Physics Letters B 655 (2007) 7–14 www.elsevier.com/locate/physletb Measurement of the top quark mass in the dilepton channel DØ Collaboration V.M. Abazov ai, B. Abbott bw, M. Abolins bm, B.S. Acharya ab, M. Adams ay, T. Adams aw, M. Agelou q, E. Aguilo e, S.H. Ahn ad, M. Ahsan bg, G.D. Alexeev ai, G. Alkhazov am, A. Alton bl, G. Alverson bk, G.A. Alves b, M. Anastasoaie ah, T. Andeen ba, S. Anderson as, B. Andrieu p, M.S. Anzelc ba, Y. Arnoud m, M. Arov az, A. Askew aw, B. Åsman an, A.C.S. Assis Jesus c, O. Atramentov aw, C. Autermann t, C. Avila g, C. Ay w, F. Badaud l, A. Baden bi, L. Bagby az, B. Baldin ax, D.V. Bandurin bg, P. Banerjee ab, S. Banerjee ab, E. Barberis bk, P. Bargassa cb, P. Baringer bf, C. Barnes aq, J. Barreto b, J.F. Bartlett ax, U. Bassler p, D. Bauer aq, S. Beale e, A. Bean bf, M. Begalli c, M. Begel bs, C. Belanger-Champagne e, L. Bellantoni ax, A. Bellavance bo, J.A. Benitez bm, S.B. Beri z, G. Bernardi p, R. Bernhard ao, L. Berntzon n, I. Bertram ap, M. Besançon q, R. Beuselinck aq, V.A. Bezzubov al, P.C. Bhat ax, V. Bhatnagar z, M. Binder x, C. Biscarat ap, K.M. Black bj, I. Blackler aq, G. Blazey az, F. Blekman aq, S. Blessing aw, D. Bloch r, K. Bloom bo, U. Blumenschein v, A. Boehnlein ax, O. Boeriu bc, D. Boline bj, T.A. Bolton bg, G. Borissov ap, K. Bos ag, T. Bose by, A. Brandt bz, R. Brock bm, G. Brooijmans br, A. Bross ax, D. Brown bz, N.J. Buchanan aw, D. Buchholz ba, M. Buehler cc, V. Buescher v, S. Burdin ax, S. Burke as, T.H. Burnett cd, E. Busato p, C.P. Buszello aq, J.M. Butler bj, P. Calfayan x, S. Calvet n, J. Cammin bs, S. Caron ag, W. Carvalho c, B.C.K. Casey by, N.M. Cason bc, H. Castilla-Valdez af, S. Chakrabarti ab, D. Chakraborty az, K.M. Chan bs, A. Chandra av, F. Charles r, E. Cheu as, F. Chevallier m, D.K. Cho bj, S. Choi ae, B. Choudhary aa, L. Christofek by, D. Claes bo, B. Clément r, C. Clément an, Y. Coadou e, M. Cooke cb, W.E. Cooper ax, D. Coppage bf, M. Corcoran cb, M.-C. Cousinou n, B. Cox ar, S. Crépé-Renaudin m, D. Cutts by, M. Ćwiok ac, H. da Motta b, A. Das bj, M. Das bh, B. Davies ap, G. Davies aq, G.A. Davis ba, K. De bz, P. de Jong ag, S.J. de Jong ah, E. De La Cruz-Burelo bl, C. De Oliveira Martins c, J.D. Degenhardt bl, F. Déliot q, M. Demarteau ax, R. Demina bs, P. Demine q, D. Denisov ax, S.P. Denisov al, S. Desai bt, H.T. Diehl ax, M. Diesburg ax, M. Doidge ap, A. Dominguez bo, H. Dong bt, L.V. Dudko ak, L. Duflot o, S.R. Dugad ab, D. Duggan aw, A. Duperrin n, J. Dyer bm, A. Dyshkant az, M. Eads bo, D. Edmunds bm, T. Edwards ar, J. Ellison av, J. Elmsheuser x, V.D. Elvira ax, S. Eno bi, P. Ermolov ak, H. Evans bb, A. Evdokimov aj, V.N. Evdokimov al, S.N. Fatakia bj, L. Feligioni bj, A.V. Ferapontov bg, T. Ferbel bs, F. Fiedler x, F. Filthaut ah, W. Fisher ax, H.E. Fisk ax, I. Fleck v, M. Ford ar, M. Fortner az, H. Fox v, S. Fu ax, S. Fuess ax, T. Gadfort cd, C.F. Galea ah, E. Gallas ax, E. Galyaev bc, C. Garcia bs, A. Garcia-Bellido cd, J. Gardner bf, V. Gavrilov aj, A. Gay r, P. Gay l, D. Gelé r, R. Gelhaus av, C.E. Gerber ay, Y. Gershtein aw, D. Gillberg e, G. Ginther bs, N. Gollub an, B. Gómez g, A. Goussiou bc, P.D. Grannis bt, H. Greenlee ax, Z.D. Greenwood bh, E.M. Gregores d, G. Grenier s, Ph. Gris l, J.-F. Grivaz o, S. Grünendahl ax, M.W. Grünewald ac, F. Guo bt, J. Guo bt, G. Gutierrez ax, P. Gutierrez bw, A. Haas br, N.J. Hadley bi, P. Haefner x, S. Hagopian aw, J. Haley bp, I. Hall bw, R.E. Hall au, L. Han f, K. Hanagaki ax, 0370-2693/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2007.08.074 http://www.elsevier.com/locate/physletb http://dx.doi.org/10.1016/j.physletb.2007.08.074 8 DØ Collaboration / Physics Letters B 655 (2007) 7–14 P. Hansson an, K. Harder bg, A. Harel bs, R. Harrington bk, J.M. Hauptman be, R. Hauser bm, J. Hays ba, T. Hebbeker t, D. Hedin az, J.G. Hegeman ag, J.M. Heinmiller ay, A.P. Heinson av, U. Heintz bj,∗, C. Hensel bf, K. Herner bt, G. Hesketh bk, M.D. Hildreth bc, R. Hirosky cc, J.D. Hobbs bt, B. Hoeneisen k, H. Hoeth y, M. Hohlfeld o, S.J. Hong ad, R. Hooper by, P. Houben ag, Y. Hu bt, Z. Hubacek i, V. Hynek h, I. Iashvili bq, R. Illingworth ax, A.S. Ito ax, S. Jabeen bj, M. Jaffré o, S. Jain bw, K. Jakobs v, C. Jarvis bi, A. Jenkins aq, R. Jesik aq, K. Johns as, C. Johnson br, M. Johnson ax, A. Jonckheere ax, P. Jonsson aq, A. Juste ax, D. Käfer t, S. Kahn bu, E. Kajfasz n, A.M. Kalinin ai, J.M. Kalk bh, J.R. Kalk bm, S. Kappler t, D. Karmanov ak, J. Kasper bj, P. Kasper ax, I. Katsanos br, D. Kau aw, R. Kaur z, R. Kehoe ca, S. Kermiche n, N. Khalatyan bj, A. Khanov bx, A. Kharchilava bq, Y.M. Kharzheev ai, D. Khatidze br, H. Kim bz, T.J. Kim ad, M.H. Kirby ah, B. Klima ax, J.M. Kohli z, J.-P. Konrath v, M. Kopal bw, V.M. Korablev al, J. Kotcher bu, B. Kothari br, A. Koubarovsky ak, A.V. Kozelov al, D. Krop bb, A. Kryemadhi cc, T. Kuhl w, A. Kumar bq, S. Kunori bi, A. Kupco j, T. Kurča s,1, J. Kvita h, S. Lammers br, G. Landsberg by, J. Lazoflores aw, A.-C. Le Bihan r, P. Lebrun s, W.M. Lee az, A. Leflat ak, F. Lehner ao, V. Lesne l, J. Leveque as, P. Lewis aq, J. Li bz, Q.Z. Li ax, J.G.R. Lima az, D. Lincoln ax, J. Linnemann bm, V.V. Lipaev al, R. Lipton ax, Z. Liu e, L. Lobo aq, A. Lobodenko am, M. Lokajicek j, A. Lounis r, P. Love ap, H.J. Lubatti cd, M. Lynker bc, A.L. Lyon ax, A.K.A. Maciel b, R.J. Madaras at, P. Mättig y, C. Magass t, A. Magerkurth bl, A.-M. Magnan m, N. Makovec o, P.K. Mal bc, H.B. Malbouisson c, S. Malik bo, V.L. Malyshev ai, H.S. Mao ax, Y. Maravin bg, M. Martens ax, R. McCarthy bt, D. Meder w, A. Melnitchouk bn, A. Mendes n, L. Mendoza g, M. Merkin ak, K.W. Merritt ax, A. Meyer t, J. Meyer u, M. Michaut q, H. Miettinen cb, T. Millet s, J. Mitrevski br, J. Molina c, N.K. Mondal ab, J. Monk ar, R.W. Moore e, T. Moulik bf, G.S. Muanza o, M. Mulders ax, M. Mulhearn br, O. Mundal v, L. Mundim c, Y.D. Mutaf bt, E. Nagy n, M. Naimuddin aa, M. Narain bj, N.A. Naumann ah, H.A. Neal bl, J.P. Negret g, P. Neustroev am, C. Noeding v, A. Nomerotski ax, S.F. Novaes d, T. Nunnemann x, V. O’Dell ax, D.C. O’Neil e, G. Obrant am, V. Oguri c, N. Oliveira c, D. Onoprienko bg, N. Oshima ax, R. Otec i, G.J. Otero y Garzón ay, M. Owen ar, P. Padley cb, N. Parashar bd, S.-J. Park bs, S.K. Park ad, J. Parsons br, R. Partridge by, N. Parua bt, A. Patwa bu, G. Pawloski cb, P.M. Perea av, E. Perez q, K. Peters ar, P. Pétroff o, M. Petteni aq, R. Piegaia a, J. Piper bm, M.-A. Pleier u, P.L.M. Podesta-Lerma af, V.M. Podstavkov ax, Y. Pogorelov bc, M.-E. Pol b, A. Pompoš bw, B.G. Pope bm, A.V. Popov al, C. Potter e, W.L. Prado da Silva c, H.B. Prosper aw, S. Protopopescu bu, J. Qian bl, A. Quadt u, B. Quinn bn, M.S. Rangel b, K.J. Rani ab, K. Ranjan aa, P.N. Ratoff ap, P. Renkel ca, S. Reucroft bk, M. Rijssenbeek bt, I. Ripp-Baudot r, F. Rizatdinova bx, S. Robinson aq, R.F. Rodrigues c, C. Royon q, P. Rubinov ax, R. Ruchti bc, V.I. Rud ak, G. Sajot m, A. Sánchez-Hernández af, M.P. Sanders bi, A. Santoro c, G. Savage ax, L. Sawyer bh, T. Scanlon aq, D. Schaile x, R.D. Schamberger bt, Y. Scheglov am, H. Schellman ba, P. Schieferdecker x, C. Schmitt y, C. Schwanenberger ar, A. Schwartzman bp, R. Schwienhorst bm, J. Sekaric aw, S. Sengupta aw, H. Severini bw, E. Shabalina ay, M. Shamim bg, V. Shary q, A.A. Shchukin al, W.D. Shephard bc, R.K. Shivpuri aa, D. Shpakov ax, V. Siccardi r, R.A. Sidwell bg, V. Simak i, V. Sirotenko ax, P. Skubic bw, P. Slattery bs, R.P. Smith ax, G.R. Snow bo, J. Snow bv, S. Snyder bu, S. Söldner-Rembold ar, X. Song az, L. Sonnenschein p, A. Sopczak ap, M. Sosebee bz, K. Soustruznik h, M. Souza b, B. Spurlock bz, J. Stark m, J. Steele bh, V. Stolin aj, A. Stone ay, D.A. Stoyanova al, J. Strandberg bl, S. Strandberg an, M.A. Strang bq, M. Strauss bw, R. Ströhmer x, D. Strom ba, M. Strovink at, L. Stutte ax, S. Sumowidagdo aw, P. Svoisky bc, A. Sznajder c, M. Talby n, P. Tamburello as, W. Taylor e, P. Telford ar, J. Temple as, B. Tiller x, M. Titov v, V.V. Tokmenin ai, M. Tomoto ax, T. Toole bi, I. Torchiani v, S. Towers ap, T. Trefzger w, S. Trincaz-Duvoid p, D. Tsybychev bt, B. Tuchming q, C. Tully bp, A.S. Turcot ar, P.M. Tuts br, R. Unalan bm, L. Uvarov am, DØ Collaboration / Physics Letters B 655 (2007) 7–14 9 S. Uvarov am, S. Uzunyan az, B. Vachon e, P.J. van den Berg ag, R. Van Kooten bb, W.M. van Leeuwen ag, N. Varelas ay, E.W. Varnes as, A. Vartapetian bz, I.A. Vasilyev al, M. Vaupel y, P. Verdier s, L.S. Vertogradov ai, M. Verzocchi ax, F. Villeneuve-Seguier aq, P. Vint aq, J.-R. Vlimant p, E. Von Toerne bg, M. Voutilainen bo,2, M. Vreeswijk ag, H.D. Wahl aw, L. Wang bi, M.H.L.S. Wang ax, J. Warchol bc, G. Watts cd, M. Wayne bc, G. Weber w, M. Weber ax, H. Weerts bm, N. Wermes u, M. Wetstein bi, A. White bz, D. Wicke y, G.W. Wilson bf, S.J. Wimpenny av, M. Wobisch ax, J. Womersley ax, D.R. Wood bk, T.R. Wyatt ar, Y. Xie by, N. Xuan bc, S. Yacoob ba, R. Yamada ax, M. Yan bi, T. Yasuda ax, Y.A. Yatsunenko ai, K. Yip bu, H.D. Yoo by, S.W. Youn ba, C. Yu m, J. Yu bz, A. Yurkewicz bt, A. Zatserklyaniy az, C. Zeitnitz y, D. Zhang ax, T. Zhao cd, B. Zhou bl, J. Zhu bt, M. Zielinski bs, D. Zieminska bb, A. Zieminski bb, V. Zutshi az, E.G. Zverev ak a Universidad de Buenos Aires, Buenos Aires, Argentina b LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil c Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil d Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil e University of Alberta, Edmonton, Alberta, and Simon Fraser University, Burnaby, British Columbia, and York University, Toronto, Ontario, and McGill University, Montreal, Quebec, Canada f University of Science and Technology of China, Hefei, People’s Republic of China g Universidad de los Andes, Bogotá, Colombia h Center for Particle Physics, Charles University, Prague, Czech Republic i Czech Technical University, Prague, Czech Republic j Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic k Universidad San Francisco de Quito, Quito, Ecuador l Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Université Blaise Pascal, Clermont-Ferrand, France m Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France n CPPM, IN2P3-CNRS, Université de la Méditerranée, Marseille, France o IN2P3-CNRS, Laboratoire de l’Accélérateur Linéaire, Orsay, France p LPNHE, IN2P3-CNRS, Universités Paris VI and VII, Paris, France q DAPNIA/Service de Physique des Particules, CEA, Saclay, France r IPHC, IN2P3-CNRS, Université Louis Pasteur, Strasbourg, and Université de Haute Alsace, Mulhouse, France s Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, Villeurbanne, France t III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany u Physikalisches Institut, Universität Bonn, Bonn, Germany v Physikalisches Institut, Universität Freiburg, Freiburg, Germany w Institut für Physik, Universität Mainz, Mainz, Germany x Ludwig-Maximilians-Universität München, München, Germany y Fachbereich Physik, University of Wuppertal, Wuppertal, Germany z Panjab University, Chandigarh, India aa Delhi University, Delhi, India ab Tata Institute of Fundamental Research, Mumbai, India ac University College Dublin, Dublin, Ireland ad Korea Detector Laboratory, Korea University, Seoul, South Korea ae SungKyunKwan University, Suwon, South Korea af CINVESTAV, Mexico City, Mexico ag FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands ah Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands ai Joint Institute for Nuclear Research, Dubna, Russia aj Institute for Theoretical and Experimental Physics, Moscow, Russia ak Moscow State University, Moscow, Russia al Institute for High Energy Physics, Protvino, Russia am Petersburg Nuclear Physics Institute, St. Petersburg, Russia an Lund University, Lund, and Royal Institute of Technology and Stockholm University, Stockholm, and Uppsala University, Uppsala, Sweden ao Physik Institut der Universität Zürich, Zürich, Switzerland ap Lancaster University, Lancaster, United Kingdom aq Imperial College, London, United Kingdom ar University of Manchester, Manchester, United Kingdom as University of Arizona, Tucson, AZ 85721, USA at Lawrence Berkeley National Laboratory and University of California, Berkeley, CA 94720, USA au California State University, Fresno, CA 93740, USA av University of California, Riverside, CA 92521, USA aw Florida State University, Tallahassee, FL 32306, USA ax Fermi National Accelerator Laboratory, Batavia, IL 60510, USA ay University of Illinois at Chicago, Chicago, IL 60607, USA 10 DØ Collaboration / Physics Letters B 655 (2007) 7–14 az Northern Illinois University, DeKalb, IL 60115, USA ba Northwestern University, Evanston, IL 60208, USA bb Indiana University, Bloomington, IN 47405, USA bc University of Notre Dame, Notre Dame, IN 46556, USA bd Purdue University Calumet, Hammond, IN 46323, USA be Iowa State University, Ames, IA 50011, USA bf University of Kansas, Lawrence, KS 66045, USA bg Kansas State University, Manhattan, KS 66506, USA bh Louisiana Tech University, Ruston, LA 71272, USA bi University of Maryland, College Park, MD 20742, USA bj Boston University, Boston, MA 02215, USA bk Northeastern University, Boston, MA 02115, USA bl University of Michigan, Ann Arbor, MI 48109, USA bm Michigan State University, East Lansing, MI 48824, USA bn University of Mississippi, University, MS 38677, USA bo University of Nebraska, Lincoln, NE 68588, USA bp Princeton University, Princeton, NJ 08544, USA bq State University of New York, Buffalo, NY 14260, USA br Columbia University, New York, NY 10027, USA bs University of Rochester, Rochester, NY 14627, USA bt State University of New York, Stony Brook, NY 11794, USA bu Brookhaven National Laboratory, Upton, NY 11973, USA bv Langston University, Langston, OK 73050, USA bw University of Oklahoma, Norman, OK 73019, USA bx Oklahoma State University, Stillwater, OK 74078, USA by Brown University, Providence, RI 02912, USA bz University of Texas, Arlington, TX 76019, USA ca Southern Methodist University, Dallas, TX 75275, USA cb Rice University, Houston, TX 77005, USA cc University of Virginia, Charlottesville, VA 22901, USA cd University of Washington, Seattle, WA 98195, USA Received 30 May 2007; received in revised form 20 July 2007; accepted 3 August 2007 Available online 6 September 2007 Editor: M. Doser Abstract We present a measurement of the top quark mass in the dilepton channel based on approximately 370 pb−1 of data collected by the DØ experiment during Run II of the Fermilab Tevatron collider. We employ two different methods to extract the top quark mass. We show that both methods yield consistent results using ensemble tests of events generated with the DØ Monte Carlo simulation. We combine the results from the two methods to obtain a top quark mass mt = 178.1 ± 8.2 GeV. The statistical uncertainty is 6.7 GeV and the systematic uncertainty is 4.8 GeV. © 2007 Elsevier B.V. All rights reserved. PACS: 14.65.Ha The top quark mass is an important parameter in Standard Model [1] predictions. For example, loops involving top quarks provide the dominant radiative corrections to the value of the W boson mass. Precise measurements of the W boson and top quark masses provide a constraint on the Higgs boson mass [2]. At the Tevatron, top and antitop quarks are predominantly pair-produced. Top quarks decay to a W boson and a b quark. If the W bosons from the top and the antitop quarks both de- cay leptonically (to eν or μν) the final state consists of two charged leptons, missing transverse momentum (/pT ) from the * Corresponding author. E-mail address: heintz@bu.edu (U. Heintz). 1 On leave from IEP SAS Kosice, Slovakia. 2 Visitor from Helsinki Institute of Physics, Helsinki, Finland. undetected neutrinos, and two jets from the fragmentation of the b quarks. We call this the dilepton channel. It has a relatively small branching fraction (≈ 5%) but very low backgrounds. The measurement of the top quark mass in the dilepton channel is statistically limited. It provides an independent measurement of the top quark mass that can be compared with measurements in other t t̄ decay channels, and a consistency check on the t t̄ hypothesis in the dilepton channel. The DØ detector is a multipurpose collider detector [3]. The central tracker employs silicon microstrips close to the beam and concentric cylinders covered with scintillating fibers in a 2 T axial magnetic field. The liquid-argon/uranium calorime- ter is divided into a central section covering pseudorapidity |η| � 1.1 and two endcap calorimeters extending coverage to |η| � 4.2 [4], where η = − ln[tan(θ/2)] and θ is the polar mailto:heintz@bu.edu DØ Collaboration / Physics Letters B 655 (2007) 7–14 11 angle with respect to the proton beam direction. The muon spectrometer consists of a layer of tracking detectors and scin- tillation trigger counters between the calorimeter and 1.8 T toroidal iron magnets, followed by two similar layers outside the toroids. We present here two measurements that were carried out in- dependently by two groups of analyzers. Both groups chose to optimize their analyses in different ways, one using a rela- tively loose event selection, the other taking advantage of the low background in top–antitop samples selected using tagging of b-quark jets. In the end, we combine the results from both analyses taking into account the correlations between the re- sults. The event selection is based on the measurement of the cross section for t t̄ -production in the dilepton channel [5] with a few modifications. The analyses use about 370 pb−1 of data from pp̄ collisions at √ s = 1.96 TeV collected with the DØ detector at the Fermilab Tevatron collider. We select events with two oppositely charged, isolated lep- tons (e or μ) with transverse momentum pT > 15 GeV and at least two jets with pT > 20 GeV. Electron candidates are isolated clusters of energy in the electromagnetic section of the calorimeter that agree in their profile with that expected from electromagnetic showers, based on Monte Carlo simula- tions, and that are matched with a charged particle track re- constructed in the central tracker. Electrons must be either in the central calorimeter (pseudorapidity |η| < 1.1) or in the for- ward calorimeter (1.5 < |η| < 2.5). Muons are reconstructed as tracks in the muon spectrometer with |η| < 2, matched to a charged particle track in the central tracker. They must be iso- lated from other activity in the calorimeter and in the tracker. Jets are reconstructed with the improved legacy cone algo- rithm [6] with cone size �R = √ �η2 + �φ2 = 0.5 and are restricted to |η| < 2.5. All jets were corrected using the stan- dard DØ jet energy scale corrections [7]. We distinguish eμ, ee, and μμ events. For eμ events we require HT > 122 GeV, where HT is the scalar sum of the larger of the two lepton pT values and the pT values of the leading two jets. For ee events we require sphericity S > 0.15 and missing transverse momentum /pT > 35–40 GeV, depend- ing on the dielectron invariant mass m(ee), and we reject events with 80 < m(ee) < 100 GeV to reduce the background from Z → ee decays. Sphericity is defined as 1.5 times the sum of the first two eigenvalues of the normalized momentum tensor calculated using all electrons, muons and jets in the event. For μμ events we require inconsistency with the Z → μμ hypothesis based on the χ2 of a kinematic fit. In some Z → μμ events a muon momentum is significantly mismeasured. These events are not consistent kinematically with Z decays and they are therefore not eliminated by the kinematic fit. The mismeasured muon momentum gives rise to pT imbalance in the muon direction. We therefore require /pT > 35 GeV if the azimuthal angle between the leading muon and the direction of /pT , �φ(/pT ,μ) < 175◦. We tighten the /pT requirement to 85 GeV if the leading muon and the /pT are approximately collinear in the transverse direction. Table 1 Expected and observed dilepton event yields for t t̄ production with mt = 175 GeV and the backgrounds from WW and Z production based on Monte Carlo, and from misidentified leptons (mis-id) based on collider data Sample t t̄ WW Z Mis-id Total Data �� no-tag 7.2 1.1 2.6 2.2 13.2 (+2.8 −2.1 ) 12 �� b-tag 9.9 0.05 0.12 0.09 10.1 ± 0.9 14 �� tight 15.8 1.1 2.4 0.5 19.8 ± 0.6 21 � + track 6.3 0.01 1.8 0.4 8.5 ± 0.3 9 For our mass measurements we use the following samples of events. The “b-tag” sample consists of events that have at least one jet that contains a secondary vertex tag with transverse decay length significance Λxy > 7 [8]. This sample has very low backgrounds. The “no-tag” sample consists of events that have no such secondary vertex tags. The 26 events in these two samples consist of 20 eμ events, 5 ee, and 1 μμ event. The “tight” sample does not use the b-tagging information. It contains all ee and μμ events that are in either the b-tag or the no-tag samples. For eμ events the tight sample requires the more restrictive cuts HT > 140 GeV, /pT > 25 GeV and tighter electron identification cuts to reduce backgrounds. To increase the acceptance for dilepton decays, we also analyze a sample of events that requires only one well-identified lepton (e or μ) with pT > 15 GeV and an isolated track with pT > 15 GeV instead of the second identified lepton. The events must also have at least one jet with a secondary vertex tag, and /pT > 15–35 GeV, depending on lepton flavor and the invariant mass of the lep- ton + track system. We call this the “� + track” sample. Events with two well-identified leptons are vetoed from this sample so that there is no overlap between the � + track sample and the other dilepton samples. There are 6 e + track events and 3 μ + track events in this sample. The observed event yields for each of the data samples are listed in Table 1. Monte Carlo samples are generated for nineteen values of the top quark mass between 120 and 230 GeV. The simula- tion uses ALPGEN [9] with CTEQ5L parton distribution func- tions [10] as the event generator, PYTHIA [11] for fragmentation and decay, and GEANT [12] for the detector simulation. No parton-shower matching algorithm was used in the generation of these event samples. We simulate diboson production with ALPGEN and PYTHIA and Z/γ ∗ → ττ processes with PYTHIA. The number of expected events are determined by applying the selection cuts to these Monte Carlo event samples. These samples are corrected for lepton, jet and b-tagging efficiencies determined from collider data. The tagging efficiency for b-jets is measured in a data sam- ple enhanced in heavy flavor jets by requiring at least one jet with a muon in each event. Monte Carlo based corrections are applied to correct for sample biases. The probability to tag a light-flavor jet is measured from collider data using events with a secondary vertex with negative decay length, meaning that the tracks forming the secondary vertex meet in the hemisphere that is on the opposite side of the primary vertex from the jet. The energy of Monte Carlo jets is increased by 3.4% in addi- tion to the nominal jet energy scale corrections. This factor was determined by fitting the top mass and the jet energy scale in 12 DØ Collaboration / Physics Letters B 655 (2007) 7–14 lepton + jets events and brings the invariant mass distribution of the two jets from the W boson decay in lepton + jets Monte Carlo events in agreement with that observed in the data. Event yield normalizations for Z → ee and Z → μμ are obtained from data. The number of events with misidentified leptons is dominated by jets misidentified as electrons. We con- struct a likelihood discriminant to distinguish electrons from misidentified jets based on the shape of the energy cluster in the calorimeter and the on the matched track. We determine the contamination by misidentified jets in our sample by fitting the distribution of this likelihood discriminant before we cut on it. Expected yields for signal and background are given in Table 1. We use only the two jets with the highest pT in this analysis. We assign these two jets to the b and b̄ quarks from the decay of the t and t̄ quarks. If we assume a value mt for the top quark mass, we can determine the pairs of t and t̄ momenta that are consistent with the observed lepton and jet momenta and /pT . A solution refers to a pair of top–antitop quark momenta that is consistent with the observed event. For each assignment of observed momenta to the final state particles and for each hy- pothesized value of mt , there may be up to four solutions. We assign a weight function w(mt) to each solution, as described below. Events for which no solution exists are rejected from our data and Monte Carlo event samples. The event yields in Table 1 include this additional selection requirement. Two events from the collider data are rejected with this requirement. We consider each of the two possible assignments of the two jets to the b and b̄ quarks. We account for detector resolutions by repeating the weight calculation with input values for the lepton and jet momenta that are drawn from the detector res- olution functions for objects with the observed momenta. We refer to this procedure as resolution sampling. For each event we obtain a weight W(mt) = 1/N × ∑N j=1 ∑n i=1 w(mt)ij by summing over all n solutions and averaging over N resolution samples. This weight characterizes the likelihood that the event is produced in the decay of a t t̄ pair as a function of mt . The techniques we use are similar to those used by the DØ Collaboration to measure the top quark mass in the dilepton channel using Run I data [13]. The data are analyzed using two different methods that differ in the event samples that they are based on, in the calculation of the event weight, and in the al- gorithm that compares the weights for the observed events to Monte Carlo predictions to extract the top quark mass. The matrix-element weighting technique (MWT) follows the ideas proposed by Dalitz and Goldstein [14] and Kondo [15]. The solution weight is w(mt) = f (x)f (x̄)p(E∗ � |mt)p(E∗̄ � |mt), where f (x) is the parton distribution function of the proton and x (x̄) is the momentum fraction carried by the initial (anti)quark. The quantity p(E∗ � |mt) is the probability that the lepton has energy E∗ � in the top quark rest frame for the hy- pothesized top quark mass mt . For each event we use the value of the hypothesized top quark mass mpeak at which W(mt) reaches its maximum as the estimator for the mass of the top quark. We generate probability density functions of mpeak for a range of top quark masses using Monte Carlo simulations. We call these distributions templates. To compute the contribution of backgrounds to the templates, we use Z → ττ and WW Monte Carlo events. Backgrounds arising from detector signals that are misidentified as electrons or muons are estimated from collider data samples. We compare the distribution of mpeak for the observed events to these templates using a binned maximum likelihood fit. The likelihood is calculated as L(mt) = nbin∏ i=1 [ nssi(mt ) + nbbi ns + nb ]ni , where ni is the number of data events observed in bin i, si(mt ) is the normalized signal template contents for bin i at top quark mass mt , bi is the normalized background template contents for bin i. The product runs over all nbin bins. The background template consists of events from all background sources added in the expected relative proportions. The signal-to-background fraction is fixed to ns/nb with the numbers of signal and back- ground events (ns , nb) taken from Table 1. To calibrate the performance of our method, we generate a large number of simulated experiments for several input top quark mass values. We refer to each of these experiments as an ensemble. Each ensemble consists of as many events of each type as we have in our collider data sample. A given event is taken from the signal and background samples with probabil- ities that correspond to the fraction of events expected from each sample. We use a quadratic function of mt to fit the − lnL points to thirteen mass points centered on the point with the smallest value of − lnL. The distribution of measured top quark mass values from the ensemble fits gives an estimate of the par- ent distribution of our measurement. The ensemble test results indicate that the measured mass tracks the input mass with an offset of 1.9 ± 0.8 GeV, which we correct for in the final result. In general, the tails of the likelihood distribution for an en- semble are not well approximated by a Gaussian. Thus it is necessary to restrict the range of mass points that is included in the fit to points near the observed minimum in − lnL. For small data samples, however, there is a substantial statistical uncertainty in the computed likelihood values which can be re- duced by increasing the number of mass points used in the fit. Thus the range of mass points that are included in the likeli- hood fit must be optimized for the observed data sample size to obtain the best possible agreement between measured top quark mass and input top quark mass. This was done for both analyses based on Monte Carlo ensembles that contain exactly as many events as we observe in the data. The MWT analysis uses the no-tag and b-tag samples of events. Separating out the very-low-background b-tagged events improves the precision of the result. The analysis is performed with separate templates for ee, eμ, and μμ events and separate signal-to-background fractions for events with- out a b-tag and � 1 b-tags. The maximum of the joint like- lihood for all events, shown in Fig. 1, corresponds to mt = 176.2 ± 9.2(stat) GeV after the offset correction. Fig. 2 shows the distribution of mpeak from collider data compared to the sum of Monte Carlo templates with mt = 180 GeV. DØ Collaboration / Physics Letters B 655 (2007) 7–14 13 Fig. 1. Joint likelihoods from the MWT analysis (closed circles) and the νWT analysis (open circles). The minima of the likelihood curves do not include the correction for the offset in the response. Fig. 2. Distribution of mpeak from the MWT analysis (circles) compared to the sum of Monte Carlo templates for the no-tag and b-tag channels and all lepton flavors for mt = 180 GeV (open histogram). The shaded histogram indicates the background contribution. The neutrino weighting technique (νWT) ignores the mea- sured /pT in reconstructing the event. Instead we assume a rep- resentative range of values for the pseudorapidities of the two neutrinos and the solution weight w(mt) = 1 Nη Nη∑ i=1 exp [−(/pxi − /px) 2 2σ 2 x ] exp [−(/pyi − /py) 2 2σ 2 y ] characterizes the consistency of the resulting solutions with the observed /pT . The sum is over the Nη steps of neutrino rapidity values, /pxi and /pyi are the x and y components of the sum of the neutrino momenta computed for step i, and σx and σy are the measurement resolutions for /px and /py . We then normal- ize the event weight W(mt) over the range 80 < mt < 330 GeV and integrate it over ten bins in mt . Every event is thus charac- terized by a 9-component vector �W = (W1, . . . ,W9) (the 10th bin is fixed by the first nine and the normalization condition). We compare the vectors from the collider data events to sets of N Monte Carlo events generated with different values of mt by Table 2 Summary of dilepton mass measurements MWT νWT Combined Top quark mass 176.2 179.5 178.1 GeV Statistical uncertainty 9.2 7.4 6.7 GeV Systematic uncertainty 3.9 5.6 4.8 GeV Jet energy scale 3.6 4.8 4.3 GeV Parton distribution functions 0.9 0.7 0.8 GeV Gluon radiation 0.8 2.0 1.5 GeV Background 0.2 1.4 0.9 GeV Heavy flavor content – 0.6 0.3 GeV Monte Carlo statistics 0.8 1.0 0.9 GeV Jet resolution – 0.6 0.3 GeV Muon resolution – 0.4 0.2 GeV Total uncertainty 10.0 9.3 8.2 GeV computing the signal probability fs( �W |mt) = 1 N N∑ j=1 9∏ i=1 exp[−(Wi − WMC ij )2/2h2]∫ 1 0 exp[−(W ′ − WMC ij )2/2h2]dW ′ , where �WMC j is the vector of weights from Monte Carlo event j . The value of the resolution parameter h is optimized using en- semble tests based on simulated events to give the best agree- ment between input mass and measured mass. We compute a similar probability fb( �W) for backgrounds and combine them in the likelihood L(mt , n̄b, n) = G(nb − n̄b, σ )P (ns + nb,n) × n∏ i=1 [ nsfs( �Wi |mt) + nbfb( �Wi) ns + nb ] , which we optimize with respect to mt , the number of signal events ns , and the number of background events nb. G is a Gaussian constraint on the difference between nb and the ex- pected number of background events n̄b, and P is a Poisson constraint on ns + nb to the number of events n observed in data. The νWT analysis uses the tight sample and the � + track sample. The analysis is performed with separate templates for ee, eμ, and μμ events in the tight sample and the two lepton flavors in the � + track sample. We fit the − lnL points for val- ues of mt within 20 GeV of the point with the smallest value of − lnL with a quadratic function of mt . The performance of the νWT algorithm is checked using ensemble tests as described for the MWT algorithm. The average measured values of mt track the input values with an offset of 1.7 ± 0.2 GeV. For the νWT analysis, the maximum of the joint likelihood of all events (Fig. 1) corresponds to mt = 179.5 ± 7.4(stat) GeV after the offset correction. We also use ensemble tests to study the size of systematic uncertainties (see Table 2). By far the largest systematic uncer- tainty originates from the uncertainty in the calibration of the jet energy scale of 4.1%. We determine the effect of the uncer- tainty on the measurement by generating ensemble tests with the jet energy scale increased and decreased by one standard deviation. 14 DØ Collaboration / Physics Letters B 655 (2007) 7–14 We estimate the sensitivity of the result to uncertainties in the parton distribution functions by analyzing ensembles gener- ated with a range of available parton distribution function sets. The next to largest uncertainty originates from the modeling of gluon radiation in the Monte Carlo. Gluon radiation can give rise to additional jets in the event. In the data about one third of the events have more than two jets. The two analyses used dif- ferent procedures to estimate this effect. For the νWT analysis, events with three reconstructed jets from t t̄ + 1 parton events generated with ALPGEN were analyzed in ensemble tests with templates derived from t t̄ events with only two jets and the difference in reconstructed top quark mass was applied as an uncertainty to the fraction of events with more than two jets. In the MWT analysis the fraction of events with only two jets was varied in ensemble tests within the range that is consistent with the jet multiplicity spectrum observed in the data and analyzed with the nominal templates. The observed variation in the result was applied as systematic error. We estimate the effect of uncertainties in the shape of the background distributions to determine the background uncer- tainty. For the MWT analysis we also perform tests with en- sembles in which we varied the background fraction, which was fixed in the mass fit, by its uncertainty. For the � + track sample, the heavy flavor content in the background is a signif- icant source of uncertainty. This only contributed to the νWT analysis. The finite size of the Monte Carlo samples limits the statistical precision with which we can extract the top quark mass. This is accounted for in the Monte Carlo statistics un- certainty. Finally, we generated ensembles with varied jet and muon momentum resolutions to estimate the effect of their un- certainties. The resulting uncertainties for the νWT analysis are quoted in Table 2. The effect on the result of the MWT analysis was negligible. We follow the method for combining correlated measure- ments from Ref. [16] in combining the results from the MWT and νWT analyses. We determine the statistical correlation be- tween the two measurements using ensemble tests. The corre- lation factor between the two analyses is 0.35. The systematic uncertainties from each source in Table 2 are taken to be com- pletely correlated between the two analyses. The results of the combination are also listed in Table 2. In conclusion, we measure the top quark mass in the dilepton channel. We obtain mt = 178.1 ± 6.7(stat) ± 4.8(syst) GeV as our best estimate of the top quark mass. This is in good agree- ment with the world average mt = 172.5±2.3 GeV [17], based on Run I and Run II data collected by the CDF and DØ Collab- orations. Acknowledgements 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); CAPES, CNPq, FAPERJ, FAPESP and FUN- DUNESP (Brazil); DAE and DST (India); Colciencias (Colom- bia); CONACyT (Mexico); KRF and KOSEF (South Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); PPARC (United Kingdom); MSMT (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); Research Corporation; Alexander von Hum- boldt Foundation; and the Marie Curie Program. References [1] S.L. Glashow, Nucl. Phys. 22 (1961) 579; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264; A. Salam, in: N. Svartholm (Ed.), Elementary Particle Theory: Relativis- tic Groups and Analyticity, in: Nobel Symposium, vol. 8, Almqvist and Wiksell, Stockholm, 1968, p. 367. [2] G. Degrassi, et al., Phys. Lett. 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