Measurement of the Electron Charge Asymmetry in p �p ! W þ X ! e� þ X Events at ffiffiffi s p ¼ 1:96 TeV V.M. Abazov,36 B. Abbott,75 M. Abolins,65 B. S. Acharya,29 M. Adams,51 T. Adams,49 E. Aguilo,6 M. Ahsan,59 G. D. Alexeev,36 G. Alkhazov,40 A. Alton,64,* G. Alverson,63 G.A. Alves,2 M. Anastasoaie,35 L. S. Ancu,35 T. Andeen,53 B. Andrieu,17 M. S. Anzelc,53 M. Aoki,50 Y. Arnoud,14 M. Arov,60 M. Arthaud,18 A. Askew,49 B. Åsman,41 A. C. S. Assis Jesus,3 O. Atramentov,49 C. Avila,8 F. Badaud,13 L. Bagby,50 B. Baldin,50 D. V. Bandurin,59 P. Banerjee,29 S. Banerjee,29 E. Barberis,63 A.-F. Barfuss,15 P. Bargassa,80 P. Baringer,58 J. Barreto,2 J. F. Bartlett,50 U. Bassler,18 D. Bauer,43 S. Beale,6 A. Bean,58 M. Begalli,3 M. Begel,73 C. Belanger-Champagne,41 L. Bellantoni,50 A. Bellavance,50 J. A. Benitez,65 S. B. Beri,27 G. Bernardi,17 R. Bernhard,23 I. Bertram,42 M. Besançon,18 R. Beuselinck,43 V. A. Bezzubov,39 P. C. Bhat,50 V. Bhatnagar,27 C. Biscarat,20 G. Blazey,52 F. Blekman,43 S. Blessing,49 D. Bloch,19 K. Bloom,67 A. Boehnlein,50 D. Boline,62 T. A. Bolton,59 E. E. Boos,38 G. Borissov,42 T. Bose,77 A. Brandt,78 R. Brock,65 G. Brooijmans,70 A. Bross,50 D. Brown,81 X. B. Bu,7 N. J. Buchanan,49 D. Buchholz,53 M. Buehler,81 V. Buescher,22 V. Bunichev,38 S. Burdin,42,† T. H. Burnett,82 C. P. Buszello,43 J.M. Butler,62 P. Calfayan,25 S. Calvet,16 J. Cammin,71 E. Carrera,49 W. Carvalho,3 B. C. K. Casey,50 H. Castilla-Valdez,33 S. Chakrabarti,18 D. Chakraborty,52 K.M. Chan,55 A. Chandra,48 E. Cheu,45 F. Chevallier,14 D. K. Cho,62 S. Choi,32 B. Choudhary,28 L. Christofek,77 T. Christoudias,43 S. Cihangir,50 D. Claes,67 J. Clutter,58 M. Cooke,50 W. E. Cooper,50 M. Corcoran,80 F. Couderc,18 M.-C. Cousinou,15 S. Crépé-Renaudin,14 V. Cuplov,59 D. Cutts,77 M. Ćwiok,30 H. da Motta,2 A. Das,45 G. Davies,43 K. De,78 S. J. de Jong,35 E. De La Cruz-Burelo,64 C. De Oliveira Martins,3 J. D. Degenhardt,64 F. Déliot,18 M. Demarteau,50 R. Demina,71 D. Denisov,50 S. P. Denisov,39 S. Desai,50 H. T. Diehl,50 M. Diesburg,50 A. Dominguez,67 H. Dong,72 T. Dorland,82 A. Dubey,28 L. V. Dudko,38 L. Duflot,16 S. R. Dugad,29 D. Duggan,49 A. Duperrin,15 J. Dyer,65 A. Dyshkant,52 M. Eads,67 D. Edmunds,65 J. Ellison,48 V. D. Elvira,50 Y. Enari,77 S. Eno,61 P. Ermolov,38,†† H. Evans,54 A. Evdokimov,73 V.N. Evdokimov,39 A.V. Ferapontov,59 T. Ferbel,71 F. Fiedler,24 F. Filthaut,35 W. Fisher,50 H. E. Fisk,50 M. Fortner,52 H. Fox,42 S. Fu,50 S. Fuess,50 T. Gadfort,70 C. F. Galea,35 C. Garcia,71 A. Garcia-Bellido,82 V. Gavrilov,37 P. Gay,13 W. Geist,19 D. Gelé,19 W. Geng,15,65 C. E. Gerber,51 Y. Gershtein,49 D. Gillberg,6 G. Ginther,71 N. Gollub,41 B. Gómez,8 A. Goussiou,82 P. D. Grannis,72 H. Greenlee,50 Z. D. Greenwood,60 E.M. Gregores,4 G. Grenier,20 Ph. Gris,13 J.-F. Grivaz,16 A. Grohsjean,25 S. Grünendahl,50 M.W. Grünewald,30 F. Guo,72 J. Guo,72 G. Gutierrez,50 P. Gutierrez,75 A. Haas,70 N. J. Hadley,61 P. Haefner,25 S. Hagopian,49 J. Haley,68 I. Hall,65 R. E. Hall,47 L. Han,7 K. Harder,44 A. Harel,71 J.M. Hauptman,57 R. Hauser,65 J. Hays,43 T. Hebbeker,21 D. Hedin,52 J. G. Hegeman,34 A. P. Heinson,48 U. Heintz,62 C. Hensel,22,x K. Herner,72 G. Hesketh,63 M.D. Hildreth,55 R. Hirosky,81 J. D. Hobbs,72 B. Hoeneisen,12 H. Hoeth,26 M. Hohlfeld,22 S. Hossain,75 P. Houben,34 Y. Hu,72 Z. Hubacek,10 V. Hynek,9 I. Iashvili,69 R. Illingworth,50 A. S. Ito,50 S. Jabeen,62 M. Jaffré,16 S. Jain,75 K. Jakobs,23 C. Jarvis,61 R. Jesik,43 K. Johns,45 C. Johnson,70 M. Johnson,50 A. Jonckheere,50 P. Jonsson,43 A. Juste,50 E. Kajfasz,15 J.M. Kalk,60 D. Karmanov,38 P. A. Kasper,50 I. Katsanos,70 D. Kau,49 V. Kaushik,78 R. Kehoe,79 S. Kermiche,15 N. Khalatyan,50 A. Khanov,76 A. Kharchilava,69 Y.M. Kharzheev,36 D. Khatidze,70 T. J. Kim,31 M.H. Kirby,53 M. Kirsch,21 B. Klima,50 J.M. Kohli,27 J.-P. Konrath,23 A. V. Kozelov,39 J. Kraus,65 T. Kuhl,24 A. Kumar,69 A. Kupco,11 T. Kurča,20 V. A. Kuzmin,38 J. Kvita,9 F. Lacroix,13 D. Lam,55 S. Lammers,70 G. Landsberg,77 P. Lebrun,20 W.M. Lee,50 A. Leflat,38 J. Lellouch,17 J. Li,78,†† L. Li,48 Q. Z. Li,50 S.M. Lietti,5 J. K. Lim,31 J. G. R. Lima,52 D. Lincoln,50 J. Linnemann,65 V.V. Lipaev,39 R. Lipton,50 Y. Liu,7 Z. Liu,6 A. Lobodenko,40 M. Lokajicek,11 P. Love,42 H. J. Lubatti,82 R. Luna,3 A. L. Lyon,50 A. K.A. Maciel,2 D. Mackin,80 R. J. Madaras,46 P. Mättig,26 C. Magass,21 A. Magerkurth,64 P. K. Mal,82 H. B. Malbouisson,3 S. Malik,67 V. L. Malyshev,36 H. S. Mao,50 Y. Maravin,59 B. Martin,14 R. McCarthy,72 A. Melnitchouk,66 L. Mendoza,8 P. G. Mercadante,5 M. Merkin,38 K.W. Merritt,50 A. Meyer,21 J. Meyer,22,x T. Millet,20 J. Mitrevski,70 R. K. Mommsen,44 N.K. Mondal,29 R.W. Moore,6 T. Moulik,58 G. S. Muanza,20 M. Mulhearn,70 O. Mundal,22 L. Mundim,3 E. Nagy,15 M. Naimuddin,50 M. Narain,77 N. A. Naumann,35 H.A. Neal,64 J. P. Negret,8 P. Neustroev,40 H. Nilsen,23 H. Nogima,3 S. F. Novaes,5 T. Nunnemann,25 V. O’Dell,50 D. C. O’Neil,6 G. Obrant,40 C. Ochando,16 D. Onoprienko,59 N. Oshima,50 N. Osman,43 J. Osta,55 R. Otec,10 G. J. Otero y Garzón,50 M. Owen,44 P. Padley,80 M. Pangilinan,77 N. Parashar,56 S.-J. Park,22,x S.K. Park,31 J. Parsons,70 R. Partridge,77 N. Parua,54 A. Patwa,73 G. Pawloski,80 B. Penning,23 M. Perfilov,38 K. Peters,44 Y. Peters,26 P. Pétroff,16 M. Petteni,43 R. Piegaia,1 J. Piper,65 M.-A. Pleier,22 P. L.M. Podesta-Lerma,33,‡ V.M. Podstavkov,50 Y. Pogorelov,55 M.-E. Pol,2 P. Polozov,37 B.G. Pope,65 A.V. Popov,39 C. Potter,6 W. L. Prado da Silva,3 H. B. Prosper,49 S. Protopopescu,73 J. Qian,64 A. Quadt,22,x B. Quinn,66 A. Rakitine,42 M. S. Rangel,2 K. Ranjan,28 P. N. Ratoff,42 P. Renkel,79 S. Reucroft,63 PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 0031-9007=08=101(21)=211801(7) 211801-1 � 2008 The American Physical Society P. Rich,44 J. Rieger,54 M. Rijssenbeek,72 I. Ripp-Baudot,19 F. Rizatdinova,76 S. Robinson,43 R. F. Rodrigues,3 M. Rominsky,75 C. Royon,18 P. Rubinov,50 R. Ruchti,55 G. Safronov,37 G. Sajot,14 A. Sánchez-Hernández,33 M. P. Sanders,17 B. Sanghi,50 G. Savage,50 L. Sawyer,60 T. Scanlon,43 D. Schaile,25 R.D. Schamberger,72 Y. Scheglov,40 H. Schellman,53 T. Schliephake,26 S. Schlobohm,82 C. Schwanenberger,44 A. Schwartzman,68 R. Schwienhorst,65 J. Sekaric,49 H. Severini,75 E. Shabalina,51 M. Shamim,59 V. Shary,18 A.A. Shchukin,39 R.K. Shivpuri,28 V. Siccardi,19 V. Simak,10 V. Sirotenko,50 P. Skubic,75 P. Slattery,71 D. Smirnov,55 G. R. Snow,67 J. Snow,74 S. Snyder,73 S. Söldner-Rembold,44 L. Sonnenschein,17 A. Sopczak,42 M. Sosebee,78 K. Soustruznik,9 B. Spurlock,78 J. Stark,14 J. Steele,60 V. Stolin,37 D.A. Stoyanova,39 J. Strandberg,64 S. Strandberg,41 M.A. Strang,69 E. Strauss,72 M. Strauss,75 R. Ströhmer,25 D. Strom,53 L. Stutte,50 S. Sumowidagdo,49 P. Svoisky,55 A. Sznajder,3 P. Tamburello,45 A. Tanasijczuk,1 W. Taylor,6 B. Tiller,25 F. Tissandier,13 M. Titov,18 V. V. Tokmenin,36 I. Torchiani,23 D. Tsybychev,72 B. Tuchming,18 C. Tully,68 P.M. Tuts,70 R. Unalan,65 L. Uvarov,40 S. Uvarov,40 S. Uzunyan,52 B. Vachon,6 P. J. van den Berg,34 R. Van Kooten,54 W.M. van Leeuwen,34 N. Varelas,51 E.W. Varnes,45 I. A. Vasilyev,39 M. Vaupel,26 P. Verdier,20 L. S. Vertogradov,36 M. Verzocchi,50 D. Vilanova,18 F. Villeneuve-Seguier,43 P. Vint,43 P. Vokac,10 E. Von Toerne,59 M. Voutilainen,68,k R. Wagner,68 H. D. Wahl,49 L. Wang,61 M.H. L. S. Wang,50 J. Warchol,55 G. Watts,82 M. Wayne,55 G. Weber,24 M. Weber,50,{ L. Welty-Rieger,54 A. Wenger,23,** N. Wermes,22 M. Wetstein,61 A. White,78 D. Wicke,26 G.W. Wilson,58 S. J. Wimpenny,48 M. Wobisch,60 D. R. Wood,63 T. R. Wyatt,44 Y. Xie,77 S. Yacoob,53 R. Yamada,50 W.-C. Yang,44 T. Yasuda,50 Y. A. Yatsunenko,36 H. Yin,7 K. Yip,73 H.D. Yoo,77 S.W. Youn,53 J. Yu,78 C. Zeitnitz,26 S. Zelitch,81 T. Zhao,82 B. Zhou,64 J. Zhu,72 M. Zielinski,71 D. Zieminska,54 A. Zieminski,54,†† L. Zivkovic,70 V. Zutshi,52 and E.G. Zverev38 (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 6University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada, York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada 7University of Science and Technology of China, Hefei, People’s Republic of China 8Universidad de los Andes, Bogotá, Colombia 9Center for Particle Physics, Charles University, Prague, Czech Republic 10Czech Technical University, 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, IN2P3/CNRS, Orsay, France 17LPNHE, IN2P3/CNRS, Universités Paris VI and VII, Paris, France 18CEA, Irfu, SPP, Saclay, France 19IPHC, Université Louis Pasteur, 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 Bonn, Bonn, Germany 23Physikalisches Institut, Universität Freiburg, Freiburg, Germany 24Institut für Physik, Universität Mainz, Mainz, Germany 25Ludwig-Maximilians-Universität München, München, Germany 26Fachbereich Physik, University of 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 32SungKyunKwan University, Suwon, Korea PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 211801-2 33CINVESTAV, Mexico City, Mexico 34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 35Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands 36Joint Institute for Nuclear Research, Dubna, Russia 37Institute for Theoretical and Experimental Physics, Moscow, Russia 38Moscow State University, Moscow, Russia 39Institute for High Energy Physics, Protvino, Russia 40Petersburg Nuclear Physics Institute, St. Petersburg, Russia 41Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden 42Lancaster University, Lancaster, United Kingdom 43Imperial College, London, United Kingdom 44University of Manchester, Manchester, United Kingdom 45University of Arizona, Tucson, Arizona 85721, USA 46Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 47California State University, Fresno, California 93740, USA 48University of California, Riverside, California 92521, USA 49Florida State University, Tallahassee, Florida 32306, USA 50Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 51University of Illinois at Chicago, Chicago, Illinois 60607, USA 52Northern Illinois University, DeKalb, Illinois 60115, USA 53Northwestern University, Evanston, Illinois 60208, USA 54Indiana University, Bloomington, Indiana 47405, USA 55University of Notre Dame, Notre Dame, Indiana 46556, USA 56Purdue University Calumet, Hammond, Indiana 46323, USA 57Iowa State University, Ames, Iowa 50011, USA 58University of Kansas, Lawrence, Kansas 66045, USA 59Kansas State University, Manhattan, Kansas 66506, USA 60Louisiana Tech University, Ruston, Louisiana 71272, USA 61University of Maryland, College Park, Maryland 20742, USA 62Boston University, Boston, Massachusetts 02215, USA 63Northeastern University, Boston, Massachusetts 02115, USA 64University of Michigan, Ann Arbor, Michigan 48109, USA 65Michigan State University, East Lansing, Michigan 48824, USA 66University of Mississippi, University, Mississippi 38677, USA 67University of Nebraska, Lincoln, Nebraska 68588, USA 68Princeton University, Princeton, New Jersey 08544, USA 69State University of New York, Buffalo, New York 14260, USA 70Columbia University, New York, New York 10027, USA 71University of Rochester, Rochester, New York 14627, USA 72State University of New York, Stony Brook, New York 11794, USA 73Brookhaven National Laboratory, Upton, New York 11973, USA 74Langston University, Langston, Oklahoma 73050, USA 75University of Oklahoma, Norman, Oklahoma 73019, USA 76Oklahoma State University, Stillwater, Oklahoma 74078, USA 77Brown University, Providence, Rhode Island 02912, USA 78University of Texas, Arlington, Texas 76019, USA 79Southern Methodist University, Dallas, Texas 75275, USA 80Rice University, Houston, Texas 77005, USA 81University of Virginia, Charlottesville, Virginia 22901, USA 82University of Washington, Seattle, Washington 98195, USA (Received 21 July 2008; published 19 November 2008) We present a measurement of the electron charge asymmetry in p �p ! W þ X ! e�þ X events at a center of mass energy of 1.96 TeV using 0:75 fb�1 of data collected with the D0 detector at the Fermilab Tevatron Collider. The asymmetry is measured as a function of the electron transverse momentum and pseudorapidity in the interval (�3:2, 3.2) and is compared with expectations from next-to-leading order calculations in perturbative quantum chromodynamics. These measurements will allow more accurate determinations of the proton parton distribution functions. DOI: 10.1103/PhysRevLett.101.211801 PACS numbers: 13.38.Be, 13.85.Qk, 14.60.Cd, 14.70.Fm PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 211801-3 http://dx.doi.org/10.1103/PhysRevLett.101.211801 In p �p collisions, WþðW�Þ bosons are produced primar- ily by the annihilation of uðdÞ quarks in the proton with �dð �uÞ quarks in the antiproton. The probability of finding a parton carrying momentum fraction x of the proton can be expressed by parton distribution functions (PDFs). Any difference between the u- and d-quark PDFs will result in an asymmetry in the W boson rapidity distribution between Wþ and W� boson production [1]. In this Letter, we present a measurement of the charged lepton asymmetry with much larger statistical precision and over a wider kinematic range than previous measurements [2,3]. This information provides constraints on the ratio of u- and d- quark PDFs, uðxÞ=dðxÞ. PDFs are necessary inputs for cross section calculations at hadron colliders. Many mea- surements have significant uncertainties associated with the accuracy of the PDFs; therefore, understanding the PDFs is extremely important. Throughout this Letter, we use the notation ‘‘electron’’ to mean ‘‘electron and posi- tron,’’ unless specified otherwise. We detect W bosons via the direct decay W ! e�. The boson rapidity (yW) cannot be measured due to the un- known longitudinal momentum of the neutrino. We instead measure the electron charge asymmetry, which is a con- volution of the W boson production asymmetry and the parity violating asymmetry from theW boson decay. Since the V-A interaction is well understood, the lepton charge asymmetry retains sensitivity to the underlying W boson asymmetry. The electron charge asymmetry (Að�eÞ) is defined as: Að�eÞ ¼ d�þ=d�e � d��=d�e d�þ=d�e þ d��=d�e ; (1) where �e is the pseudorapidity of the electron [4] and d�þ=d�e (d��=d�e) is the differential cross section for the electrons from Wþ (W�) bosons as a function of the electron pseudorapidity. When the detection efficiencies and acceptances for positrons and electrons are identical, the asymmetry becomes the difference in the number of positron and electron events over the sum. In this Letter, we present results obtained from more than twice the integrated luminosity of previous measure- ments by the CDF [2] and D0 [3] collaborations and extend the measurement for leptons with j�‘j< 3:2, compared to j�‘j< 2:5 for CDF and j�‘j< 2:0 for the previous D0 measurement. By extending to higher rapidity leptons, we can provide information about the PDFs for a broader x range (0:002< x< 1:0 for jyW j< 3:2) at high Q2 �M2 W , where Q2 is the momentum transfer squared andMW is the W boson mass. The data sample used in this measurement was collected with the D0 detector [5] at the Fermilab Tevatron Collider using a set of inclusive single-electron triggers based only on calorimeter information [6]. The integrated luminosity is 750� 46 pb�1 [7]. The D0 detector includes a central tracking system, composed of a silicon microstrip tracker (SMT) and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet and covering pseudor- apidities of j�Dj< 3:0 and j�Dj< 2:5, respectively [4]. Three liquid argon and uranium calorimeters provide cov- erage out to j�Dj � 4:2: a central section (CC) with cover- age of j�Dj< 1:1 and two end calorimeters (EC) with a coverage of 1:5< j�Dj< 4:2. W boson candidates are identified by one isolated elec- tromagnetic cluster accompanied by large missing trans- verse energy (E6 T). E6 T is determined by the vector sum of the transverse components of the energy deposited in the calorimeter and the transverse momentum (ET) of the electron. Electron candidates are further required to have shower shapes consistent with that of an electron. The ET of the electron and the E6 T are required to be greater than 25 GeV. Additionally, the transverse mass MT of the elec- tron and E6 T is required to be greater than 50 GeV, where MT ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ETE6 Tð1� cos��Þp , and �� is the azimuthal angle between the electron and E6 T . Electrons are required to fall within the fiducial region of the calorimeters, and must be spatially matched to a re- constructed track in the central tracking system. Because of the different geometrical coverage of the calorimeters and the tracker, the electrons are divided into four different types depending on the locations of the electrons in the calorimeter and the associated track polar angle and the collision vertex: CC electrons within the full coverage of the CFT, EC electrons within the full coverage of the CFT, EC electrons within the partial coverage of the CFT, and EC electrons outside the coverage of the CFT. Optimized choices for selection criteria are established for each type. SMT hits are required in all four types, with tracks outside the CFT fiducial region requiring at least nine SMT hits. A total of 491 250 events satisfy the selection, with 358 336 events with electrons in the CC and 132 914 events with electrons in the EC. The charge asymmetry is measured in 24 electron pseudorapidity bins for j�ej< 3:2. The asymmetry measurement is sensitive to misidenti- fication of the electron charge. We measure the charge misidentification rate with Z ! ee events using a ‘‘tag- and-probe’’ method [7] where a track matched to one electron tags the charge of the other. Tight conditions are applied on the tag electron to make sure its charge is correctly determined. The rate ranges from 0.2% at j�ej � 0 to 9% at j�ej � 3. The absolute uncertainty in the charge misidentification changes from 0.1% to 2.6% depending on the electron pseudorapidity, and is dominated by the sta- tistics of the Z boson sample. Sources of charge bias in the event selection are inves- tigated by studying Z ! ee events. All selection efficien- cies are measured for electrons and positrons separately, and no charge dependent biases in acceptance or efficien- cies are found. To reduce any possible residual charge PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 211801-4 determination biases due to instrumental effects, the direc- tion of the magnetic field in the solenoidal magnet was regularly reversed. Approximately 46% of the selected W bosons were collected with the solenoid at forward polar- ity, and 54% at reverse polarity. The charge asymmetry is measured separately for each solenoid polarity and no significant differences are observed. Three sources of background can dilute the charge asymmetry: Z ! ee events where one electron is not de- tected by the calorimeter, W ! �� ! e��� events, and multijet events in which one jet is misidentified as an electron and a large E6 T is produced by fragmentation fluctuations or misreconstruction. The Að�eÞ values are corrected for the backgrounds in each bin. Events with electrons from Z ! ee and W ! �� ! e��� decays exhibit charge asymmetries, and these two background contributions are evaluated using Monte Carlo (MC) events generated with PYTHIA [8] and processed with a detailed detector simulation based on GEANT [9]. The fractions of Z ! ee and W ! �� ! e��� events esti- mated to contribute to the candidate sample are ð1:3� 0:1Þ% and ð2:1� 0:1Þ%, respectively. The background fraction from multijet events is esti- mated by starting from a sample of candidate events with loose shower shape requirements and then selecting a subset of events which satisfy the final tighter requirement. From Z ! ee events, and a sample of multijet events passing the preselection but with low E6 T , we determine the probabilities with which real and fake electrons will pass the final shower shape requirement. These two prob- abilities (verified to be charge symmetric), along with the number of events selected in the loose and tight samples allow us to calculate the fraction of multijet events within our final selection. The final background contamination from multijet events is estimated to be ð0:8� 0:4Þ%. The final charge asymmetry is corrected for electron energy scale and resolution, E6 T resolution and trigger efficiency. The correction is estimated by comparing the asymmetry from the generator level PYTHIA W ! e� MC calculations to the GEANT-simulated results for each elec- tron type. The electron charge asymmetry is determined separately for each electron pseudorapidity bin and for each of the four electron types and then combined. The charge mis- identification and background estimations are performed |eη| 0 0.5 1 1.5 2 2.5 3 A sy m m et ry -0.6 -0.4 -0.2 -0 0.2 -1DØ, L=0.75 fb >25 GeVT eE >25 GeVT νE CTEQ6.6 central value MRST04NLO central value CTEQ6.6 uncertainty band FIG. 1 (color online). The folded electron charge asymmetry distribution. The horizontal bars show the statistical uncertainty and the full vertical lines show the total uncertainty on each point. The total uncertainty is the sum in quadrature of the statistical and systematic uncertainties. The solid (dashed) line is the theoretical prediction for the asymmetry using the CTEQ6.6 (MRST04NLO) central PDF set. The shaded band is the uncertainty band determined using the 44 CTEQ6.6 PDF uncertainty sets. All three were determined using RESBOS with PHOTOS. |eη| 0 0.5 1 1.5 2 2.5 3 A sy m m et ry -0.8 -0.6 -0.4 -0.2 -0 0.2 -1(a) DØ, L=0.75 fb <35 GeVT e2525 GeVT νE CTEQ6.6 central value MRST04NLO central value CTEQ6.6 uncertainty band |eη| 0 0.5 1 1.5 2 2.5 3 A sy m m et ry -0.2 -0.1 0 0.1 0.2 -1(b) DØ, L=0.75 fb >35 GeVT eE >25 GeVT νE CTEQ6.6 central value MRST04NLO central value CTEQ6.6 uncertainty band FIG. 2 (color online). The folded electron charge asymmetry distribution in two electron ET bins: 25< ET < 35 GeV for (a) and ET > 35 GeV for (b). In each plot, the horizontal bars show the statistical uncertainty and the full vertical lines show the total uncertainty on each point. The total uncertainty is the sum in quadrature of the statistical and systematic uncertainties. The solid (dashed) line is the theoretical prediction for the asymme- try using the CTEQ6.6 (MRST04NLO) central PDF set. The shaded band is the uncertainty band determined using the 44 CTEQ6.6 PDF uncertainty sets. All three were determined using RESBOS with PHOTOS. PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 211801-5 independently for each of these measurements. Assuming Að��eÞ ¼ �Að�eÞ due to CP invariance, we fold the data to increase the available statistics and obtain a more precise measurement of Að�eÞ. Figure 1 shows the folded electron charge asymmetry. The dominant sources of systematic uncertainties originate from the estimation of charge misidentification and multi- jet backgrounds. The bin-by-bin correlations of these sys- tematic uncertainties are negligible. Also shown in Fig. 1 are the theoretical predictions obtained using the RESBOS event generator [10] (with gluon resummation at low boson pT and next-to-leading order (NLO) perturbative QCD calculations at high boson pT) with PHOTOS [11] (for QED final state radiation). The PDFs used to generate these predictions are the CTEQ6.6 NLO PDFs [12] and MRST04NLO PDFs [13]. Theoretical uncertainties de- rived from the 44 CTEQ6.6 PDF uncertainty sets are also shown. These curves are generated by applying a 25 GeV cut on the electron and neutrino generator-level transverse momenta. The asymmetric PDF uncertainty band is calcu- lated using the formula described in Ref. [14]. We also measure the asymmetry in two bins of electron ET : 25< ET < 35 GeV and ET > 35 GeV. For a given�e, the two ET regions probe different ranges of yW and thus allow a finer probe of the x dependence. The folded elec- tron charge asymmetries, along with the theoretical pre- dictions, for the two ET bins are shown in Fig. 2. The measured values of the asymmetry and uncertain- ties, together with the CTEQ6.6 predictions, for ET > 25 GeV and the two separate ET bins are listed in Table I. The measured charge asymmetries tend to be lower than the theoretical predictions using both the CTEQ6.6 and MRST04NLO central PDF sets for high pseudorapid- ity electrons. For most �e bins, the experimental uncer- tainties are smaller than the uncertainties given by the most recent CTEQ6.6 uncertainty sets, demonstrating the sensi- tivity of our measurement. A complete interpretation of the impact of these data on the PDFs will require revised NLOQCD fits to all available data. However, we can estimate the impact of this mea- surement by investigating the behavior of the uðxÞ=dðxÞ ratio at Q2 ¼ M2 W for the 44 CTEQ6.6 PDF uncertainty sets. We observe that they differ by 10%–20% for x > 0:2, which illustrates the current limited knowledge on this ratio at high x. We find that the sets which best match our data consistently correspond to uðxÞ=dðxÞ ratios which lie below the central prediction by 5%–10% for x > 0:2, while those with the worst agreement lie above the central prediction by a similar amount. We conclude that our data favor smaller uðxÞ=dðxÞ ratios at high x. In summary, we have measured the charge asymmetry of electrons in p �p ! W þ X ! e�þ X using 0:75 fb�1 of data. The electron coverage is extended to j�ej< 3:2 and the asymmetry is measured for electron ET > 25 GeV, as well as two separate ET bins to improve sensitivity to the PDFs. This measurement is the most precise electron charge asymmetry measurement to date, and the experi- mental uncertainties are smaller than the theoretical un- certainties across almost all electron pseudorapidities. Our result can be used to improve the precision and accuracy of next generation PDF sets, and will help to reduce the PDF uncertainty for high precision MW measurements and also improve the predictions for the Higgs boson production at the hadron colliders. TABLE I. Folded electron charge asymmetry for data and predictions from RESBOS with PHOTOS using CTEQ6.6 PDFs tabulated in percent. hj�eji is the cross section weighted average of electron pseudorapidity in each bin from RESBOS with PHOTOS. For data, the first uncertainty is statistical and the second is systematic. For the predictions, the uncertainties are from the PDFs only. A (j�ej) �e region hj�eji ET > 25 GeV 25 35 GeV Data Prediction Data Prediction Data Prediction 0.0–0.2 0.10 1:6� 0:4� 0:3 1:9þ0:4 �0:5 1:9� 0:6� 0:5 2:1þ0:5 �0:8 1:4� 0:5� 0:4 1:8þ0:5 �0:7 0.2–0.4 0.30 5:6� 0:4� 0:3 5:7þ0:4 �1:2 6:8� 0:6� 0:5 6:2þ0:8 �1:3 4:8� 0:5� 0:4 5:3þ0:5 �1:3 0.4–0.6 0.50 8:2� 0:4� 0:3 9:1þ1:2 �0:9 9:3� 0:6� 0:5 9:8þ1:2 �0:8 7:5� 0:5� 0:4 8:5þ1:3 �1:1 0.6–0.8 0.70 13:0� 0:4� 0:3 12:2þ1:5 �1:2 13:8� 0:6� 0:5 12:4þ3:1 �0:3 12:4� 0:5� 0:4 12:1þ1:0 �2:3 0.8–1.0 0.90 14:6� 0:4� 0:3 14:8þ1:3 �1:8 15:8� 0:7� 0:6 14:6þ1:7 �1:3 13:9� 0:5� 0:4 15:0þ1:3 �2:4 1.0–1.2 1.10 15:5� 0:6� 0:5 16:6þ1:0 �2:5 15:8� 1:0� 0:8 15:2þ0:7 �3:0 15:2� 0:8� 0:6 17:6þ1:5 �2:4 1.2–1.6 1.39 14:4� 0:6� 0:5 16:4þ1:8 �2:2 12:9� 1:0� 0:8 11:1þ1:8 �1:8 17:0� 0:8� 0:6 20:4þ2:2 �2:6 1.6–1.8 1.70 10:2� 0:5� 0:4 13:0þ2:3 �2:2 �0:1� 0:8� 0:6 0:7þ3:2 �1:3 17:9� 0:6� 0:6 21:7þ2:0 �3:1 1.8–2.0 1.90 6:6� 0:6� 0:5 8:3þ2:2 �3:3 �12:0� 1:0� 0:8 �10:1þ2:2 �2:7 19:7� 0:8� 0:7 21:2þ2:7 �4:1 2.0–2.2 2.09 �2:5� 0:9� 0:6 0:9þ4:3 �3:0 �24:7� 1:3� 1:2 �23:6þ4:1 �2:2 14:4� 1:2� 0:9 18:7þ4:8 �3:9 2.2–2.6 2.37 �19:8� 1:0� 0:7 �12:0þ5:1 �5:1 �42:9� 1:4� 1:6 �39:4þ3:2 �3:3 1:1� 1:4� 0:7 12:6þ7:4 �7:5 2.6–3.2 2.80 �54:3� 4:2� 4:2 �36:1þ9:4 �7:2 �76:2� 5:0� 7:1 �55:1þ6:0 �4:3 �14:8� 6:7� 2:6 �1:7þ17:9 �14:4 PRL 101, 211801 (2008) P HY S I CA L R EV I EW LE T T E R S week ending 21 NOVEMBER 2008 211801-6 We thank P. Nadolsky for many useful discussions about the theoretical predictions. We thank the staffs at Fermilab and collaborating institutions, 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 (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); and the Alexander von Humboldt Foundation (Germany). *Visitor from Augustana College, Sioux Falls, SD, USA. †Visitor from The University of Liverpool, Liverpool, United Kingdom. ‡Visitor from ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico. xVisitor from II. Physikalisches Institut, Georg-August- University, Göttingen, Germany. kVisitor from Helsinki Institute of Physics, Helsinki, Finland. {Visitor from Universität Bern, Bern, Switzerland. **Visitor from Universität Zürich, Zürich, Switzerland. ††Deceased. [1] E. L. Berger, F. Halzen, C. S. Kim, and S. Willenbrock, Phys. Rev. D 40, 83 (1989); 40, 3789 (1989). [2] F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 74, 850 (1995); 81, 5754 (1998); D. Acosta et al. (CDF Collaboration), Phys. Rev. D 71, 051104(R) (2005). [3] V. Abazov et al. (D0 Collaboration), Phys. Rev. D 77, 011106(R) (2008). [4] D0 uses a cylindrical coordinate system with the z axis running along the beam axis in the proton direction. Angles � and � are the polar and azimuthal angles, respectively. Pseudorapidity is defined as � ¼ � ln½tanð�=2Þ� where � is measured with respect to the interaction vertex. In the massless limit, � is equivalent to the rapidity y ¼ ð1=2Þ ln½ðEþ pzÞ=ðE� pzÞ�. �D is the pseudorapidity measured with respect to the center of the detector. Because of the distribution of the interactions within the detector, electrons may have larger � than �D. [5] V. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 565, 463 (2006). [6] V. Abazov et al. (D0 Collaboration), Phys. Rev. D 76, 012003 (2007). [7] T. Andeen et al., Fermilab Report No. FERMILAB-TM- 2365, 2007. [8] T. Sjőstrand et al., Comput. Phys. Commun. 135, 238 (2001). [9] R. Brun and F. Carminati, CERN Program Library Long Writeup Report No. W5013, 1993 (unpublished). [10] C. Balazs and C. P. Yuan, Phys. Rev. D 56, 5558 (1997). [11] E. Barberio and Z. Was, Comput. Phys. Commun. 79, 291 (1994); we use PHOTOS version 2.0. [12] P.M. Nadolsky et al., Phys. Rev. D 78, 013004 (2008). [13] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Phys. Lett. B 604, 61 (2004). [14] D. 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