Measurement of theW boson helicity in top quark decays using 5:4 fb�1 of p �p collision data 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 Y. Arnoud,14 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,2 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 M. Ćwiok,30 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 G. Hesketh,59 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 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 P. Rich,43 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, 032009 (2011) 1550-7998=2011=83(3)=032009(18) 032009-1 � 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. Zivkovic67 (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, 032009 (2011) 032009-2 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 1 December 2010; published 18 February 2011) We present a measurement of the helicity of the W boson produced in top quark decays using t�t decays in the ‘þ jets and dilepton final states selected from a sample of 5:4 fb�1 of collisions recorded using the D0 detector at the Fermilab Tevatron p �p collider. We measure the fractions of longitudinal and right-handed W bosons to be f0 ¼ 0:669� 0:102½�0:078ðstat:Þ � 0:065ðsyst:Þ� and fþ ¼ 0:023� 0:053½�0:041ðstat:Þ � 0:034ðsyst:Þ�, respectively. This result is consistent at the 98% level with the standard model. A measurement with f0 fixed to the value from the standard model yields fþ ¼ 0:010� 0:037½�0:022ðstat:Þ � 0:030ðsyst:Þ:�. DOI: 10.1103/PhysRevD.83.032009 PACS numbers: 14.65.Ha, 12.15.Ji, 12.38.Qk, 14.70.Fm I. INTRODUCTION The top quark is the heaviest known fundamental parti- cle and was discovered in 1995 [1,2] at the Tevatron proton-antiproton collider at Fermilab. The dominant top quark production mode at the Tevatron is p �p ! t�tX. Since the time of discovery, over 100 times more integrated luminosity has been collected, providing a large number of t�t events with which to study the properties of the top quark. In the standard model (SM), the branching ratio for the top quark to decay to a W boson and a b quark is >99:8%. The on shell W boson from the top quark decay has three possible helicity states, and we define the fraction of W bosons produced in these states as f0 (longitudinal), f� (left-handed), and fþ (right-handed). In the SM, the top quark decays via the V � A charged weak current interac- tion, which strongly suppresses right-handedW bosons and predicts f0 and f� at leading-order in terms of the top quark mass (mt), W boson mass (MW), and b quark mass (mb) to be [3] f0 ¼ ð1� y2Þ2 � x2ð1þ y2Þ ð1� y2Þ2 þ x2ð1� 2x2 þ y2Þ (1) f� ¼ x2 � 1� x2 þ y2 þ ffiffiffiffi � p � ð1� y2Þ2 þ x2ð1� 2x2 þ y2Þ (2) *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 THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-3 http://dx.doi.org/10.1103/PhysRevD.83.032009 fþ ¼ x2 � 1� x2 þ y2 � ffiffiffiffi � p � ð1� y2Þ2 þ x2ð1� 2x2 þ y2Þ ; (3) where x ¼ MW=mt, y ¼ mb=mt, and � ¼ 1þ x4 þ y4 � 2x2y2 � 2x2 � 2y2. With the present measurements of mt ¼ 173:3� 1:1 GeV=c2 [4] and MW ¼ 80:399� 0:023 GeV=c2 [5], and taking mb to be 5 GeV=c2, the SM expected values are f0 ¼ 0:698, f� ¼ 0:301, and fþ ¼ 4:1� 10�4. The absolute uncertainties on the SM expectations, which arise from uncertainties on the particle masses as well as contributions from higher-order effects, are � ð0:01–0:02Þ for f0 and f� and Oð10�3Þ for fþ [3]. In this paper, we present a measurement of the W boson helicity fractions f0 and fþ and constrain the fraction f� through the unitarity requirement of f� þ fþ þ f0 ¼ 1. Any significant deviation from the SM expectation would be an indication of new physics, arising from either a deviation from the expected V � A coupling of the tWb vertex or the presence of non-SM events in the data sample. The most recently published results are summarized in Table I. The extraction of the W boson helicities is based on the measurement of the angle �? between the opposite of the direction of the top quark and the direction of the down- type fermion (charged lepton or d, s quark) decay product of theW boson in theW boson rest frame. The dependence of the distribution of cos�� on the W boson helicity frac- tions is given by !ðcÞ / 2ð1� c2Þf0 þ ð1� cÞ2f� þ ð1þ cÞ2fþ (4) with c ¼ cos��. After selection of a t�t enriched sample the four-momenta of the t�t decay products in each event are reconstructed as described below, permitting the calcula- tion of cos��. Once the cos�� distribution is measured, the values of f0 and fþ are extracted with a binned Poisson likelihood fit to the data. The measurement presented here is based on p �p collisions at a center-of-mass energyffiffiffi s p ¼ 1:96 TeV corresponding to an integrated luminosity of 5:4 fb�1, 5 times more than the amount used in the result in Ref. [6]. II. DETECTOR The D0 Run II detector [8] is a multipurpose detector which consists of three primary systems: a central tracking system, calorimeters, and a muon spectrometer. We use a standard right-handed coordinate system. The nominal collision point is the center of the detector with coordinate (0,0,0). The direction of the proton beam is the positiveþz axis. The þx axis is horizontal, pointing away from the center of the Tevatron ring. The þy axis points vertically upwards. The polar angle, �, is defined such that � ¼ 0 is theþz direction. Usually, the polar angle is replaced by the pseudorapidity � ¼ � ln tanð�2Þ. The azimuthal angle, �, is defined such that � ¼ 0 points along the þx axis, away from the center of the Tevatron ring. The silicon microstrip tracker (SMT) is the innermost part of the tracking system and has a six-barrel longitudinal structure, where each barrel consists of a set of four layers arranged axially around the beam pipe. A fifth layer of SMT sensors was installed near the beam pipe in 2006 [9]. The data set recorded before this addition is referred to as the ‘‘Run IIa’’ sample, and the subsequent data set is referred to as the ‘‘Run IIb’’ sample. Radial disks are interspersed between the barrel segments. The SMT pro- vides a spatial resolution of approximately 10 �m in r�� and 100 �m in r� z (where r is the radial distance in the x-y plane) and covers j�j< 3. The central fiber tracker (CFT) surrounds the SMT and consists of eight concentric carbon fiber barrels holding doublet layers of scintillating fibers (one axial and one small-angle stereo layer), with the outermost barrel covering j�j< 1:7. The solenoid surrounds the CFT and provides a 2 T uniform axial magnetic field. The liquid-argon/uranium calorimeter system is housed in three cryostats, with the central calo- rimeter (CC) covering j�j< 1:1 and two end calorimeters (EC) covering 1:5< j�j< 4:2. The calorimeter is made up of unit cells consisting of an absorber plate and a signal board; liquid-argon, the active material of the calorimeter, fills the gap. The inner part of the calorimeter is the electromagnetic (EM) section and the outer part is the hadronic section. The muon system is the outermost part of the D0 detector and covers j�j< 2. It is primarily made of two types of detectors, drift tubes and scintillators, and consists of three layers (A,B, and C). Between layer A and layer B, there is magnetized steel with a 1.8 T toroidal field. III. DATA AND SIMULATION SAMPLES At the Tevatron, with proton and antiproton bunches colliding at intervals of 396 ns, the collision rate is about 2.5 MHz. Out of these 2:5� 106 beam crossings per sec- ond at D0, only those that produce events which are identified by a three-level trigger system as having prop- erties matching the characteristics of physics events of interest are retained, at a rate of �100 Hz [8,10]. This TABLE I. Summary of the most recent W boson helicity measurements from the D0 [6] and CDF [7] Collaborations. The first uncertainty is statistical and the second systematic. D0, 1 fb�1 [6] f0 ¼ 0:425� 0:166� 0:102, fþ ¼ 0:119� 0:090� 0:053 fþ fixed: f0 ¼ 0:619� 0:090� 0:052 f0 fixed: fþ ¼ �0:002� 0:047� 0:047 CDF, 2:7 fb�1 [7] f0 ¼ 0:88� 0:11� 0:06, fþ ¼ �0:15� 0:07� 0:06 fþ fixed: f0 ¼ 0:70� 0:07� 0:04 f0 fixed: fþ ¼ �0:01� 0:02� 0:05 V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-4 analysis is performed using events collected with the trig- gers applicable for ‘þ jets and dilepton final states be- tween April 2002 and June 2009, corresponding to a total integrated luminosity of 5:4 fb�1. Analysis of the Run IIa sample, which totals about 1 fb�1, was presented in Ref. [6]. Here, we describe the analysis of the Run IIb data sample and then combine our result with the result from Ref. [6] when reporting our measurement from the full data sample. The Monte Carlo (MC) simulated samples used for modeling the data are generated with ALPGEN [11] inter- faced to PYTHIA [12] for parton shower simulation, passed through a detailed detector simulation based on GEANT [13], overlaid with data collected from a random subsam- ple of beam crossings to model the effects of noise and multiple interactions, and reconstructed using the same algorithms that are used for data. For the signal (t�t) sample, we must model the distribution of cos�� corresponding to any set of values for the W boson helicity fractions, a task that is complicated by the fact that ALPGEN can only produce linear combinations of V � A and V þ A tWb couplings. Hence, for this analysis, we use samples that are either purely V � A or purely V þ A, and use a re- weighting procedure (described below) to form models of arbitrary helicity states. ALPGEN is also used for generating all V þ jets processes, where V represents the vector bo- sons. PYTHIA is used for generating diboson (WW,WZ, and ZZ) backgrounds in the dilepton channels. Background from multijet production is modeled using data. IV. EVENT SELECTION We expect a priori that our measurement will be limited by statistics, so our analysis strategy aims to maximize the acceptance for t�t events. The selection is done in two steps. In the first step, a loose initial selection using data quality, trigger, object identification, and kinematic criteria is ap- plied to define a sample with the characteristics of t�t events. Subsequently, a multivariate likelihood discrimi- nant is defined to separate the t�t signal from the back- ground in the data. We use events in the ‘þ jets and dilepton t�t decay channels, which are defined below. In the ‘þ jets decay t�t ! WþW�b �b ! ‘�qq0b �b, events contain one charged lepton (where lepton here refers to an electron or a muon), at least four jets with two of them being b quark jets, and significant missing transverse energy ET (defined as the opposite of the vector sum of the transverse energies in each calorimeter cell, corrected for the energy carried by identified muons and energy added or subtracted due to the jet energy calibration described below). The event selection requires at least four jets with transverse momentum pT > 20 GeV=c and j�j< 2:5 with the leading jet pT > 40 GeV=c. At least one lepton is required with pT > 20 GeV=c and j�j< 1:1 (2.0) for electrons (muons). Requirements are also made on the value of ET and the angle between the ET vector and the lepton (to reduce the contribution of events in which mismeasurement of the lepton energy gives rise to spurious ET): in the eþ jets channel the requirement is ET > 20 GeV and ��ðe; ETÞ> 0:7�� 0:045 � ET=GeV, and in the �þ jets channel the requirement is ET > 25 GeV and ��ð�;ETÞ> 2:1� 0:035 � ET=GeV. In ad- dition, for the �þ jets channel, the invariant mass of the selected muon and any other muon in the event is required to be outside of the Z boson mass window (< 70 GeV=c2 or >100 GeV=c2). For the dilepton decay channel, t�t ! WþW�b �b ! �‘�‘0 ��0b �b, the signature is two leptons of opposite charge, two b quark jets, and significant ET . The event selection requires at least two jets with pT > 20 GeV=c and j�j< 2:5 and two leptons (electron or muon) with pT > 20 GeV=c. The muons are required to have j�j< 2:0, and the electrons are required to have j�j< 1:1 or 1:5< j�j< 2:5. Jets are defined using a midpoint cone algorithm [14] with radius 0.5. Their energies are first calibrated to be equal, on average, to the sums of the energies of the particles within the jet cone. This calibration accounts for the energy response of the calorimeters, the energy that crosses the cone boundary due to the transverse shower size, and the additional energy from event pileup and multiple p �p interactions in a single beam crossing. The energy added to or subtracted from each jet due to the above calibration is propagated to the calculation of ET . Subsequently, an additional correction to for the average energy radiated by gluons outside of the jet cone is applied to the jet energy. Electrons are identified by their energy deposition and shower shape in the calorimeter combined with information from the tracking system. Muons are identified using information from the muon detector and the tracking system. We require the (two) highest-pT lep- ton(s) to be isolated from other tracks and calorimeter energy deposits in the ‘þ jets (dilepton) channel. For all channels, we require a well-reconstructed p �p vertex (PV) with the distance in z between this vertex and the point of closest approach of the lepton track being less than 1 cm. The main sources of background after the initial selec- tion in the ‘þ jets channel are W þ jets and multijet production; in the dilepton channels they are Z boson and diboson production as well as multijet and W þ jets production. Events with fewer leptons than required (mul- tijet events, orW þ jets events in the dilepton channel) can enter the sample when jets are either misidentified as leptons or contain a lepton from semileptonic quark decay that passes the electron likelihood or muon isolation crite- rion. In all cases they are modeled using data with relaxed lepton identification or isolation criteria. The multijet con- tribution to the ‘þ jets final states in the initially-selected sample is estimated from data following the method de- scribed in Ref. [15]. This method relies on the selection of two data samples, one (the tight sample) with the standard MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-5 lepton criteria, and the other (the loose sample) with re- laxed isolation or identification criteria. The numbers of events in each sample are Nloose ¼ Nt�tþW þ NMJ (5) Ntight ¼ "‘N t�tþW þ "MJN MJ: (6) Here the coefficient "‘ is the efficiency for isolated leptons in t�t orWjjjj events to satisfy the standard lepton require- ments, while "MJ is the efficiency for a jet in multijet events to satisfy those requirements. We measure "‘ in Z ! ‘‘ control samples and "MJ in multijet control samples. Inserting the measured values, we solve Eqs. (5) and (6) to obtain the number of multijet events (NMJ) and the number of events with isolated leptons (Nt�tþW). In the dilepton channels, we model the background due to jets being misidentified as isolated leptons using data events where both leptons have the same charge. This background originates from multijets events with two jets misidentified as leptons and from W þ jets events with one jet misiden- tified as a lepton. To separate the t�t signal from these sources of back- ground, we define a multivariate likelihood and retain only events above a certain threshold in the value of that like- lihood. The set of variables used in the likelihood and the threshold value are optimized separately for each t�t decay channel. The first step in the optimization procedure is to identify a set of candidate variables that may be used in the likelihood. The set we consider is (i) Aplanarity A, defined as 3=2 of the smallest eigen- value of the normalized momentum tensor for the jets (in the ‘þ jets channels) or jets and leptons (in the dilepton channels). The aplanarity A is a mea- sure of the deviation from flatness of the event, and t�t events tend to have larger values than background. (ii) Sphericity S, defined as 3=2 of the sum of the two smallest eigenvalues of the normalized momentum tensor for the jets (in the ‘þ jets channels) or jets and leptons (in the dilepton channels). This variable is a measure of the isotropy of the energy flow in the event, and t�t events tend to have larger values than background. (iii) HT , introduced in Refs. [16,17], is defined as the scalar sum of the jets’ pT values. Jets arising from gluon radiation often have lower pT than jets in t�t events, so background events tend to have smaller values of HT than signal. (iv) Centrality C, defined as HT HE , where HE is the sum of all jet energies. The centrality C is similar toHT but normalized in a way to minimize dependence on the top quark mass. (v) K0 Tmin, defined as �Rjjmin � ETmin EW T , where �Rjjmin is the distance in ��� space between the closest pair of jets, ETmin is the lowest jet ET value in the pair, and EW T is the transverse energy of the leptonically- decaying W boson (in the dilepton channels EW T is the magnitude of the vector sum of the ET and leading lepton pT). Only the four leading-ET jets are considered in computing this variable. Jets aris- ing from gluon radiation (as is the case for most of the background) tend to have lower values of K0 Tmin. (vi) mjjmin, defined as the smallest dijet mass of pairs of selected jets. This variable is sensitive to gluon radiation and tends to be smaller for background than signal. (vii) h, defined as the scalar sum of all the selected jet and lepton energies. Jets arising from gluon radia- tion often have lower energy than jets in t�t events, and leptons arising from the decay of heavy flavor jets often have lower energy than leptons from W boson decay, so background events tend to have smaller values of h than signal. (viii) �2 k, defined as the � 2 for a kinematic fit of ‘þ jets final states to the t�t hypothesis. Signal events tend to have smaller �2 values than background. This variable is not used for dilepton events, for which a kinematic fit is underconstrained. (ix) ��ðlepton; ETÞ, defined as the angle between the leading lepton and the ET .W þ jets events with ET arising from mismeasured lepton pT tend to have ��ðlepton; ETÞ � 0 or �. (x) b jet content of the event. Because of the long life- time of the b quark, tracks within jets arising from b quarks have different properties (such as larger impact parameters with respect to the PV and the presence of secondary decay vertices) than tracks within light-quark or gluon jets. The consistency of a given jet with the hypothesis that the jet was produced by a b quark is quantified with a neural network (NN) that considers several properties of the tracks contained within the jet cone [18]. In the ‘þ jets channels, we take the average of the NN values NNb of the two most b-like jets to form a variable called NNbavg, and in the dilepton channels we take theNNb values of the two most b-like jets as separate variables NNb1 (the largest NNb value) and NNb2 (the second-largest NNb value). For top quark events, these variables tend to be close to 1, while for events containing only light jets they tend to be close to zero. (xi) ET or �2 Z. For the e� and ee channels only, ET is considered as a variable in the likelihood discrimi- nant. In the �� channel, where spurious ET can arise from mismeasurement of the muon momen- tum, we instead use �2 Z, the � 2 of a kinematic fit to the Z ! �� hypothesis. (xii) Dilepton mass m‘‘. Also for the dilepton channels only, the invariant mass of the lepton pairs is considered as a variable in the classical likelihood. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-6 The motivation is to discriminate against Z boson production. We consider all combinations of the above variables to select the optimal set to use for each t�t decay channel. For a given combination of variables, the likelihood ratio Lt is defined as Lt ¼ exp nPNvar i¼1½lnðSBÞfiti � o exp nPNvar i¼1½lnðSBÞfiti � o þ 1 ; (7) where Nvar is the number of input variables used in the likelihood and ðSBÞfiti is the ratio of the parameterized signal and background probability density functions. We consider all possible subsets of the above variables to be used in Lt and scan across all potential selection criteria on Lt. For each Lt definition and prospective selection criterion, we compute the following figure of merit (FOM): FOM ¼ NSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NS þ NB þ 2 B q ; (8) where NS and NB are the numbers of signal and back- ground events expected to satisfy the Lt selection. The term B reflects the uncertainty in the background selection efficiency arising from any mismodeling of the input variables in the MC. To assess B, we compare each variable in data and MC in background-dominated samples. The background-dominated samples are created by forming a multivariate likelihood ratio (Eq. (7)) that does not use the variable under study, nor any variable that is strongly correlated with it, where the criterion is a correlation coefficient between �0:10 and 0.10. We select events that have low values of this likelihood and are therefore unlikely to be t�t events, such that 95% of MC t�t events are rejected. Because the t�t contribution to the selected data sample is negligible, we can directly compare the background model to data. The impact of any mismod- eling on the likelihood distribution is assessed by taking the ratio of the observed to the expected distributions as a function of each variable and fitting this to a polynomial. The result is that for each variable i we build a function ki that encodes the data/MC discrepancies in that variable. For each simulated background event, we reweight each likelihood according to the data/MC differences. For example, for a likelihood that uses n of the possible vari- ables, the likelihood is given a weight w ¼ Yn i¼1 kiðviÞ: (9) The quantity B is the difference in the predicted back- ground yield when the unweighted and weighted Lt dis- tributions are used for background. This uncertainty is propagated through the analysis as one component of the total uncertainty in the background yield. The sets of variables and Lt selection criteria that max- imize the FOM defined in Eq. (8) for each t�t final state are shown in Tables II and III. Figures 1–5 show the distribu- tions of the variables in the best likelihood discriminant Lt for the events passing the preselection cuts, where the signal and background contributions are normalized as described below. In addition, we use Lt to determine the signal and background content of the initially-selected sample by performing a binned Poisson maximum like- lihood fit to the Lt distribution where the signal and total background normalizations are free parameters. The W þ jets contribution is determined by the fit to the Lt TABLE III. The set of variables chosen for use in Lt for the dilepton channels. The number of background and t�t events in the initially-selected data, as determined from a fit to the Lt distribution, are also presented. e� ee �� Events passing initial selection 323 3275 5740 Variables in optimized Lt A, S, h, mjjmin A, S, mjjmin A, S, mjjmin, K 0 Tmin K0 Tmin, ET , NNb1, m‘‘ ET , NNb1, m‘‘ �2 Z, NNb1 N (t�t) 178:7� 15:6 74:9� 10:7 86:0� 13:8 N (background) 144:3� 14:5 3200� 57 5654� 76 TABLE II. The set of variables chosen for use in Lt for the eþ jets and �þ jets channels. The numbers of background and t�t events in the initially-selected data, as determined from a fit to the Lt distribution, are also presented. eþ jets �þ jets Events passing initial selection 1442 1250 Variables in best Lt C C HT HT K0 Tmin K0 Tmin NNbavg NNbavg �2 k h mjjmin A N (t�t) 592:6� 31:8 612:7� 31:0 N (W þ jets) 690:2� 21:8 579:8� 18:6 N (multijet) 180:3� 9:9 6:5� 4:9 MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-7 Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb Aplanarity 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 E n tr ie s/ 0. 04 0 100 200 300 400 500 600 700 800 Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb Centrality 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 50 100 150 200 250 300 350 Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(c) DØ, L=4.3 fb (GeV/c)TH 0 50 100 150 200 250 300 350 400 450 E n tr ie s/ (4 0 G eV /c ) 0 50 100 150 200 250 300 350 400 Data Multijet Wjj Wcc Wbb t t -1(c) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(d) DØ, L=4.3 fb k 2χ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 05 0 50 100 150 200 250 300 Data Multijet Wjj Wcc Wbb t t -1(d) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(e) DØ, L=4.3 fb 0 20 40 60 80 100 120 140 160 180 200 )2 (GeV/cmjjmin )2 E n tr ie s/ (1 0 G eV /c 0 50 100 150 200 250 300 350 400 Data Multijet Wjj Wcc Wbb t t -1(e) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(f) DØ, L=4.3 fb Tmin ’ K 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 E n tr ie s/ 0. 25 0 100 200 300 400 500 Data Multijet Wjj Wcc Wbb t t -1(f) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(g) DØ, L=4.3 fb bavgNN 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 100 200 300 400 500 600 700 800 Data Multijet Wjj Wcc Wbb t t -1(g) DØ, L=4.3 fb FIG. 1 (color online). Comparison of data and MC of the variables for preselected events, chosen for the best likelihood discriminant Lt in the eþ jets channel: (a) A, (b) C, (c) HT , (d) � 2 k, (e) mjjmin, (f) K 0 Tmin, and (g) NNbavg. The uncertainties on the data points are statistical only. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-8 distribution, while the multijet component is constrained to be consistent with the value determined from Eqs. (5) and (6). In the dilepton channels, the relative contributions of the different background sources are fixed according to their expected yield, but the total background is allowed to float. The signal and background yields in the initially- selected sample for the ‘þ jets channels are listed in Table II and for the dilepton channels in Table III. Figures 6 and 7 show the distribution of the best likelihood discriminant for each channel, where the signal and back- ground contributions are normalized according to the val- ues returned by the fit. Tables IVand V show the optimal Lt cut value for each channel and the final number of events in data and the expected numbers of signal and background events after applying the Lt requirement. V. TEMPLATES After the final event selection, cos�� is calculated for each event by using the reconstructed top quark and W boson four-momenta. In the ‘þ jets decay channel, the four-momenta are reconstructed using a kinematic fit with the constraints: (i) two jets should give the invariant mass of the W boson (80:4 GeV=c2), (ii) the invariant mass of the lepton and neutrino should be the W boson mass, (iii) the mass of the reconstructed top and antitop quark Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb Centrality 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 50 100 150 200 250 300 Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb h (GeV) 0 100 200 300 400 500 600 700 800 900 1000 E n tr ie s/ 40 G eV 0 20 40 60 80 100 120 140 160 180 200 220 240 Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(c) DØ, L=4.3 fb TminK 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ’ E n tr ie s/ 0. 25 0 50 100 150 200 250 300 350 400 450 Data Multijet Wjj Wcc Wbb t t -1(c) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(d) DØ, L=4.3 fb bavgNN 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 100 200 300 400 500 600 Data Multijet Wjj Wcc Wbb t t -1(d) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(e) DØ, L=4.3 fb (GeV/c)TH 0 50 100 150 200 250 300 350 400 450 E n tr ie s/ (4 0 G eV /c ) 0 50 100 150 200 250 300 350 Data Multijet Wjj Wcc Wbb t t -1(e) DØ, L=4.3 fb FIG. 2 (color online). Comparison of data and MC of the variables for preselected events, chosen for the best likelihood discriminant Lt in the �þ jets channel: (a) C, (b) h, (c) K0 Tmin, (d) NNbavg, and (e) HT . The uncertainties on the data points are statistical only. MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-9 Aplanarity 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 E n tr ie s/ 0. 05 0 20 40 60 80 100 120 140 160 180 200 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 20 40 60 80 100 120 140 160 180 200 -1DØ, L=4.3 fb(a) Data Fake lepton ZZ WZ WW ττ→Z tt Sphericity 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 10 20 30 40 50 60 70 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 -1DØ, L=4.3 fb(b) Data Fake lepton ZZ WZ WW ττ→Z tt )2 (GeV/cjjminm 0 20 40 60 80 100 120 140 160 180 200 )2 E n tr ie s/ (2 0 G eV /c 0 10 20 30 40 50 60 70 80 0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 50 60 70 80 -1DØ, L=4.3 fb(c) Data Fake lepton ZZ WZ WW ττ→Z tt ’ TminK 0 5 10 15 20 25 E n tr ie s/ 2. 5 0 50 100 150 200 250 300 0 5 10 15 20 25 0 50 100 150 200 250 300 -1DØ, L=4.3 fb(d) Data Fake lepton ZZ WZ WW ττ→Z tt (GeV)TE 0 20 40 60 80 100 120 140 160 180 200 E n tr ie s/ 10 G eV 0 10 20 30 40 50 0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 50 -1DØ, L=4.3 fb(e) Data Fake lepton ZZ WZ WW ττ→Z tt b1NN 0 0.2 0.4 0.6 0.8 1 1.2 E n tr ie s/ 0. 12 0 20 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 1.2 0 20 40 60 80 100 120 140 160 180 -1DØ, L=4.3 fb(f) Data Fake lepton ZZ WZ WW ττ→Z tt h (GeV) 0 100 200 300 400 500 E n tr ie s/ 55 G eV 0 20 40 60 80 100 120 0 100 200 300 400 500 0 20 40 60 80 100 120 -1DØ, L=4.3 fb(g) Data Fake lepton ZZ WZ WW ττ→Z tt )2Dilepton mass (GeV/c 0 20 40 60 80 100 120 140 160 180 200 )2 E n tr ie s/ (2 0 G eV /c 0 20 40 60 80 100 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 -1DØ, L=4.3 fb(h) Data Fake lepton ZZ WZ WW ττ→Z tt FIG. 3 (color online). Comparison of data and MC of the variables for preselected events, chosen for the best likelihood discriminant Lt in the e� channel: (a)A, (b) S, (c) mjjmin, (d) K 0 Tmin, (e) ET , (f) NNb1, (g) h, and (h) m‘‘. The uncertainties on the data points are statistical only. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-10 should be 172:5 GeV=c2, and (iv) the ~pT of the t�t system should be opposite that of the unclustered energy in the event. The four highest-pT jets in each event are used in the fit, and among the 12 possible permutations in the assign- ment of the jets to initial partons, the solution with the highest probability is chosen, considering both the NNb values of the four jets and �2 k. This procedure selects the correct jet assignment in 59% of MC t�t events. With the jet assigned, the complete kinematics of the t�t decay products (i.e., including the neutrino) are determined, allowing us to boost to the rest frames of each W boson in the event. We compute cos�� for the W boson that decays leptonically. The hadronic W boson decay from the other top quark in the event also contains information about the helicity of that W boson, but since we do not distinguish between jets formed from up-type and down-type quarks, we can not identify the down-type fermion to calculate cos��. We therefore calculate only j cos��j, which is identical for both jets in the rest frame of the hadronically-decaying W boson. Left-handed and right-handed W bosons have identical j cos��j distributions, but we can distinguish ei- ther of those states from longitudinal W bosons, thereby improving the precision of the measurement. In the dilepton decay channel, the presence of two neutrinos prevents a constrained kinematic fit but with the assumption that the top quark mass is 172:5 GeV=c2, an algebraic solution for the neutrino momenta can be obtained (up to a two-fold ambiguity in pairing the jets and leptons, and a four-fold solution ambiguity). To account for the lepton and jet energy resolutions, the Aplanarity 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 E n tr ie s/ 0. 05 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(a) Sphericity 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 100 200 300 400 500 600 700 800 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 700 800 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(b) )2 (GeV/cjjminm 0 20 40 60 80 100 120 140 160 180 200 )2 E n tr ie s/ (2 0 G eV /c 0 200 400 600 800 1000 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(c) (GeV)TE 0 20 40 60 80 100 120 140 160 180 200 E n tr ie s/ 10 G eV 0 200 400 600 800 1000 1200 1400 1600 1800 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 1600 1800 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(d) b1NN 0 0.2 0.4 0.6 0.8 1 1.2 E n tr ie s/ 0. 12 0 500 1000 1500 2000 2500 3000 0 0.2 0.4 0.6 0.8 1 1.2 0 500 1000 1500 2000 2500 3000 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(e) )2Dilepton mass (GeV/c 0 20 40 60 80 100 120 140 160 180 200 )2 E n tr ie s/ (5 G eV /c 0 200 400 600 800 1000 1200 1400 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(f) FIG. 4 (color online). Comparison of data and MC of the variables for preselected events, chosen for the best likelihood discriminant Lt in the ee channel: (a) A, (b) S, (c) mjjmin, (d) ET , (e) NNb1, and (f) m‘‘. The uncertainties on the data points are statistical only. MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-11 procedure described above is repeated 500 times with the energies fluctuated according to their uncertainties, and the average of all the solutions is used as the value of cos�� for each top quark. As mentioned above, the extraction of both f0 and fþ requires comparing the data with the MC models in which both of these values are varied. Since ALPGEN can only produce linear combinations of V � A and V þ A tWb couplings, it is unable to produce non-SM f0 values, and can produce fþ values only in the range [0, 0.30]. We therefore start with ALPGEN V � A and V þ A samples and divide the samples in bins of parton-level cos��. For each bin, we note the efficiency for the event to satisfy the event selection and the distribution of reconstructed cos�� values. With this information, we determine the expected distribution of reconstructed cos�� values for any assumed W helicity fractions, and, in particular, we choose to derive the distributions expected for purely left-handed, longitu- dinal, or right-handed W bosons, as shown in Fig. 8. The deficit of entries near cos�� ¼ �1 relative to the expecta- tion from Eq. (4) is due to the pT requirement imposed when selecting leptons. We verify the reweighting proce- dure by comparing the generated V � A ALPGEN samples with the combination of reweighted distributions expected for V � A couplings and find that these distributions agree within the MC statistics. The templates for background samples are obtained directly from the relevant MC or data background samples and are shown in Fig. 9. Aplanarity 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 E n tr ie s/ 0. 05 0 500 1000 1500 2000 2500 3000 3500 4000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 500 1000 1500 2000 2500 3000 3500 4000 -1DØ, L=4.3 fb(a) Data µFake ZZ WZ WW ττ→Z µµ→Z tt Sphericity 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 200 400 600 800 1000 1200 1400 1600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 200 400 600 800 1000 1200 1400 1600 -1DØ, L=4.3 fb(b) Data µFake ZZ WZ WW ττ→Z µµ→Z tt ’ TminK 0 5 10 15 20 25 E n tr ie s/ 2. 5 0 1000 2000 3000 4000 5000 6000 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 6000 -1DØ, L=4.3 fb(c) Data µFake ZZ WZ WW ττ→Z µµ→Z tt )2 (GeV/cjjminm 0 20 40 60 80 100 120 140 160 180 200 )2 E n tr ie s/ (2 0 G eV /c 0 200 400 600 800 1000 1200 1400 1600 1800 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 1600 1800 -1DØ, L=4.3 fb(d) Data µFake ZZ WZ WW ττ→Z µµ→Z tt Z 2χ 0 20 40 60 80 100 120 140 160 180 200 E n tr ie s/ 10 0 500 1000 1500 2000 2500 0 20 40 60 80 100 120 140 160 180 200 0 500 1000 1500 2000 2500 -1DØ, L=4.3 fb(e) Data µFake ZZ WZ WW ττ→Z µµ→Z tt b1NN 0 0.2 0.4 0.6 0.8 1 1.2 E n tr ie s/ 0. 12 0 1000 2000 3000 4000 5000 0 0.2 0.4 0.6 0.8 1 1.2 0 1000 2000 3000 4000 5000 -1DØ, L=4.3 fb(f) Data µFake ZZ WZ WW ττ→Z µµ→Z tt FIG. 5 (color online). Comparison of data and MC of the variables for preselected events, chosen for the best likelihood discriminant Lt in the�� channel: (a)A, (b) S, (c) K0 Tmin, (d)mjjmin, (e) � 2 Z, and (f) NNb1. The uncertainties on the data points are statistical only. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-12 VI. MODEL-INDEPENDENT W HELICITY FIT TheW boson helicity fractions are extracted by comput- ing a binned Poisson likelihood Lðf0; fþÞ with the distri- bution of cos�� in the data to be consistent with the sum of signal and background templates. The likelihood is a func- tion of theW boson helicity fractions f0 and fþ, defined as Lðf0; fþÞ ¼ YNchan i¼1 YNbkg;i j¼1 e�ðnb;ij� �nb;ijÞ2=2 2 b;ij � YNbins;i k¼1 Pðdik; nikÞ; (10) where Pðdik; nikÞ is the Poisson probability for observing dik events given a mean expectation value nik, Nchan is the number of channels in the fit (a maximum of five in this analysis: eþ jets, �þ jets, e�, ee, and ��), Nbkg;i is the number of background sources in the ith channel, Nbins;i is the number of bins in the cos�� distribution for any given channel (plus the number of bins in the j cos��j distribution for hadronicW boson decays in the ‘þ jets channels), �nb;ij is the nominal number of cos�� measurements from the jth background contributing to the ith channel, b;ij is the uncertainty on �nb;ij, nb;ij is the fitted number of cos�� measurements for this background, dik is the number of Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb t Optimal L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 04 0 20 40 60 80 100 120 140 160 180 200 Data Multijet Wjj Wcc Wbb t t -1(a) DØ, L=4.3 fb Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb t Optimal L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 04 0 50 100 150 200 250 Data Multijet Wjj Wcc Wbb t t -1(b) DØ, L=4.3 fb FIG. 6 (color online). Best Lt variable for the (a) �þ jets and (b) eþ jets channels. The normalization of the signal and background models is determined by the Poisson maximum likelihood fit to the Lt distribution. The arrows mark the required Lt values for events in each channel. t Optimal L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 01 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 -1DØ, L=4.3 fb(a) Data Fake lepton ZZ WZ WW ττ→Z tt t Optimal L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 01 1 10 210 310 410 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10 210 310 410 Data Fake e ZZ WZ WW ττ→Z ee→Z tt -1DØ, L=4.3 fb(b) t Optimal L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 01 1 10 210 310 410 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10 210 310 410 -1DØ, L=4.3 fb(c) Data µFake ZZ WZ WW ττ→Z µµ→Z tt FIG. 7 (color online). Best Lt variable for the (a) e�, (b) ee, and (c) �� decay channels. The normalization of the signal and background models is determined by the Poisson maximum likelihood fit to the Lt distribution. The arrows mark the required Lt values for events in each channel. TABLE IV. Expected background and t�t yields, and the num- ber of events observed, after the selection on Lt in the ‘þ jets decay channels. eþ jets �þ jets Optimized Lt requirement >0:58 >0:29 t�t 484:4� 41:4 567:2� 47:3 W þ jets 111:7� 12:6 227:7� 19:2 Multijet 58:1� 3:9 4:0� 3:1 Total 656:2� 43:4 798:9� 51:2 Observed 628 803 MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-13 data events in the kth bin of cos�� for the ith channel, and nik is the predicted sum of signal and background events in that bin. The nik can be expressed as nik ¼ ns;i "0f0p0;ik þ "þfþpþ;ik þ "�ð1� f0 � fþÞp�;ik f�"� þ f0"0 þ fþ"þ þ XNbkg j¼1 nb;ijpb;ijk; (11) where ns;i represents the number of cos�� measurements from signal events in a given channel, the p represent the probabilities for an event from some source to appear in bin k for channel i (as determined from the templates), the subscripts 0, þ, � refer to the templates for t�t events in which the W bosons have zero, negative, or positive helic- ity, and the subscript b, i refers to the templates for the ith background source. The efficiency for a t�t event to satisfy the selection criteria depends upon the helicity states of the two W bosons in the event; the " are therefore necessary to translate the fractions of events with different helicity states in the selected sample to the fractions that were produced. The quantity "� is defined as "� ¼ X �0 f�0"��0 ; (12) where "��0 is the relative efficiency for events with W bosons in the � and �0 helicity states to satisfy the selection criteria. The values of "��0 for each t�t decay channel are given in Table VI. While performing the fit, both f0 and fþ are allowed to float freely, and the measured W helicity fractions correspond to those leading to the highest like- lihood value. We check the performance of the fit using simulated ensembles of events, with all values of f0 and fþ from 0 through 1 as inputs in increments of 0.1, with the sum of f0 and fþ not exceeding unity. We simulate input data distributions for the various values by combining the pure left-handed, longitudinal, and right-handed templates in the assumed proportions. In these ensembles, we draw a random subset of the simulated events, with the number of events chosen in each channel fixed to the number ob- served in data. Within the constant total number of events, the numbers of signal and background events are fluctuated binomially around the expected values. Each of these sets of simulated events is passed through the maximum like- lihood fit using the standard cos�� templates. We find that the average fit output value is close to the input value across the entire range of possible values for the helicity fractions, with the small differences between the input and output values being consistent with statistical fluctuations in the ensembles. As an example, the set of f0 and fþ TABLE V. Expected background and t�t yields, and the number of events observed, after the selection on Lt in the dilepton decay channels. Source e� ee �� Optimized Lt requirement >0:28 >0:934 >0:972 t�t 186:6� 0:4 44:5� 0:3 43:6� 0:3 Z= � ! ‘þ‘� N/A 7:4� 1:0 19:1� 1:3 Z= � ! �� 11:2� 3:7 0:8� 0:3 0:35� 0:05 WW 5:6� 1:4 0:3� 0:1 0:13� 0:05 WZ 1:5� 0:5 0:28� 0:04 0:16� 0:01 ZZ 1:0� 0:5 0:34� 0:04 0:57� 0:04 Misidentified jets 15:9� 3:1 0:54� 0:48 3:7� 2:5 Total 221:7� 5:1 54:2� 1:2 67:7� 3:9 Observed 193 58 68 *|θ|cos 0 0.2 0.4 0.6 0.8 1 *θcos -1 -0.5 0 0.5 1 *θcos -1 -0.5 0 0.5 1 P ro b ab ili ty /0 .1 0.02 0.04 0.06 0.08 0.1 0.12 Left-handed Longitudinal Right-handed DØ (a) P ro b ab ili ty /0 .1 0.05 0.1 0.15 0.2 Left- or right-handed Longitudinal DØ(b) P ro b ab ili ty /0 .1 0 0.02 0.04 0.06 0.08 0.1 0.12 Left-handed Longitudinal Right-handed DØ (c) FIG. 8. Distribution of cos�� in t�t MC samples that were reweighted to derive the distributions for purely left-handed, longitudinal, or right-handed W bosons. The distribution for leptonically- and hadronically-decaying W bosons in ‘þ jets events are shown in (a) and (b), respectively, and the distribution for dilepton events is shown in (c). For hadronically-decaying W bosons the cos�� distribution for left- and right-handedW bosons is identical. All of the distributions are normalized to unity. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-14 values obtained when t�t events are drawn in the proportions expected in the SM is shown in Fig. 10. VII. SYSTEMATIC UNCERTAINTIES Systematic uncertainties are evaluated using simulated event ensembles in which both changes in the background yield and changes in the shape of the cos�� templates in signal and background are considered. The simulated samples from which the events are drawn can be either the nominal samples or samples in which the systematic effect under study has been shifted away from the nominal value. In general, the systematic uncertainties assigned to f0 and fþ are determined by taking an average of the absolute values of the differences in the average fit output values between the nominal and shifted V � A and V þ A samples. The jet energy scale, jet energy resolution, and jet iden- tification efficiency each have relatively small uncertain- ties that are difficult to observe above fluctuations in the MC samples. To make the effects more visible, we vary these quantities by�5 standard deviations and then divide the resulting differences in the average fit output by 5. The top quark mass uncertainty corresponds to shifting *θcos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 2 0 10 20 30 40 50 *θcos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 2 0 10 20 30 40 50 Wbb Wcc Wjj Multijet (a) DØ *|θ|cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 10 20 30 40 50 60 70 *|θ|cos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E n tr ie s/ 0. 1 0 10 20 30 40 50 60 70 Wbb Wcc Wjj Multijet (b) DØ *θcos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 2 0 5 10 15 20 25 *θcos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 2 0 5 10 15 20 25 ZZ WZ WW ττ→Z µµ ee or →Z Fake leptons (c) DØ FIG. 9 (color online). Distribution of cos�� in background samples. The distribution for leptonically- and hadronically- decaying W bosons in ‘þ jets events is shown in (a) and (b), respectively, and the distribution for dilepton events is shown in (c). All of the distributions are normalized to the expected yield for each source of background. TABLE VI. Efficiencies of differentW boson helicity configu- rations in t�t events to pass the selection criteria, relative to the efficiencies for a mixture of V � A and V þ A events. The indices �, 0, and þ correspond to the helicity states of the two W bosons, and their order is leptonic W, hadronic W for the ‘þ jets channel, and arbitrary for dilepton channels (where there is no distinction between the two W bosons in the event). Small differences in values in the dilepton channels under interchange of the indices are from variations in MC statistics. eþ jets �þ jets e� ee �� "�� 0.76 0.73 0.67 0.68 0.68 "�0 0.87 0.83 0.84 0.86 0.85 "�þ 0.76 0.73 0.88 0.89 0.89 "0� 0.94 0.95 0.85 0.86 0.87 "00 1.08 1.09 1.06 1.05 1.05 "0þ 0.94 0.95 1.10 1.05 1.05 "þ� 0.92 0.96 0.89 0.88 0.91 "þ0 1.06 1.11 1.12 1.03 1.07 "þþ 0.92 0.96 1.15 0.99 1.03 +f 0 0.2 0.4 0.6 0.8 1 0f 0 0.2 0.4 0.6 0.8 1 SM value DØ FIG. 10. Fit values for f0 and fþ obtained with 1000 MC simulations of the W boson helicity measurement. The SM helicity fractions, marked by the star, were taken as input to the simulations. The triangle corresponds to the physically allowed region where f0 þ fþ 1. MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-15 mt by 1:4 GeV=c2, which is the sum in quadrature of the uncertainty on the world average mt (1:1 GeV=c2) and the difference between the world average value (173:3 GeV=c2) and the value assumed in the analysis (172:5 GeV=c2). We evaluate the contribution of template statistics to the uncertainty by repeating the fit to the data 1000 times, fluctuating the signal and background distri- butions according to their statistics in each fit. The uncer- tainties due to the modeling of t�t events are separated into several categories and evaluated using special-purpose MC samples. The uncertainty in the model of gluon radiation is assessed using PYTHIA MC samples in which the amount of gluon radiation is shifted upwards and downwards; the impact of NLO effects is assessed by comparing the default leading-order ALPGEN generator with the NLO generator MC@NLO [19]; the uncertainty in the hadronic showering model is assessed by comparing ALPGEN events showered with PYTHIA and with HERWIG [20]; and lastly, the impact of color reconnection effects is assessed by comparing PYTHIA samples where the underlying event model does and does not include color reconnection. The uncertainty due to data and MC differences in the background cos�� distribution is derived by taking the ratio of the data and the MC distribution for a background-enriched sample (de- fined by requiring that events have low values of Lt) and then using that ratio to reweight the distribution of back- ground MC events that satisfy the standard selection. The uncertainty in the heavy flavor content of the background is estimated by varying the fraction of background events with heavy flavor jets by �20%. Uncertainties due to the fragmentation of b jets are evaluated by comparing the default fragmentation model, the Bowler scheme [21] tuned to data collected at the CERN LEP collider, with an alternate model tuned to data collected by the SLD collaboration [22]. Uncertainties in the parton distribution functions (PDFs) are estimated using the set of 2� 20 errors provided for the CTEQ6M [23] PDF. The analysis consistency uncertainty reflects the typical difference be- tween the input helicity fractions and the average output values observed in fits to simulated event ensembles. Finally, we include an uncertainty corresponding to muon triggers and identification, as control samples indicate some substantial data/MC discrepancies for the loose se- lection we use. All the systematic uncertainties are sum- marized in Table VII. VIII. RESULT Applying the model-independent fit to the Run IIb data, we find f0 ¼ 0:739� 0:091ðstat:Þ � 0:060ðsyst:Þ fþ ¼ �0:002� 0:045ðstat:Þ � 0:032ðsyst:Þ: (13) TABLE VII. Summary of the absolute systematic uncertainties on fþ and f0. Source Uncertainty (fþ) Uncertainty (f0) Jet energy scale 0.007 0.009 Jet energy resolution 0.004 0.009 Jet ID 0.004 0.004 Top quark mass 0.011 0.009 Template statistics 0.012 0.023 t�t model 0.022 0.033 Background model 0.006 0.017 Heavy flavor fraction 0.011 0.026 b fragmentation 0.000 0.001 PDF 0.000 0.000 Analysis consistency 0.004 0.006 Muon ID 0.003 0.021 Muon trigger 0.004 0.020 Total 0.032 0.060 *θcos -1 -0.5 0 0.5 1 E n tr ie s/ 0. 1 20 40 60 80 100 120 (a) -1DØ, L=4.3 fb *θcos -1 -0.5 0 0.5 1 E n tr ie s/ 0. 1 20 40 60 80 100 120 *|θ|cos 0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 1 0 50 100 150 200 (b) -1DØ, L=4.3 fb *|θ|cos 0 0.2 0.4 0.6 0.8 1 E n tr ie s/ 0. 1 0 50 100 150 200 *θcos -1 -0.5 0 0.5 1 E n tr ie s/ 0. 2 0 50 100 150 (c) -1DØ, L=4.3 fb *θcos -1 -0.5 0 0.5 1 E n tr ie s/ 0. 2 0 50 100 150 DØ data Signal + bkg. SM Signal + bkg. Bkg. FIG. 11 (color online). Comparison of the cos�� distribution in Run IIb data and the global best-fit model (solid line) and the SM (dashed line) for (a) leptonic W boson decays in ‘þ jets events, (b) hadronic W boson decays in ‘þ jets events, and (c) dilepton events. V.M. ABAZOV et al. PHYSICAL REVIEW D 83, 032009 (2011) 032009-16 The comparison between the best-fit model and the data is shown in Fig. 11, and the 68% and 95% C.L. contours in the ðfþ; f0Þ plane are shown in Fig. 12(a). To account for systematic uncertainties, we perform aMC smearing of the L distribution, where the width of the smearing in f0 and fþ is given by the systematic uncertainty on each helicity fraction and the correlation coefficient of �0:83 between them is taken into account. To assess the consistency of the result with the SM, we note that the change in � lnLðf0; fþÞ [Eq. (10)] between the best fit and the SM points is 0.24 considering only statistical uncertainties and 0.16 when systematic uncer- tainties are included. The probability of observing a greater deviation from the SM due to fluctuations in the data is 78% when only the statistical uncertainty is considered and 85% when both statistical and systematic uncertainties are considered. We have also split the data sample in various ways to check the internal consistency of the measurement. Using ‘þ jets events only, we find f0 ¼ 0:767� 0:117ðstat:Þ; fþ ¼ 0:018� 0:061ðstat:Þ; (14) and when using only dilepton events we find f0 ¼ 0:677� 0:144ðstat:Þ; fþ ¼ �0:013� 0:065ðstat:Þ: (15) We also divide the sample into events with only elec- trons (eþ jets and ee) and events with only muons (�þ jets and ��). The results for electrons only are f0 ¼ 0:816� 0:142ðstat:Þ; fþ ¼ �0:063� 0:066ðstat:Þ; (16) and for muons only are f0 ¼ 0:618� 0:150ðstat:Þ; fþ ¼ 0:130� 0:081ðstat:Þ: (17) Finally, we perform fits in which one of the two helicity fractions is fixed to its SM value. Constraining f0, we find fþ ¼ 0:014� 0:025ðstat:Þ � 0:028ðsyst:Þ: (18) We also constrain fþ and measure f0, finding f0 ¼ 0:735� 0:051ðstat:Þ � 0:051ðsyst:Þ: (19) IX. COMBINATION WITH OUR PREVIOUS MEASUREMENT To combine this result with the previous measurement from Ref. [6], we repeat the maximum likelihood fit with the earlier and current data samples and their respective MC models, treating them as separate channels in the fit. This is equivalent to multiplying the two-dimensional like- lihood distributions in f0 and fþ corresponding to the two data sets. We determine the systematic uncertainty on the combined result by treating most uncertainties as corre- lated (the exception is template statistics) and propagating the uncertainties to the combined result. The results are presented in Table VIII. The combined result for the entire 5:4 fb�1 sample is f0 ¼ 0:669� 0:078ðstat:Þ � 0:065ðsyst:Þ; fþ ¼ 0:023� 0:041ðstat:Þ � 0:034ðsyst:Þ: (20) +f 0 0.2 0.4 0.6 0.8 1 0f 0 0.2 0.4 0.6 0.8 1 Best-fit value SM value (a) DØ, L = 4.3 fb -1 +f 0 0.2 0.4 0.6 0.8 1 0f 0 0.2 0.4 0.6 0.8 1 Best-fit value SM value (b) DØ, L = 5.4 fb -1 FIG. 12. Result of the model-independentW boson helicity fit for (a) the Run IIb data sample and (b) the combined Run IIa and Run IIb data sample. In both plots, the ellipses indicate the 68% and 95% C.L. contours, the dot shows the best-fit value, the triangle corresponds to the physically allowed region where f0 þ fþ 1, and the star marks the expectation from the SM. MEASUREMENT OF THE W BOSON HELICITY IN TOP . . . PHYSICAL REVIEW D 83, 032009 (2011) 032009-17 The combined likelihood distribution is presented in Fig. 12(b). The probability of observing a greater deviation from the SM due to fluctuations in the data is 83% when only statistical uncertainties are considered and 98% when systematic uncertainties are included. Constraining f0 to the SM value, we find fþ ¼ 0:010� 0:022ðstat:Þ � 0:030ðsyst:Þ; (21) and constraining fþ to the SM value gives f0 ¼ 0:708� 0:044ðstat:Þ � 0:048ðsyst:Þ: (22) X. CONCLUSION We have measured the helicity ofW bosons arising from top quark decay in t�t events using both the ‘þ jets and dilepton decay channels and find f0 ¼ 0:669� 0:102½�0:078ðstat:Þ � 0:065ðsyst:Þ�; fþ ¼ 0:023� 0:053½�0:041ðstat:Þ � 0:034ðsyst:Þ�: (23) in a model-independent fit. The consistency of this measurement with the SM values f0 ¼ 0:698, fþ ¼ 3:6� 10�4 is 98%. Therefore, we report no evi- dence for new physics at the tWb decay vertex. ACKNOWLEDGMENTS 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 and NSERC (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China). [1] F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 74, 2626 (1995). [2] S. Abachi et al. (D0 Collaboration), Phys. Rev. Lett. 74, 2632 (1995). [3] M. Fischer et al., Phys. Rev. D 63, 031501(R) (2001). [4] Tevatron Electroweak Working Group, arXiv:1007.3178. [5] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010). [6] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. 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High Energy Phys. 06 (2002) 29. [20] G. Corcella et al., J. High Energy Phys. 01 (2001) 010. [21] M.G. Bowler, Z. Phys. C 11, 169 (1981). [22] Y. Peters et al., Report No. FERMILAB-TM-2425-E, 2006. [23] J. Pumplin et al., J. High Energy Phys. 07 (2002) 012. TABLE VIII. Summary of the combined systematic uncertain- ties on fþ and f0 for Run IIa and Run IIb. Source Uncertainty (fþ) Uncertainty (f0) Jet energy scale 0.009 0.010 Jet energy resolution 0.004 0.008 Jet ID 0.005 0.007 Top quark mass 0.012 0.009 Template statistics 0.011 0.021 t�t model 0.024 0.039 Background model 0.008 0.023 Heavy flavor fraction 0.010 0.022 b fragmentation 0.002 0.004 PDF 0.000 0.001 Analysis consistency 0.004 0.006 Muon ID 0.002 0.017 Muon trigger 0.003 0.024 Total 0.034 0.065 V.M. ABAZOV et al. 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