France 21III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany

22

Physikalisches Institut, Universita¨t Bonn, Bonn, Germany

23Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany 24

II. Physikalisches Institut, Georg-August-Universita¨t Go¨ttingen, Go¨ttingen, Germany

25Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 26Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 27Fachbereich Physik, University of Wuppertal, Wuppertal, Germany

28Panjab University, Chandigarh, India 29

Delhi University, Delhi, India

30Tata Institute of Fundamental Research, Mumbai, India 31

University College Dublin, Dublin, Ireland

32Korea Detector Laboratory, Korea University, Seoul, Korea 33

SungKyunKwan University, Suwon, Korea

34CINVESTAV, Mexico City, Mexico

35FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 36Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands

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38Institute for Theoretical and Experimental Physics, Moscow, Russia 39Moscow State University, Moscow, Russia

40Institute for High Energy Physics, Protvino, Russia 41Petersburg Nuclear Physics Institute, St. Petersburg, Russia 42

Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden

43Lancaster University, Lancaster, United Kingdom 44

Imperial College, London, United Kingdom

45University of Manchester, Manchester, United Kingdom 46

University of Arizona, Tucson, Arizona 85721, USA

47California State University, Fresno, California 93740, USA 48University of California, Riverside, California 92521, USA 49

Florida State University, Tallahassee, Florida 32306, USA

50Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 51

University of Illinois at Chicago, Chicago, Illinois 60607, USA

52Northern Illinois University, DeKalb, Illinois 60115, USA 53

Northwestern University, Evanston, Illinois 60208, USA

54Indiana University, Bloomington, Indiana 47405, USA 55University of Notre Dame, Notre Dame, Indiana 46556, USA

56Purdue University Calumet, Hammond, Indiana 46323, USA 57Iowa State University, Ames, Iowa 50011, USA 58

University of Kansas, Lawrence, Kansas 66045, USA

59Kansas State University, Manhattan, Kansas 66506, USA 60

Louisiana Tech University, Ruston, Louisiana 71272, USA

61University of Maryland, College Park, Maryland 20742, USA 62

Boston University, Boston, Massachusetts 02215, USA

63Northeastern University, Boston, Massachusetts 02115, USA 64University of Michigan, Ann Arbor, Michigan 48109, USA 65

Michigan State University, East Lansing, Michigan 48824, USA

66University of Mississippi, University, Mississippi 38677, USA 67

University of Nebraska, Lincoln, Nebraska 68588, USA

68Princeton University, Princeton, New Jersey 08544, USA 69

State University of New York, Buffalo, New York 14260, USA

70Columbia University, New York, New York 10027, USA 71University of Rochester, Rochester, New York 14627, USA 72State University of New York, Stony Brook, New York 11794, USA

73Brookhaven National Laboratory, Upton, New York 11973, USA 74

Langston University, Langston, Oklahoma 73050, USA

75University of Oklahoma, Norman, Oklahoma 73019, USA 76

Oklahoma State University, Stillwater, Oklahoma 74078, USA

77Brown University, Providence, Rhode Island 02912, USA 78University of Texas, Arlington, Texas 76019, USA 79Southern Methodist University, Dallas, Texas 75275, USA

80Rice University, Houston, Texas 77005, USA 81

University of Virginia, Charlottesville, Virginia 22901, USA

82University of Washington, Seattle, Washington 98195, USA

(Received 5 June 2009; published 21 September 2009)

We present a measurement of the mass difference betweentandtquarks in leptonþjets final states of ttevents in1 fb 1of data collected with the D0 detector from Fermilab Tevatron Colliderppcollisions at

ffiffiffi

s

p

¼1:96 TeV. The measured mass difference of3:83:7 GeVis consistent with the equality oftandt

masses. This is the first direct measurement of a mass difference between a quark and its antiquark partner.

DOI:10.1103/PhysRevLett.103.132001 PACS numbers: 14.65.Ha, 11.30.Er, 12.15.Ff

TheCPTtheorem [1], which is fundamental to any local Lorentz-invariant quantum field theory, requires that the mass of a particle and that of its antiparticle be identical. Tests ofCPT invariance for many of the elementary par-ticles accommodated within the standard model (SM) are available in the literature [2]. Despite the fact that no

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character-istics of the initially produced quarks, such as their charges, spin states, and masses. If the lifetimes of quarks are much longer than the time scale for QCD processes, the quarks form hadrons before they emerge from collisions, and decay from within bound hadronic states. This makes it difficult to measure aq q mass difference because of the model dependence of QCD binding and evolution processes. However, since the lifetime of the top quark is far shorter than the time scale for QCD interactions, the top-quark sector provides a way to measure the mass difference less ambiguously [3].

In this Letter, we report a measurement of the difference between the mass of the top quark (t) and that of its anti-particle (t) produced in pp collisions atpffiffiffis¼1:96 TeV. Our measurement is based on data corresponding to 1 fb 1of integrated luminosity collected with the D0

de-tector [4] during run II of the Fermilab Tevatron Collider. The events used in this analysis, identical to those in Ref. [5], are top-quark pair (tt) events in the leptonþjets channel (‘þjets) where each top quark is assumed to always decay into aW boson and a b quark. One of the W bosons decays via W!‘into two leptons, and the other one throughW !qq0 into two quarks, and all four quarks (qq0bb) evolve into jets.

We select events having one isolated electron (muon) with transverse momentum pT >20 GeV and jj<1:1

(jj<2), missing transverse momentum p6 T >20 GeV, and exactly four jets with pT>20 GeV and jj<2:5, where the pseudorapidity ¼ ln½tanð=2ފ, and is the polar angle with respect to the proton beam direction. At least one of the jets is required to be identified as ab-jet candidate. A minimum azimuthal separation is required between leptonpT andp6 T vectors to further reduce multi-jet background arising from lepton or multi-jet energy mismea-surements. The positively (negatively) charged leptons are used to tag thet(t) in each event. To reduce instrumental effects that can cause charge dependent asymmetries in lepton energy scale and resolution, solenoid and toroid magnetic field polarities are routinely reversed.

The selected data sample consists of 110eþjets and 110þjets events. TheWþ(W ) boson decays into had-rons in 105 (115) events and into leptons in 115 (105) events, consistent with invariance under charge conjuga-tion. The fraction ofttevents in this sample is estimated to be 74%. The background consists ofWþjets and multijet events, with the latter comprising 12% of the entire background.

This analysis uses the matrix element (ME) method which relies on the extraction of the properties of the top quark (e.g., the mass) through a likelihood technique based on probability densities (PD) for each event, calculated from the ME for the two major processes (ttandWþjets production) that contribute to the selected‘þjets sample. In calculating the PD forttproduction, we include only the leading-order (LO) ME fromqq !ttproduction [6]. We

assume SM-like ttproduction and decay, where identical particle and antiparticle masses are assumed for bquarks and W bosons but not for top quarks. For Wþjets pro-duction, we use the ME provided in VECBOS[7]. The PD for each event is given in terms of the fraction of signal (f) and of background (1 f) in the data and the masses of the t(mt) and thet(mt):

Pevt ¼AðxÞ½fPsigðx;mt; mtÞ þ ð1 fÞPbkgðxފ; (1)

wherexdenotes the measured jet and lepton energies and angles, AðxÞ is a function only of xand accounts for the geometrical acceptance and efficiencies, andPsigandPbkg

represent the PD for ttand Wþjets production, respec-tively. Multijet events are also represented by Pbkg since

PbkgPsig for such events [8].

The free parameters in Eq. (1) are determined from a likelihoodLðx;mt; mt; fÞconstructed from the product of

thePevtfor all events. Jet energies are scaled by an overall jet energy scale (JES) calibration factor derived by con-straining the reconstructed mass of the two jets fromW! qq0decays inttevents to 80.4 GeV [2,5]. The likelihood is maximized as a function offfor each (mt,mt) hypothesis

to determinefbest. An integration of the likelihood forf¼

fbest over the sum m

sum ¼ ðmtþmtÞ=2 results in a

one-dimensional likelihoodLðx; Þas a function of mass dif-ference ¼mt mt. This is used to extract the mean

value ofand its uncertainty. A similar procedure involv-ing an integration overgivesLðx;msumÞwhich is used to

extract the mean value ofmsumand its uncertainty.

The variables in any ME refer to nascent produced particles (leptons and partons), but the measured quantities correspond to physical leptons and jets. This difference is taken into account in the calculation of the event probabil-ity by convoluting over phase space a transfer function, Wðy; xÞ, that provides the resolution for the lepton in question or a mapping of the observed jet variables in an event (x) to their progenitor parton variables (y):

Psig¼

1

tt norm

Z Xdðy;mt; mtÞdq1dq2Fðq1ÞFðq2ÞWðy; xÞ;

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wheredðy;mt; mtÞis the leading-order partonic

differen-tial cross section,q1andq2are the momentum fractions of

the colliding partons (assumed to be massless) within the incident p and p, and the sum runs over all possible combinations of initial-state parton flavors, jet-to-parton assignments, and allW !‘neutrino solutions [9]. In the sum over jet-to-parton assignments inPsig, each

permuta-tion of jets carries a weight wi, which is the normalized

product of probabilities for tagging any jet under a given parton flavor hypothesis [5]. TheFðqiÞinclude the

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longitudinal momentum fraction in theporpassuming the CTEQ6L1 [10] distribution functions (PDF), as well as the probability densities for the transverse components of the qiobtained from the LO event generatorPYTHIA[11]. The normalization termtt

normis described below.

The overall detection efficiency fortt depends on the values of both mt and mt. This is taken into account

through the normalization by the observed cross section tt

norm¼

R

AðxÞPsigdx¼ttðmt; mtÞhAðmt; mtÞi, where

ttðm

t; mtÞis the total cross section calculated by

integrat-ing the partonic cross sectiontt

qq [12], corresponding to

the specific ME used in the analysis, over initial and final parton distributions and summing over initial parton fla-vors.hAðmt; mtÞiis the mean acceptance determined from

the generatedttevents. The expressions forPbkg are simi-lar, except that the probability does not depend onmtormt.

Samples ofttMC events with different values ofmtand mtare required to simulatettproduction and decay in order

to calibrate the results of the analysis. These events are generated with a version of the PYTHIA generator [11] modified to provide independent values of mt and mt.

The specific values chosen for (mt, mt) form a square

grid spaced at 5 GeV intervals between (165, 165) and (180, 180), excluding the two extreme points at (165, 180) and (180, 165). The MC events for equal values ofmtand

mtare generated with the default version ofPYTHIA.

Approximations made in formulating the likelihood can bias the final result. This issue is examined by comparing the measured and input values ofin pseudo experiments composed of MCttandWþjets events. The calibration is shown in Fig. 1 in terms of the measured mean as a function of its input value (in), separately for theeþjets

andþjets MC samples, for all MC samples generated at the input reference points on the (mt,mt) grid. There are 2,

3, 4, 3, and 2 different (mt,mt) points with a commonin

of 10, 5, 0, þ5, and þ10 GeV, respectively. The dispersions in the measured values of meanfor different (mt,mt) points, but with same values ofin, are consistent

with expected statistical fluctuations, as can be observed in

Fig.1. The fit2=d:o:f. for the points in Figs.1(a)and1(b)

are 1.8 and 0.84, respectively. The parameterizations shown in Fig. 1 are used to calibrate Lðx; Þ for the selected data sample.

We define the pull as ð hiÞ=ðÞ where is the measured mass difference for a given pseudo experiment, hi is the mean measured mass difference for all pseudo experiments, andðÞis the uncertainty of the measured mass difference for the given pseudo experiment. The mean widths of the pull distributions for all samples used in Fig.1are 1.2 and 1.1 foreþjets andþjets, respec-tively. The deviations of these widths from 1 are used to correct the measured uncertainties in data.

Fitted two-dimensional Gaussian contours of equal probability (in terms of the standard deviation sd) for Lðx;mt; mtÞ are shown for the electron and muon data

samples in Figs. 2(a) and 2(b), respectively. The corre-spondingLðx; Þfor both channels are given in Figs.3(a)

and 3(b). The two sets of data are consistent within their respective uncertainties, and the small correlations (eþjets¼ 0:05,þjets ¼ 0:01) extracted from the fits

in Fig.2betweenmtandmtare not statistically significant,

nor are the shifts in the projections shown in Fig.3. Results from the two channels are combined through a weighted average of the separate electron and muon values. This has the advantage of using their respective pulls to adjust the uncertainties of each measurement before com-bining the two results. Using this averaging process, we quote the final combined means and their statistical un-certainties as ¼3:83:4ðstatÞ GeV and msum¼

170:91:5ðstatÞ GeV. The latter is consistent with the previous measurement of Ref. [5] (see also Ref. [13]).

The systematic uncertainties are summarized in TableI. The first category,physics modeling, comprises the uncer-tainties in MC modeling of ttand Wþjets events. The second category, detector modeling, addresses uncertain-ties in the calibration of jet energy and simulation of detector response. The last category, Method, addresses uncertainties in the calibration and possible systematic

[GeV]

in

-15 -10 -5 0 5 10 15

[GeV]-15 -10 -5 0 5 10 15 in ∆ × = 0.97

+ 0.34 GeV (a)

e+jets

[GeV]

in

-15 -10 -5 0 5 10 15

[GeV]-15 -10 -5 0 5 10 15 in ∆ × = 0.99

+ 0.15 GeV +jets µ (b)

FIG. 1. Values of the measured mean from MC pseudo experiments as a function ofin, parameterized by straight lines

for (a) eþjets and (b) þjets MC events. Dotted lines represent complete equality between measured and input values. Results from pseudo experiments with same in but different msumcorrespond to the extra points for fixedin(see text).

[GeV]

t

m

165 170 175 180

[GeV]t m 165 170 175 180

(a) e+jets DØ, 1 fb -1

1sd 2sd 3sd [GeV] t m

165 170 175 180

[GeV]t

m

160 165 170

175 µ+jets

(b) -1

DØ, 1 fb

1sd 2sd

3sd

FIG. 2 (color online). Fitted contours of equal probability for the two-dimensional likelihoods as a function ofmt andmt for

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effects due to assumptions made in the analysis. Except for two, all systematic uncertainties are identical to those described previously [5]. Many of these uncertainties (e.g., uncertainties in JES, PDF, jet resolution, multijet contamination) are expected to partially cancel in the measurement of the mass difference, but are often domi-nated by the statistics of the samples used to evaluate them. The two new contributions address the possibilities of (i) reconstructing leptons with the wrong charge, and (ii) uncertainties from modeling differences in the response of the calorimeter tobandbjets [14], which can affect the measurement of the mass difference. These were evaluated for (i) by estimating the effect of an increase in charge misidentification in MC simuulations that would match that found in data (1%for botheand). For (ii), studies were performed on MC samples and on data seeking any

difference in detector response to bandbquarks beyond expectations from interactions of their decay products, which are accommodated in the MC simulations. The observed differences were limited by the statistics of both samples. The total systematic uncertainty is 1.2 GeV. Combining the systematic and statistical uncer-tainties of the measurement in quadrature yields ¼ 3:83:7 GeV, a value consistent withCPTinvariance.

In summary, we have measured thetandtmass differ-ence in1 fb 1 of data inþjetsttevents and find the

mass difference to be mt mt¼3:83:7 GeV,

corre-sponding to a relative mass difference of=msum¼ ð2:2

2:2Þ%. This is the first direct measurement of a mass difference between a quark and its antiquark partner.

We thank the staffs at Fermilab and collaborating insti-tutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and West-Grid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); and the Alexander von Humboldt Foundation (Germany).

*Visitor from Augustana College, Sioux Falls, SD, USA. †Visitor from Rutgers University, Piscataway, NJ, USA.

Visitor from The University of Liverpool, Liverpool, UK.

xVisitor from Centro de Investigacion en Computacion

-IPN, Mexico City, Mexico.

kVisitor from ECFM, Universidad Autonoma de Sinaloa,

Culiaca´n, Mexico.

{Visitor from Helsinki Institute of Physics, Helsinki,

Finland.

**Visitor from Universita¨t Bern, Bern, Switzerland. ††Visitor from Universita¨t Zu¨rich, Zu¨rich, Switzerland.

‡‡Deceased.

[1] J. Schwinger, Phys. Rev.82, 914 (1951); G. Luders, K. Dan. Vidensk. Selsk. Mat. Fys. Medd.28, 5 (1954);Niels Bohr and the Development of Physics, edited by W. Pauli (McGraw-Hill, New York, 1955), p. 30; D. Colladay and V. A. Kostelecky, Phys. Rev. D55, 6760 (1997); J. S. Bell, Proc. R. Soc. A231, 479 (1955).

[2] C. Amsleret al.(Particle Data Group), Phys. Lett. B667, 93 (2008).

[3] J. A. R. Cembranos, A. Rajaraman, and F. Takayama, Europhys. Lett.82, 21001 (2008).

[4] V. M. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A565, 463 (2006).

[5] V. M. Abazovet al.(D0 Collaboration), Phys. Rev. Lett.

101, 182001 (2008). TABLE I. Summary of systematic uncertainties on.

Source Uncertainty (GeV)

Physics modeling:

Signal 0:85

PDF uncertainty 0:26

Background modeling 0:03

Heavy flavor scale factor 0:07

bfragmentation 0:12

Detector modeling:

b=light response ratio 0:04

Jet identification 0:16

Jet resolution 0:39

Trigger 0:09

Overall jet energy scale 0:08

Residual jet energy scale 0:07

Muon resolution 0:09

Wrong charge leptons 0:07

Asymmetry inbbresponse 0:42

Method:

MC calibration 0:25

b-tagging efficiency 0:25

Multijet contamination 0:40

Signal fraction 0:10

Total (in quadrature) 1:22 [GeV]

-20 -10 0 10 20

max

)/L

L(

0 0.5

1 = 0.33 ± 5.03 GeV

-1

DØ, 1 fb e+jets

(a)

[GeV]

-20 -10 0 10 20

max

)/L

L(

0 0.5

1 = 6.74 ± 4.71 GeV

-1

DØ, 1 fb µ+jets

(b)

(7)

[6] V. Abazov et al. (D0 Collaboration), Phys. Rev. D 74, 092005 (2006).

[7] F. A. Berendset al., Nucl. Phys.B357, 32 (1991). [8] When this is satisfied, the relative contribution ofPsigto

Pevt will be negligible for such events, minimizing their

influence in the determination ofmt andmt.

[9] The transverse components of the unmeasured momen-tumpare determined from thepTbalance of thettevent,

but the remaining ambiguity in the longitudinal compo-nent ofpleaves more than one possibility or ‘‘solution’’

forp.

[10] J. Pumplin et al.(CTEQ Collaboration), J. High Energy Phys. 07 (2002) 012.

[11] T. Sjo¨strand et al., Comput. Phys. Commun. 135, 238 (2001).

[12] tt qq ¼8

2

s

27s5=2pð3E2t þ3Et2þ2p2þ6mtmtÞ where s is

the strong coupling constant, s is the square of the center-of-mass energy in the incoming qq rest frame, and Ei and p are the energies of the t or tand their

common momentum, respectively, in theqqframe. [13] The result in Ref. [5] was obtained by further constraining

the jet energy scale to the one derived from photonþjets and dijet samples. This constraint is not used in the present analysis since it shiftsmtandmtin the same way and has

no effect on.

[14] Differences in the composition of band bjets, such as differentKþ=K fractions, can cause differences in

calo-rimeter response because of differences inKþ=K

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