Measurement of color flow in t �t events from p �p collisions at ffiffiffi s p ¼ 1:96 TeV V.M. Abazov,35 B. Abbott,72 B. S. Acharya,29 M. Adams,48 T. Adams,46 G. D. Alexeev,35 G. Alkhazov,39 A. Alton,60,* G. Alverson,59 G.A. Alves,2 L. S. Ancu,34 M. Aoki,47 M. Arov,57 A. Askew,46 B. Åsman,40 O. Atramentov,64 C. Avila,8 J. BackusMayes,79 F. Badaud,13 L. Bagby,47 B. Baldin,47 D.V. Bandurin,46 S. Banerjee,29 E. Barberis,59 P. Baringer,55 J. Barreto,3 J. F. Bartlett,47 U. Bassler,18 V. Bazterra,48 S. Beale,6 A. Bean,55 M. Begalli,3 M. Begel,70 C. Belanger-Champagne,40 L. Bellantoni,47 S. B. Beri,27 G. Bernardi,17 R. Bernhard,22 I. Bertram,41 M. Besançon,18 R. Beuselinck,42 V. A. Bezzubov,38 P. C. Bhat,47 V. Bhatnagar,27 G. Blazey,49 S. Blessing,46 K. Bloom,63 A. Boehnlein,47 D. Boline,69 T. A. Bolton,56 E. E. Boos,37 G. Borissov,41 T. Bose,58 A. Brandt,75 O. Brandt,23 R. Brock,61 G. Brooijmans,67 A. Bross,47 D. Brown,17 J. Brown,17 X. B. Bu,47 M. Buehler,78 V. Buescher,24 V. Bunichev,37 S. Burdin,41,† T. H. Burnett,79 C. P. Buszello,40 B. Calpas,15 E. Camacho-Pérez,32 M.A. Carrasco-Lizarraga,55 B. C. K. Casey,47 H. Castilla-Valdez,32 S. Chakrabarti,69 D. Chakraborty,49 K.M. Chan,53 A. Chandra,77 G. Chen,55 S. Chevalier-Théry,18 D.K. Cho,74 S.W. Cho,31 S. Choi,31 B. Choudhary,28 T. Christoudias,42 S. Cihangir,47 D. Claes,63 J. Clutter,55 M. Cooke,47 W. E. Cooper,47 M. Corcoran,77 F. Couderc,18 M.-C. Cousinou,15 A. Croc,18 D. Cutts,74 A. Das,44 G. Davies,42 K. De,75 S. J. de Jong,34 E. De La Cruz-Burelo,32 F. Déliot,18 M. Demarteau,47 R. Demina,68 D. Denisov,47 S. P. Denisov,38 S. Desai,47 K. DeVaughan,63 H. T. Diehl,47 M. Diesburg,47 A. Dominguez,63 T. Dorland,79 A. Dubey,28 L. V. Dudko,37 D. Duggan,64 A. Duperrin,15 S. Dutt,27 A. Dyshkant,49 M. Eads,63 D. Edmunds,61 J. Ellison,45 V. D. Elvira,47 Y. Enari,17 H. Evans,51 A. Evdokimov,70 V.N. Evdokimov,38 G. Facini,59 T. Ferbel,68 F. Fiedler,24 F. Filthaut,34 W. Fisher,61 H. E. Fisk,47 M. Fortner,49 H. Fox,41 S. Fuess,47 T. Gadfort,70 A. Garcia-Bellido,68 V. Gavrilov,36 P. Gay,13 W. Geist,19 W. Geng,15,61 D. Gerbaudo,65 C. E. Gerber,48 Y. Gershtein,64 G. Ginther,47,68 G. Golovanov,35 A. Goussiou,79 P. D. Grannis,69 S. Greder,19 H. Greenlee,47 Z. D. Greenwood,57 E.M. Gregores,4 G. Grenier,20 Ph. Gris,13 J.-F. Grivaz,16 A. Grohsjean,18 S. Grünendahl,47 M.W. Grünewald,30 F. Guo,69 G. Gutierrez,47 P. Gutierrez,72 A. Haas,67,‡ S. Hagopian,46 J. Haley,59 L. Han,7 K. Harder,43 A. Harel,68 J.M. Hauptman,54 J. Hays,42 T. Head,43 T. Hebbeker,21 D. Hedin,49 H. Hegab,73 A. P. Heinson,45 U. Heintz,74 C. Hensel,23 I. Heredia-De La Cruz,32 K. Herner,60 M.D. Hildreth,53 R. Hirosky,78 T. Hoang,46 J. D. Hobbs,69 B. Hoeneisen,12 M. Hohlfeld,24 S. Hossain,72 Z. Hubacek,10,18 N. Huske,17 V. Hynek,10 I. Iashvili,66 R. Illingworth,47 A. S. Ito,47 S. Jabeen,74 M. Jaffré,16 S. Jain,66 D. Jamin,15 R. Jesik,42 K. Johns,44 M. Johnson,47 D. Johnston,63 A. Jonckheere,47 P. Jonsson,42 J. Joshi,27 A. Juste,47,x K. Kaadze,56 E. Kajfasz,15 D. Karmanov,37 P. A. Kasper,47 I. Katsanos,63 R. Kehoe,76 S. Kermiche,15 N. Khalatyan,47 A. Khanov,73 A. Kharchilava,66 Y. N. Kharzheev,35 D. Khatidze,74 M.H. Kirby,50 J.M. Kohli,27 A.V. Kozelov,38 J. Kraus,61 A. Kumar,66 A. Kupco,11 T. Kurča,20 V. A. Kuzmin,37 J. Kvita,9 S. Lammers,51 G. Landsberg,74 P. Lebrun,20 H. S. Lee,31 S.W. Lee,54 W.M. Lee,47 J. Lellouch,17 L. Li,45 Q. Z. Li,47 S.M. Lietti,5 J. K. Lim,31 D. Lincoln,47 J. Linnemann,61 V.V. Lipaev,38 R. Lipton,47 Y. Liu,7 Z. Liu,6 A. Lobodenko,39 M. Lokajicek,11 P. Love,41 H. J. Lubatti,79 R. Luna-Garcia,32,k A. L. Lyon,47 A.K.A. Maciel,2 D. Mackin,77 R. Madar,18 R. Magaña-Villalba,32 S. Malik,63 V. L. Malyshev,35 Y. Maravin,56 J. Martı́nez-Ortega,32 R. McCarthy,69 C. L. McGivern,55 M.M. Meijer,34 A. Melnitchouk,62 D. Menezes,49 P. G. Mercadante,4 M. Merkin,37 A. Meyer,21 J. Meyer,23 F. Miconi,19 N.K. Mondal,29 G. S. Muanza,15 M. Mulhearn,78 E. Nagy,15 M. Naimuddin,28 M. Narain,74 R. Nayyar,28 H. A. Neal,60 J. P. Negret,8 P. Neustroev,39 S. F. Novaes,5 T. Nunnemann,25 G. Obrant,39 J. Orduna,32 N. Osman,42 J. Osta,53 G. J. Otero y Garzón,1 M. Owen,43 M. Padilla,45 M. Pangilinan,74 N. Parashar,52 V. Parihar,74 S. K. Park,31 J. Parsons,67 R. Partridge,74,‡ N. Parua,51 A. Patwa,70 B. Penning,47 M. Perfilov,37 K. Peters,43 Y. Peters,43 G. Petrillo,68 P. Pétroff,16 R. Piegaia,1 J. Piper,61 M.-A. Pleier,70 P. L.M. Podesta-Lerma,32,{ V.M. Podstavkov,47 M.-E. Pol,2 P. Polozov,36 A.V. Popov,38 M. Prewitt,77 D. Price,51 S. Protopopescu,70 J. Qian,60 A. Quadt,23 B. Quinn,62 M. S. Rangel,2 K. Ranjan,28 P. N. Ratoff,41 I. Razumov,38 P. Renkel,76 M. Rijssenbeek,69 I. Ripp-Baudot,19 F. Rizatdinova,73 M. Rominsky,47 C. Royon,18 P. Rubinov,47 R. Ruchti,53 G. Safronov,36 G. Sajot,14 A. Sánchez-Hernández,32 M. P. Sanders,25 B. Sanghi,47 A. S. Santos,5 G. Savage,47 L. Sawyer,57 T. Scanlon,42 R.D. Schamberger,69 Y. Scheglov,39 H. Schellman,50 T. Schliephake,26 S. Schlobohm,79 C. Schwanenberger,43 R. Schwienhorst,61 J. Sekaric,55 H. Severini,72 E. Shabalina,23 V. Shary,18 A. A. Shchukin,38 R. K. Shivpuri,28 V. Simak,10 V. Sirotenko,47 P. Skubic,72 P. Slattery,68 D. Smirnov,53 K. J. Smith,66 G. R. Snow,63 J. Snow,71 S. Snyder,70 S. Söldner-Rembold,43 L. Sonnenschein,21 A. Sopczak,41 M. Sosebee,75 K. Soustruznik,9 B. Spurlock,75 J. Stark,14 V. Stolin,36 D.A. Stoyanova,38 M. Strauss,72 D. Strom,48 L. Stutte,47 L. Suter,43 P. Svoisky,72 M. Takahashi,43 A. Tanasijczuk,1 W. Taylor,6 M. Titov,18 V. V. Tokmenin,35 Y.-T. Tsai,68 D. Tsybychev,69 B. Tuchming,18 C. Tully,65 P.M. Tuts,67 L. Uvarov,39 S. Uvarov,39 S. Uzunyan,49 R. Van Kooten,51 W.M. van Leeuwen,33 N. Varelas,48 E.W. Varnes,44 I. A. Vasilyev,38 P. Verdier,20 L. S. Vertogradov,35 M. Verzocchi,47 M. Vesterinen,43 D. Vilanova,18 PHYSICAL REVIEW D 83, 092002 (2011) 1550-7998=2011=83(9)=092002(7) 092002-1 � 2011 American Physical Society P. Vint,42 P. Vokac,10 H.D. Wahl,46 M.H. L. S. Wang,68 J. Warchol,53 G. Watts,79 M. Wayne,53 M. Weber,47,** L. Welty-Rieger,50 A. White,75 D. Wicke,26 M.R. J. Williams,41 G.W. Wilson,55 S. J. Wimpenny,45 M. Wobisch,57 D. R. Wood,59 T. R. Wyatt,43 Y. Xie,47 C. Xu,60 S. Yacoob,50 R. Yamada,47 W.-C. Yang,43 T. Yasuda,47 Y. A. Yatsunenko,35 Z. Ye,47 H. Yin,47 K. Yip,70 S.W. Youn,47 J. Yu,75 S. Zelitch,78 T. Zhao,79 B. Zhou,60 J. Zhu,60 M. Zielinski,68 D. Zieminska,51 and L. Zivkovic74 (D0 Collaboration) 1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı́sicas, Rio de Janeiro, Brazil 3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Universidade Federal do ABC, Santo André, Brazil 5Instituto de Fı́sica Teórica, Universidade Estadual Paulista, São Paulo, Brazil 6Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada 7University of Science and Technology of China, Hefei, People’s Republic of China 8Universidad de los Andes, Bogotá, Colombia 9Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic 10Czech 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 13LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France 14LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France 15CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 16LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France 17LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France 18CEA, Irfu, SPP, Saclay, France 19IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France 20IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France 21III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany 22Physikalisches Institut, Universität Freiburg, Freiburg, Germany 23II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 24Institut für Physik, Universität Mainz, Mainz, Germany 25Ludwig-Maximilians-Universität München, München, Germany 26Fachbereich Physik, Bergische Universität Wuppertal, Wuppertal, Germany 27Panjab University, Chandigarh, India 28Delhi University, Delhi, India 29Tata Institute of Fundamental Research, Mumbai, India 30University College Dublin, Dublin, Ireland 31Korea Detector Laboratory, Korea University, Seoul, Korea 32CINVESTAV, Mexico City, Mexico 33FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 34Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands 35Joint Institute for Nuclear Research, Dubna, Russia 36Institute for Theoretical and Experimental Physics, Moscow, Russia 37Moscow State University, Moscow, Russia 38Institute for High Energy Physics, Protvino, Russia 39Petersburg Nuclear Physics Institute, St. Petersburg, Russia 40Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden 41Lancaster University, Lancaster LA1 4YB, United Kingdom 42Imperial College London, London SW7 2AZ, United Kingdom 43The University of Manchester, Manchester M13 9PL, United Kingdom 44University of Arizona, Tucson, Arizona 85721, USA 45University of California Riverside, Riverside, California 92521, USA 46Florida State University, Tallahassee, Florida 32306, USA 47Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 48University of Illinois at Chicago, Chicago, Illinois 60607, USA 49Northern Illinois University, DeKalb, Illinois 60115, USA 50Northwestern University, Evanston, Illinois 60208, USA 51Indiana University, Bloomington, Indiana 47405, USA V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 092002 (2011) 092002-2 52Purdue University Calumet, Hammond, Indiana 46323, USA 53University of Notre Dame, Notre Dame, Indiana 46556, USA 54Iowa State University, Ames, Iowa 50011, USA 55University of Kansas, Lawrence, Kansas 66045, USA 56Kansas State University, Manhattan, Kansas 66506, USA 57Louisiana Tech University, Ruston, Louisiana 71272, USA 58Boston University, Boston, Massachusetts 02215, USA 59Northeastern University, Boston, Massachusetts 02115, USA 60University of Michigan, Ann Arbor, Michigan 48109, USA 61Michigan State University, East Lansing, Michigan 48824, USA 62University of Mississippi, University, Mississippi 38677, USA 63University of Nebraska, Lincoln, Nebraska 68588, USA 64Rutgers University, Piscataway, New Jersey 08855, USA 65Princeton University, Princeton, New Jersey 08544, USA 66State University of New York, Buffalo, New York 14260, USA 67Columbia University, New York, New York 10027, USA 68University of Rochester, Rochester, New York 14627, USA 69State University of New York, Stony Brook, New York 11794, USA 70Brookhaven National Laboratory, Upton, New York 11973, USA 71Langston University, Langston, Oklahoma 73050, USA 72University of Oklahoma, Norman, Oklahoma 73019, USA 73Oklahoma State University, Stillwater, Oklahoma 74078, USA 74Brown University, Providence, Rhode Island 02912, USA 75University of Texas, Arlington, Texas 76019, USA 76Southern Methodist University, Dallas, Texas 75275, USA 77Rice University, Houston, Texas 77005, USA 78University of Virginia, Charlottesville, Virginia 22901, USA 79University of Washington, Seattle, Washington 98195, USA (Received 4 January 2011; published 10 May 2011) We present the first measurement of the color representation of the hadronically decayingW boson in t�t events, from 5:3 fb�1 of integrated luminosity collected with the D0 experiment. A novel calorimeter- based vectorial variable, ‘‘jet pull,’’ is used, sensitive to the color-flow structure of the final state. We find that the fraction of uncoloredW bosons is 0:56� 0:42ðstatþ systÞ, in agreement with the standard model. DOI: 10.1103/PhysRevD.83.092002 PACS numbers: 12.38.Qk, 12.38.Aw, 14.65.Ha Color charge is conserved in quantum chromodynamics, the theory that describes strong interactions [1]. At leading order in the strong coupling constant �s, color can be traced from initial partons to final-state partons in high- energy hadron collisions. Two final-state partons on the same color-flow line are ‘‘color connected’’ and attracted by the strong force. As these colored states shower, the potential energy of the strong force between them is released in the form of hadrons. Thus, knowledge of the color connections between jets can serve as a powerful tool for separating processes that otherwise appear similar. For example, in the decay of a Higgs (H) boson to a pair of bottom (b) quarks, the two b quarks are color connected to each other, since the H is uncolored (color singlet), whereas in g ! b �b background events, they are color connected to beam remnants because the gluon carries a color and an anticolor (color octet). We follow a recent suggestion [2] for reconstructing these color connections experimentally, using observables that can be modeled reliably by available leading-log parton-shower simula- tions. The technique involves measuring a vectorial quan- tity called ‘‘jet pull,’’ related to the jet energy pattern in the �-� plane [3], using the measured energy in the calorime- ter cells (see Fig. 1). Jets tend to have their pull pointing towards their color-connected partner. For instance, in H ! b �b events, the pulls of the two b jets tend to point towards each other, whereas in g ! b �b events, they point in opposite directions along the collision axis. Verification of color-flow simulation and jet pull recon- struction for both color-singlet and color-octet configura- tions is interesting in its own right [4] and is needed before jet pull can be used in, e.g., H ! b �b searches. Color-octet patterns can be studied in many processes, such as W=Z boson production in association with jets. A pure sample of color-singlet hadronic decays is difficult to obtain at a *Visitor from Augustana College, Sioux Falls, SD, USA. †Visitor from The University of Liverpool, Liverpool, UK. ‡Visitor from SLAC, Menlo Park, CA, USA. xVisitor from ICREA/IFAE, Barcelona, Spain. kVisitor from Centro de Investigacion en Computacion–IPN, Mexico City, Mexico. {Visitor from ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico. **Visitor from Universität Bern, Bern, Switzerland. MEASUREMENT OF COLOR FLOW IN t�t EVENTS . . . PHYSICAL REVIEW D 83, 092002 (2011) 092002-3 http://dx.doi.org/10.1103/PhysRevD.83.092002 hadron collider, but t�t events with an ‘þ jets final state are good candidates since they have a characteristic signature and contain two jets from the decay of aW boson, which is a color singlet. Each of the two b jets coming from the top quark decays is color connected to one of the beam rem- nants in a color-octet pattern. In this paper, we use data collected with the D0 detector [5] at the Fermilab Tevatron p �p collider, corresponding to 5:3 fb�1 of integrated luminosity, to present the first ex- perimental results on the study of jet pull, using t�t events decaying to ‘þ jets (t�t ! WbW �b ! ‘�bj �j �b , where ‘ ¼ e, �). The object identification, event selection, and simulated Monte Carlo (MC) events are the same as those used in the t�t cross section analysis [6], except that looser b-tagging criteria [7] are used to increase the statistics of double b-tagged events. We obtain a� 90% pure t�t sample by requiring an isolated lepton with pT > 20 GeV, missing transverse energy ET > 20 GeV (> 25 GeV for the �þ jets channel), and at least four jets, reconstructed with a midpoint cone algorithm [8] of radius 0.5, with pT > 20 GeV. At least one jet must have pT > 40 GeV, and at least two jets must be identified as b jets. Table I shows the event yields for these selection criteria. To extract the fraction of color-singlet hadronicW boson decays, the data are compared to both standard model t�t MC (with a color-singlet W boson) and an alternative model of t�t with a hypothetical color-octet ‘‘W’’ boson decaying hadronically with identical properties except for its color representation. The latter is simulated using the MADGRAPH (MG) [9] event generator interfaced to PYTHIA [10] for showering and hadronization. Simulated events are processed with a GEANT3-based [11] detector simulation, overlaid with random data to account for backgrounds, and reconstructed as data. D0 uses three liquid-argon/uranium calorimeters to measure the energies of particles: a central section cover- ing j�j up to � 1:1 and two end calorimeters that extend coverage to j�j � 4:2 [3], housed in separate cryostats [12]. In addition, scintillators between the central section and end calorimeter cryostats provide sampling of devel- oping showers for 1:1< j�j< 1:4. There are approxi- mately ten layers in the radial direction (depending on �), generally composed of cells spanning 0:1� 0:1 in ���. The energy resolution is about 15%= ffiffiffiffi E p � 0:3% (in GeV) for electrons and 50%= ffiffiffiffi E p � 5% for hadrons. Pileup energy from overlapping pp interactions results in about 0.5% of cells having energy above the noise-limited energy threshold (� 50–500 MeV, depending on layer and �). This energy is roughly exponentially distributed, with a mean of � 350 MeV. The pull is determined for each jet of a pair of recon- structed jets, using the measured energies of the calorime- ter cells. Each cell within �R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið��Þ2 þ ð��Þ2p < 0:7 of the ET-weighted center of one of the jets of the pair (� jet d , �jet) is assigned to the jet nearer in�R. The contribution of each selected cell to the jet pull is ~tcell ¼ Ecell T j~rcellj~rcell, where ~rcell ¼ ð�cell d � �jet d ; �cell ��jetÞ, and Ecell T is the cell’s transverse energy with respect to the nominal center of the detector. The jet pull is ~t ¼ P cells;i ~ti=E jet T . The polar angle of the jet pull, �pull, is defined to be zero when pointing in the positive � direction along the beamline. A small correction to the jet pull is made to account for the energy response and noise in the calorimeters as a function of �d, particularly in regions between the central and forward cryostats. The angle of the jet pull direction relative to the line defined by the centers of the jet pair TABLE I. Yields of events passing selections with exactly four or � 5 jets. At least two b-tagged jets are required in the analysis, but the numbers of events with zero or one b-tagged jet are also given. The number of t�t events is calculated using the cross section determined with this data sample, �t�t ¼ 8:50 pb. Uncertainties include statistical and systematic contributions. The total uncertainties are smaller than the sum of individual uncertainties due to negative correlations between samples. Detailed selections are described in Ref. [6]. Channel Sample Zero b tags One b tag � 2 b tags ‘þ 4 jets W þ jets 576� 75 229� 32 49� 8 Multijet 115� 16 46� 7 7� 2 Zþ jets 42� 6 16� 3 4� 1 Other 31� 4 19� 2 9� 1 t�t 160� 22 417� 38 519� 51 Total 923� 62 727� 24 589� 48 Observed 923 743 572 ‘þ � 5 jets W þ jets 60� 22 26� 11 7� 3 Multijet 17� 3 12� 2 3� 1 Zþ jets 4� 1 2� 1 1� 1 Other 3� 1 3� 1 2� 1 t�t 34� 6 90� 13 132� 17 Total 118� 19 132� 7 145� 15 Observed 112 127 156 FIG. 1 (color online). Diagram showing two jets in the �-� plane, and the reconstruction of the jet pull vectors (~t), jet pull angles (�pull), and relative jet pull angles (� pull rel ). V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 092002 (2011) 092002-4 (� pull rel ) is of primary interest, as we expect color-connected jets to have pulls pointing towards each other. The �pullrel quantity is calculated for each jet in the pair of highest-pT b-tagged jets (b pair) and the pair with highest pT which are not amongst the two highest pT b-tagged jets (w pair). To select events with a higher purity of properly identi- fied jet pairs from hadronic W boson decays, we split the sample into events where the invariant mass of the w-pair jets is consistent with the W boson mass, jmjj �MW j< 30 GeV, and events where it is not. For the former, these two jets are found to match the partons from the W boson decay within �R< 0:5 in 66% of t�t MC events with four jets and 46% of events with five or more jets. In the latter case, where the mass of the w-pair jets is outside the W boson mass window, additional gluon radiation in the initial or final state leads to possible additional color configurations, diluting the measurement. Since the w-pair jets in t�t events are often from the W boson decay, we expect them to be color connected; thus the jet pulls should generally point towards each other. We expect b-pair jets to have one of the b jets color connected to the proton beam and the other to the antiproton beam; thus the jet pulls should be generally pointing away from each other. This tendency is seen in data, as shown in Fig. 2, with smaller � pull rel in the w pair than in the b pair. However, the jets in w and b pairs have different kinemat- ics, separation in the detector, and flavor. A direct inter- pretation of the effects from color flow is therefore not possible from this comparison. Furthermore, there are detector and reconstruction effects on jet pulls from over- lapping jet pull cones, calorimeter noise and pileup, and calorimeter response inhomogeneity. For instance, there would be fewer cone overlaps if the jet pull was defined using only calorimeter cells within �R< 0:5, producing on average smaller values for � pull rel . With this alternative definition the shape in Fig. 2(a) would peak more towards zero and that in Fig. 2(b) would be flatter. These effects are found to be well modeled by the simulation, and the jet pull definition based on the �R< 0:7 cone gives a slightly improved singlet-octet separation. The relative jet pulls � pull rel in data are also found to be well modeled by simula- tion for other jet pairings, such as a randomw-pair jet and a random b-pair jet. In control samples consisting of events with a leptonicW boson decay, and two, three, or four jets, none identified as b jets, various jet pairings also have jet pulls that agree with simulations. Figure 3 shows the � pull rel distributions for jets in a control sample with a leptonic W boson decay and two not-b-tagged jets. To quantify the method’s sensitivity to the color-flow structure (color singlet versus color octet) for the hadronic W boson decay, we fit the data to two hypotheses: (i) standard model t�t with a color-singlet hadronically decaying W boson (singlet MC) and (ii) t�t with a hypo- thetical color-octetW boson (octet MC). We determine the fraction of events coming from color-singlet W boson decay (fSinglet) using the fitting procedure from the D0 combined t�t cross section analysis [6]. We simultaneously measure the t�t cross section to avoid any possible influence of the t�t signal normalization on the fSinglet measurement. The discriminating variable used for the fit is derived from the �pullrel angles of the w-pair jets and depends on the �R between the two jets and their �d. We define the following subdivisions for the data sample, which were optimized by studying the t�t singlet and octet MC. For events failing the W mass requirement, we do not split the regions further; for other events we split the data sample according to the �d of the jets and �R between the jets. For events where the two jets are highly separated (�R> 2), we use the � pull rel of the leading-pT jet. Little discrimination is possible for these events, since the additional color radiation is distrib- uted over a large area of the calorimeter. When the two jets are close (�R< 2) and j�dj< 1:0 for both jets, we use the minimum �pullrel of the two jets. This is the most sensitive region, and the jet pull is accurately reconstructed in the central calorimeter due to less pileup energy and uniform- ity of response. Otherwise, if j�dj of the leading-pT jet is <1:0 (> 1:0), the �pullrel of the leading-pT (second-leading pT) jet is used. Table II lists the contribution of each non-negligible source of systematic uncertainty on fSinglet. For all but 0 10 20 30 40 50 60 70 80 for w-pair jetsrel pullθ ev en t N /ndf: 0.952χData tt Other W+jets Multijets -1DØ, L=5.3 fb 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 60 70 80 90 for b-pair jetsrel pullθ ev en t N /ndf: 0.952χData tt Other W+jets Multijets -1DØ, L=5.3 fb FIG. 2 (color online). The average of the two jet � pull rel distri- butions for jets in pairing (a) w and (b) b, in events with exactly four jets, at least two b tags, and the MW requirement on the w-pair jets. The �2/number of degrees of freedom (ndf) com- pares the data to the total MC distribution. ev en t N 0 500 1000 1500 2000 2500 3000 3500 4000 w-pair jet T for leading-prel pullθ ev en t N /ndf: 1.082χData tt Other W+jets Multijets -1DØ, L=5.3 fb 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 0 500 1000 1500 2000 2500 3000 3500 4000 w-pair jet T leading-pnd for 2rel pullθ ev en t N /ndf: 1.242χData tt Other W+jets Multijets -1DØ, L=5.3 fb FIG. 3 (color online). (a) Leading-pT and (b) second-leading-- pT jet � pull rel distributions for w-pair jets, in events with two jets and no b-tagged jets. The �2=ndf compares the data to the total MC distribution. MEASUREMENT OF COLOR FLOW IN t�t EVENTS . . . PHYSICAL REVIEW D 83, 092002 (2011) 092002-5 the theoretical cross sections, MC statistics, and normal- ization of theW þ heavy flavor jets background uncertain- ties, we apply the systematic uncertainties just to the tt signal sample and ignore the effect on background, as the purity of the tt sample is high. To estimate the possible systematic shift of the �pullrel distribution due to the different energy scale and noise of the calorimeter cells between data and MC as a function of �d, we apply�50% of the jet pull � correction and take the resulting difference in shape as the systematic uncertainty for jet pull reconstruction. This covers the differences in the average �pull when com- paring data and MC control samples. We also study sys- tematic uncertainties as in [6], the main ones being from the jet energy scale, jet energy resolution, b-tagging effi- ciency, and lepton misidentification. Additional systematic uncertainties on �pullrel are assessed to account for possible differences between MC and data related to the modeling of underlying event, hadronization, and jet showering. To estimate the variation due to these possible mismodelings, we compare �pullrel distributions in events simulated with PYTHIA to those with ALPGEN [13] or MC@NLO [14], and showering with HERWIG [15]. We also do the comparisons for various PYTHIA parameters for underlying event and color reconnection [16], such as tunes APro and NOCR [17]. When deriving fSinglet from the fit, we use the maxi- mal variation obtained with the different � pull rel distributions as an estimate of the systematic uncertainty. Since the results are statistically limited and the analysis does not yet provide sufficient sensitivity for a definitive observation of color flow, we set limits on fSinglet using the likelihood ratio ordering scheme of Feldman and Cousins [18]. We follow the same approach used for the simulta- neous extraction of the ratio of branching fractions and the t�t cross section [19] and generate ensembles of pseudoex- periments for different values of fSinglet between 0 and 1, with the t�t cross section fixed to the measured value. We then vary the systematic uncertainties using Gaussian distributions and perform the fit as for the measurement on data. Statistical uncertainties are incorporated by smearing the measured value for each pseudoexperiment with the uncertainty determined in data. We use the nuisance pa- rameters method where the expectation is fit to the data, for a variation of the initial prediction within the systematic uncertainties, allowing also the central result to change [6]. Other methods give compatible results. We measure fSinglet ¼ 0:56� 0:42½�0:36ðstatÞ � 0:22ðsystÞ� and �t�t ¼ 8:50þ0:87 �0:76 pb, consistent with our dedicated cross section measurement [6]. Figure 4 shows TABLE II. The 1 standard deviation (�) variation of fSinglet from main systematic uncertainties. The total systematic uncer- tainty includes all uncertainties, summed in quadrature. Source þ1� �1� Singlet/octet MC shapes 0.188 �0:188 Jet pull reconstruction 0.100 �0:093 Jet energy resolution 0.033 �0:013 Vertex confirmation 0.028 �0:029 PYTHIA tunes 0.023 �0:025 Jet energy scale 0.024 �0:009 Jet reconstruction and identification 0.017 �0:017 t�t modeling 0.014 �0:033 Event statistics for matrix method 0.009 �0:010 Other Monte Carlo statistics 0.009 �0:007 Multijet background 0.006 �0:007 Total systematic 0.222 �0:218 θMinimum relative jet pull 0 0.5 1 1.5 2 2.5 3 ev en t N 0 10 20 30 40 50 60 70 80 90 Data Singlet Octet tt Other W+jets Multijets -1DØ, L=5.3 fb FIG. 4 (color online). The discriminating color-flow variable, the minimum � pull rel for the w-pair jets, for events passing the MW requirement, with �R < 2, and �d < 1:0 for both jets. The t�t MC shape is obtained using the measured value of fSinglet. FIG. 5 (color online). Expected C.L. bands for fSinglet. The measured value is shown on the horizontal axis, and the input value on the vertical axis. The wide-dashed line shows the expected value, and the black-white fine-dashed line indicates the measured value of fSinglet. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 092002 (2011) 092002-6 the distribution for one of the regions of the discriminating color-flow variable, using the measured t�t cross section and measured fSinglet. The expected 99% C.L. and 95% C.L. limits are fSinglet > 0:011 and fSinglet > 0:277, respectively, corresponding to an expected sensitivity to exclude fSinglet ¼ 0 of about 3 standard deviations, based on pseu- doexperiments. The 68% C.L. allowed region from data is 0:179< fSinglet < 0:879. Figure 5 shows the expected 68%, 95%, and 99% C.L. bands for fSinglet. In summary, we have presented the first study of color flow in t�t events, with the method of jet pull, using 5:3 fb�1 of D0 integrated luminosity. The standard model MC predictions are found to be in good agreement with data, for both the jets from the hadronically decaying W boson, which should be in a color-singlet configuration, and the b-tagged jets from the top quark decays, which should be in a color-octet configuration. To quantify our ability to separate singlet from octet color flow, we measured the color representation of the hadronically decayingW boson and found fSinglet ¼ 0:56� 0:42ðstatþ systÞ, while the expected 95% C.L. limit was fSinglet > 0:277. The ability to use color-flow information experimentally will benefit a wide range of measurements and searches for new physics. We thank Jason Gallicchio, Matthew Schwartz, Steve Mrenna, Peter Skands, and Jay Wacker for discussions and guidance. 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