Direct measurement of the mass difference between top and antitop quarks
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Direct measurement of the mass difference between top and antitop quarks
V.M. Abazov, B. Abbott, B.S. Acharya, M. Adams, T. Adams, G.D. Alexeev, G. Alkhazov, A. Alton a , G. Alverson, G.A. Alves, M. Aoki, M. Arov, A. Askew, B. ˚Asman, O. Atramentov, C. Avila, J. BackusMayes, F. Badaud, L. Bagby, B. Baldin, D.V. Bandurin, S. Banerjee, E. Barberis, P. Baringer, J. Barreto, J.F. Bartlett, U. Bassler, V. Bazterra, S. Beale, A. Bean, M. Begalli, M. Begel, C. Belanger-Champagne, L. Bellantoni, S.B. Beri, G. Bernardi, R. Bernhard, I. Bertram, M. Besanc¸on, R. Beuselinck, V.A. Bezzubov, P.C. Bhat, V. Bhatnagar, G. Blazey, S. Blessing, K. Bloom, A. Boehnlein, D. Boline, E.E. Boos, G. Borissov, T. Bose, A. Brandt, O. Brandt, R. Brock, G. Brooijmans, A. Bross, D. Brown, J. Brown, X.B. Bu, M. Buehler, V. Buescher, V. Bunichev, S. Burdin b , T.H. Burnett, C.P. Buszello, B. Calpas, E. Camacho-P´erez, M.A. Carrasco-Lizarraga, B.C.K. Casey, H. Castilla-Valdez, S. Chakrabarti, D. Chakraborty, K.M. Chan, A. Chandra, G. Chen, S. Chevalier-Th´ery, D.K. Cho, S.W. Cho, S. Choi, B. Choudhary, S. Cihangir, D. Claes, J. Clutter, M. Cooke, W.E. Cooper, M. Corcoran, F. Couderc, M.-C. Cousinou, A. Croc, D. Cutts, A. Das, G. Davies, K. De, S.J. de Jong, E. De La Cruz-Burelo, F. D´eliot, M. Demarteau, R. Demina, D. Denisov, S.P. Denisov, S. Desai, C. Deterre, K. DeVaughan, H.T. Diehl, M. Diesburg, P.F. Ding, A. Dominguez, T. Dorland, A. Dubey, L.V. Dudko, D. Duggan, A. Duperrin, S. Dutt, A. Dyshkant, M. Eads, D. Edmunds, J. Ellison, V.D. Elvira, Y. Enari, H. Evans, A. Evdokimov, V.N. Evdokimov, G. Facini, T. Ferbel, F. Fiedler, F. Filthaut, W. Fisher, H.E. Fisk, M. Fortner, H. Fox, S. Fuess, A. Garcia-Bellido, V. Gavrilov, P. Gay, W. Geng,
D. Gerbaudo, C.E. Gerber, Y. Gershtein, G. Ginther,
G. Golovanov, A. Goussiou, P.D. Grannis, S. Greder, H. Greenlee, Z.D. Greenwood, E.M. Gregores, G. Grenier, Ph. Gris, J.-F. Grivaz, A. Grohsjean, S. Gr¨unendahl, M.W. Gr¨unewald, T. Guillemin, F. Guo, G. Gutierrez, P. Gutierrez, A. Haas c , S. Hagopian, J. Haley, L. Han, K. Harder, A. Harel, J.M. Hauptman, J. Hays, T. Head, T. Hebbeker, D. Hedin, H. Hegab, A.P. Heinson, U. Heintz, C. Hensel, I. Heredia-De La Cruz, K. Herner, G. Hesketh d , M.D. Hildreth, R. Hirosky, T. Hoang, J.D. Hobbs, B. Hoeneisen, M. Hohlfeld, Z. Hubacek,
N. Huske, V. Hynek, I. Iashvili, Y. Ilchenko, R. Illingworth, A.S. Ito, S. Jabeen, M. Jaffr´e, D. Jamin, A. Jayasinghe, R. Jesik, K. Johns, M. Johnson, D. Johnston, A. Jonckheere, P. Jonsson, J. Joshi, A.W. Jung, A. Juste, K. Kaadze, E. Kajfasz, D. Karmanov, P.A. Kasper, I. Katsanos, R. Kehoe, S. Kermiche, N. Khalatyan, A. Khanov, A. Kharchilava, Y.N. Kharzheev, M.H. Kirby, J.M. Kohli, A.V. Kozelov, J. Kraus, S. Kulikov, A. Kumar, A. Kupco, T. Kurˇca, V.A. Kuzmin, J. Kvita, S. Lammers, G. Landsberg, P. Lebrun, H.S. Lee, S.W. Lee, W.M. Lee, J. Lellouch, L. Li, Q.Z. Li, S.M. Lietti, J.K. Lim, D. Lincoln, J. Linnemann, V.V. Lipaev, R. Lipton, Y. Liu, Z. Liu, A. Lobodenko, M. Lokajicek, R. Lopes de Sa, H.J. Lubatti, R. Luna-Garcia e , A.L. Lyon, A.K.A. Maciel, D. Mackin, R. Madar, R. Maga˜na-Villalba, S. Malik, V.L. Malyshev, Y. Maravin, J. Mart´ınez-Ortega, R. McCarthy, C.L. McGivern, M.M. Meijer, A. Melnitchouk, D. Menezes, P.G. Mercadante, M. Merkin, A. Meyer, J. Meyer, F. Miconi, N.K. Mondal, G.S. Muanza, M. Mulhearn, E. Nagy, M. Naimuddin, M. Narain, R. Nayyar, H.A. Neal, J.P. Negret, P. Neustroev, S.F. Novaes, T. Nunnemann, G. Obrant ‡ , J. Orduna, N. Osman, J. Osta, G.J. Otero y Garz´on, M. Padilla, A. Pal, N. Parashar, V. Parihar, S.K. Park, J. Parsons, R. Partridge c , N. Parua, A. Patwa, B. Penning, M. Perfilov, K. Peters, Y. Peters, K. Petridis, G. Petrillo, P. P´etroff, R. Piegaia, M.-A. Pleier, P.L.M. Podesta-Lerma f , V.M. Podstavkov, P. Polozov, A.V. Popov, M. Prewitt, D. Price, N. Prokopenko, S. Protopopescu, J. Qian, A. Quadt, B. Quinn, M.S. Rangel, K. Ranjan, P.N. Ratoff, I. Razumov, P. Renkel, M. Rijssenbeek, I. Ripp-Baudot, F. Rizatdinova, M. Rominsky, A. Ross, C. Royon, P. Rubinov, R. Ruchti, G. Safronov, G. Sajot, P. Salcido, A. S´anchez-Hern´andez, M.P. Sanders, B. Sanghi, A.S. Santos, G. Savage, L. Sawyer, T. Scanlon, R.D. Schamberger, Y. Scheglov, H. Schellman, T. Schliephake, S. Schlobohm, C. Schwanenberger, R. Schwienhorst, J. Sekaric, H. Severini, E. Shabalina, V. Shary, A.A. Shchukin, R.K. Shivpuri, V. Simak, V. Sirotenko, P. Skubic, P. Slattery, D. Smirnov, K.J. Smith, G.R. Snow, J. Snow, S. Snyder, S. S¨oldner-Rembold, L. Sonnenschein, K. Soustruznik, J. Stark, V. Stolin, D.A. Stoyanova, M. Strauss, D. Strom, L. Stutte, L. Suter, P. Svoisky, M. Takahashi, A. Tanasijczuk, W. Taylor, M. Titov, V.V. Tokmenin, Y.-T. Tsai, D. Tsybychev, B. Tuchming, C. Tully, L. Uvarov, S. Uvarov, S. Uzunyan, R. Van Kooten, W.M. van Leeuwen, N. Varelas, E.W. Varnes, I.A. Vasilyev, P. Verdier, L.S. Vertogradov, M. Verzocchi, M. Vesterinen, D. Vilanova, P. Vokac, H.D. Wahl, M.H.L.S. Wang, J. Warchol, G. Watts, M. Wayne, M. Weber g , L. Welty-Rieger, A. White, D. Wicke, M.R.J. Williams, G.W. Wilson, M. Wobisch, D.R. Wood, T.R. Wyatt, Y. Xie, C. Xu, S. Yacoob, R. Yamada, W.-C. Yang, T. Yasuda, Y.A. Yatsunenko, Z. Ye, H. Yin, K. Yip, S.W. Youn, J. Yu, S. Zelitch, T. Zhao, B. Zhou, J. Zhu, M. Zielinski, D. Zieminska, and L. Zivkovic (The D0 Collaboration ∗ ) Universidad de Buenos Aires, Buenos Aires, Argentina LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil Universidade Federal do ABC, Santo Andr´e, Brazil Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada University of Science and Technology of China, Hefei, People’s Republic of China Universidad de los Andes, Bogot´a, Colombia Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic Czech Technical University in Prague, Prague, Czech Republic Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic Universidad San Francisco de Quito, Quito, Ecuador LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, Grenoble, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, Paris, France CEA, Irfu, SPP, Saclay, France IPHC, Universit´e de Strasbourg, CNRS/IN2P3, Strasbourg, France IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, G¨ottingen, Germany Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany Fachbereich Physik, Bergische Universit¨at Wuppertal, Wuppertal, Germany Panjab University, Chandigarh, India Delhi University, Delhi, India Tata Institute of Fundamental Research, Mumbai, India University College Dublin, Dublin, Ireland Korea Detector Laboratory, Korea University, Seoul, Korea CINVESTAV, Mexico City, Mexico Nikhef, Science Park, Amsterdam, the Netherlands Radboud University Nijmegen, Nijmegen, the Netherlands and Nikhef, Science Park, Amsterdam, the Netherlands Joint Institute for Nuclear Research, Dubna, Russia Institute for Theoretical and Experimental Physics, Moscow, Russia Moscow State University, Moscow, Russia Institute for High Energy Physics, Protvino, Russia Petersburg Nuclear Physics Institute, St. Petersburg, Russia Instituci´o Catalana de Recerca i Estudis Avanc¸ats (ICREA) and Institut de F´ısica d’Altes Energies (IFAE), Barcelona, Spain Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden Lancaster University, Lancaster LA1 4YB, United Kingdom Imperial College London, London SW7 2AZ, United Kingdom The University of Manchester, Manchester M13 9PL, United Kingdom University of Arizona, Tucson, Arizona 85721, USA University of California Riverside, Riverside, California 92521, USA Florida State University, Tallahassee, Florida 32306, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Illinois at Chicago, Chicago, Illinois 60607, USA Northern Illinois University, DeKalb, Illinois 60115, USA Northwestern University, Evanston, Illinois 60208, USA Indiana University, Bloomington, Indiana 47405, USA Purdue University Calumet, Hammond, Indiana 46323, USA University of Notre Dame, Notre Dame, Indiana 46556, USA Iowa State University, Ames, Iowa 50011, USA University of Kansas, Lawrence, Kansas 66045, USA Kansas State University, Manhattan, Kansas 66506, USA Louisiana Tech University, Ruston, Louisiana 71272, USA Boston University, Boston, Massachusetts 02215, USA Northeastern University, Boston, Massachusetts 02115, USA University of Michigan, Ann Arbor, Michigan 48109, USA Michigan State University, East Lansing, Michigan 48824, USA University of Mississippi, University, Mississippi 38677, USA University of Nebraska, Lincoln, Nebraska 68588, USA Rutgers University, Piscataway, New Jersey 08855, USA Princeton University, Princeton, New Jersey 08544, USA State University of New York, Buffalo, New York 14260, USA Columbia University, New York, New York 10027, USA University of Rochester, Rochester, New York 14627, USA State University of New York, Stony Brook, New York 11794, USA Brookhaven National Laboratory, Upton, New York 11973, USA Langston University, Langston, Oklahoma 73050, USA University of Oklahoma, Norman, Oklahoma 73019, USA Oklahoma State University, Stillwater, Oklahoma 74078, USA Brown University, Providence, Rhode Island 02912, USA University of Texas, Arlington, Texas 76019, USA Southern Methodist University, Dallas, Texas 75275, USA Rice University, Houston, Texas 77005, USA University of Virginia, Charlottesville, Virginia 22901, USA University of Washington, Seattle, Washington 98195, USA (Dated: June 10, 2011)We present a direct measurement of the mass difference between top and antitop quarks ( D m ) in lepton + jets t ¯ t final states using the “matrix element” method. The purity of the lepton + jets sample is enhanced for t ¯ t eventsby identifying at least one of the jet as originating from a b quark. The analyzed data correspond to 3.6 fb − of p ¯ p collisions at √ s = .
96 TeV acquired by D0 in Run II of the Fermilab Tevatron Collider. The combinationof the e + jets and m + jets channels yields D m = . ± . ( stat) ± . ( syst) GeV, which is in agreement withthe standard model expectation of no mass difference. PACS numbers: 14.65.Ha
I. INTRODUCTION
The standard model (SM) is a local gauge-invariant quan-tum field theory (QFT), with invariance under charge, parity,and time reversal (
CPT ) providing one of its most fundamen-tal principles [1–4], which also constrains the SM [5]. Infact, any Lorentz-invariant local QFT must conserve
CPT [6].A difference in the mass of a particle and its antiparticlewould constitute a violation of
CPT invariance. This issue hasbeen tested extensively for many elementary particles of theSM [7]. Quarks, however, carry color charge, and thereforeare not observed directly, but must first hadronize via quan-tum chromodynamic (QCD) processes into jets of colorlessparticles. These hadronization products reflect properties ofthe initially produced quarks, such as their masses, electriccharges, and spin states. Except for the top quark, the timescale for hadronization of quarks is orders of magnitude lessthan for electroweak decay, thereby favoring the formation ofQCD-bound hadronic states before decay. This introduces asignificant dependence of the mass of a quark on the model ofQCD binding and evolution. In contrast to other quarks, no ∗ with visitors from a Augustana College, Sioux Falls, SD, USA, b The Univer-sity of Liverpool, Liverpool, UK, c SLAC, Menlo Park, CA, USA, d UniversityCollege London, London, UK, e Centro de Investigacion en Computacion -IPN, Mexico City, Mexico, f ECFM, Universidad Autonoma de Sinaloa, Cu-liac´an, Mexico, and g Universit¨at Bern, Bern, Switzerland. ‡ Deceased. bound states are formed before decay of produced top quarks,thereby providing a unique opportunity to measure directlythe mass difference between a quark and its antiquark [8].In proton-antiproton collisions at the Fermilab TevatronCollider, top quarks are produced in t ¯ t pairs via the stronginteraction, or singly via the electroweak interaction. In theSM, the top quark decays almost exclusively into a W bosonand a b quark. The topology of a t ¯ t event is therefore deter-mined by the subsequent decays of the W bosons. The world’smost precise top quark mass measurements are performed inthe lepton + jets ( ℓ + jets) channels, which are characterized bythe presence of one isolated energetic electron or muon fromone W → ℓ n decay, an imbalance in transverse momentumrelative to the beam axis from the escaping neutrino, and fouror more jets from the evolution of the two b quarks and thetwo quarks from the second W → q ¯ q ′ decay.The top quark was discovered [9, 10] in proton-antiprotoncollision data at a center of mass energy of √ s = . √ s = .
96 TeV and higher luminosities,Run II of the Tevatron commenced in 2001. Since then, alarge sample of t ¯ t events has been collected, yielding precisionmeasurements of various SM parameters such as the mass ofthe top quark, which has been determined to an accuracy ofabout 0 .
6% or m top ≡ ( m t + m ¯ t ) = . ± . m t ( m ¯ t ) is the mass of the top (antitop) quark.The D0 Collaboration published the first measurement ofthe top-antitop quark mass difference, D m ≡ m t − m ¯ t , using1 fb − of Run II integrated luminosity [12]. Our new measure-ment, presented here, employs the same matrix element (ME)technique [13, 14], suggested initially by Kondo et al. [15–17], and developed to its current form by D0 [18]. Our previ-ous study measured a mass difference D m = . ± . ( stat . ) ± . ( syst . ) GeV . Recently, CDF has also measured D m [19] based on 5.6 fb − of Run II data, using a template technique, and found D m = − . ± . ( stat . ) ± . ( syst . ) GeV . In this paper, we extend our first measurement of D m us-ing an additional 2.6 fb − of Run II integrated luminosity, andcombining our two results. We also re-examine the uncer-tainties from the modeling of signal processes and of the re-sponse of the detector. Most important is a possible presenceof asymmetries in the calorimeter response to b and ¯ b -quarkjets, which we re-evaluate using a purely data-driven method.We also consider for the first time a bias from asymmetries inresponse to c and ¯ c -quark jets.This paper is arranged as follows: after a brief descripton ofthe D0 detector in Sec. II, we review the event selection andreconstruction in Sec. III. In Sec. IV, we define the samples ofMonte Carlo (MC) events used in the analysis. The extractionof the top-antitop quark mass difference using the ME tech-nique is then briefly reviewed in Sec. V. The calibration of thistechnique, based on MC events, and the measurement of themass difference in 2.6 fb − of Run II integrated luminosity arepresented in Sec. VI. The evaluation of systematic uncertain-ties and cross checks are discussed in Sec. VII and VII C, re-spectively. Finally, the combination of the measurements forthe 2.6 fb − and 1 fb − data samples is presented in Sec. VIII. II. THE D0 DETECTOR
The D0 detector has a central-tracking system, calorime-try, and a muon system. The central-tracking system con-sists of a silicon microstrip tracker (SMT) and a central fibertracker (CFT), both located within a 1.9 T superconductingsolenoidal magnet [20–22], with designs optimized for track-ing and vertexing at pseudorapidities | h | < p ¯ p interaction vertex (PV) with a precisionof about 40 m m in the plane transverse to the beam directionand determine the impact parameter of any track relative tothe PV [24] with a precision between 20 and 50 m m, depend-ing on the number of hits in the SMT. These are the key ele-ments to lifetime-based b -quark jet tagging. The liquid-argonand uranium sampling calorimeter has a central section (CC)covering pseudorapidities | h | . . | h | ≈ .
2, with all three housedin separate cryostats [20, 25]. Central and forward preshowerdetectors are positioned just before the CC and EC. An outermuon system, at | h | <
2, consists of a layer of tracking detec-tors and scintillation trigger counters in front of 1.8 T toroids,followed by two similar layers after the toroids [26]. The lu-minosity is calculated from the rate of p ¯ p inelastic collisionsmeasured with plastic scintillator arrays, which are located in front of the EC cryostats. The trigger and data acquisitionsystems are designed to accommodate the high instantaneousluminosities of Run II [27]. III. EVENT SELECTION
In this new measurement of D m , we analyze data corre-sponding to an integrated luminosity of about 2 . − for boththe e + jets and m + jets channels.Candidate t ¯ t events are required to pass an isolated ener-getic lepton trigger or a lepton + jet(s) trigger. These eventsare enriched in t ¯ t content by requiring exactly four jets re-constructed using the Run II cone algorithm [28] with coneradius D R ≡ p ( D h ) + ( D f ) = .
5, transverse momenta p T >
20 GeV, and pseudorapidities | h | < .
5. The jet ofhighest transverse momentum in a given event must have p T >
40 GeV. Furthermore, we require exactly one isolatedelectron with p T >
20 GeV and | h | < .
1, or exactly one iso-lated muon with p T >
20 GeV and | h | < .
0. The leptonsmust originate within 1 cm of the PV in the coordinate alongthe beamline. Events containing an additional isolated lep-ton (either e or m ) with p T >
15 GeV are rejected. Leptonisolation criteria are based on calorimetric and tracking infor-mation along with object identification criteria, as describedin Ref. [29]. The positively (negatively) charged leptons areused to tag the top (antitop) quark in a given event. To reduceinstrumental effects that can cause charge-dependent asym-metries in the lepton momentum scale, the polarity of thesolenoidal magnetic field is routinely reversed, splitting thetotal data into two samples of approximately equal size. ThePV must have at least three associated tracks and lie within thefiducial region of the SMT. At least one neutrino is expectedin the ℓ + jets final state; hence, an imbalance in transversemomentum (defined as the opposite of the vector sum of thetransverse energies in each calorimeter cell, corrected for theenergy carried by identified muons and energy added or sub-tracted due to the jet energy scale calibration described be-low) of p / T >
20 GeV (
25 GeV ) must be present in the e + jets( m + jets) channel. These kinematic selections are summarizedin Table 1.To reduce the contribution of multijet production (MJ) inthe e + jets channel, D f ( e , p / T ) > . − p / T × .
045 GeV − is required for the azimuthal difference D f ( e , p / T ) = | f e − f p / T | between the electron and the direction of p / T . Like-wise, D f ( m , p / T ) > . − p / T × .
035 GeV − is required inthe m + jets channel. Jets from b quarks are identified by aneural-network-based b -tagging algorithm [30], which com-bines variables that characterize properties of secondary ver-tices and tracks within the jet that have large impact parame-ters relative to the PV. Typically, its efficiency for b -quark jetsis about 65%, while the probability for misidentifying u , d , s -quark and gluon jets as b jets is about 3%. To increase t ¯ t purity, and to reduce the number of combinatoric possibilitiesfor assigning jets to t ¯ t decay products, we require at least one b -tagged jet to be present in the events used to measure D m .After all acceptance requirements, a data sample of 312(303) events is selected in the e + jets ( m + jets) channel. As TABLE 1: A summary of kinematic event selections applied.Exactly 1 charged lepton p T >
20 GeV | h | < . e ) p T >
20 GeV | h | < . m )Exactly 4 jets p T >
20 GeV | h | < . p T p T >
40 GeV | h | < . p / T >
20 GeV ( e + jets) p / T >
25 GeV ( m + jets) discussed above, each of those samples is split according tolepton charge. In the e + jets channel, 174 (138) events havea positive (negative) lepton in the final state. Likewise, the m + jets sample is split to subsets of 145 and 158 events. IV. MONTE CARLO SIMULATION
Large samples of simulated MC events are used to de-termine the resolution of the detector and to calibrate the D m measurement as well as the statistical sensitivity of themethod. After simulation of the hard scattering part of the in-teraction and parton shower corrections, MC events are passedthrough a detailed detector simulation based on GEANT [31],overlaid with data collected from a random subsample ofbeam crossings to model the effects of noise and multiple in-teractions, and reconstructed using the same algorithms thatare used for data. Although the fraction of signal events, f , isfitted in the analysis, we also cross check that the entire datasample is described adequately by the simulations. A. Monte Carlo samples for signal
Simulated t ¯ t events with different m t and m ¯ t are required tocalibrate the D m measurement. We use the PYTHIA genera-tor [32], version 6.413, to model the t ¯ t signal. This generatormodels the Breit-Wigner shape of the invariant mass distribu-tion of t and ¯ t quarks, whose correct description is importantfor the D m measurement.In the standard PYTHIA , it is not possible to generate t ¯ t events with different masses m t and m ¯ t . Therefore, we modifythe PYTHIA program to provide signal events with m t = m ¯ t .In applying these modifications, we adjust the description ofall quantities that depend on the two masses, for example, therespective decay widths G t and G ¯ t . Technical details of thisimplementation can be found in Appendix I.We generate t ¯ t events using the CTEQ6L1 parton distribu-tion function set (PDF) [33] at the momentum transfer scale Q = ( p scat T ) + (cid:8) P + P + m t + m t (cid:9) , where p scat T is thetransverse momentum for the hard scattering process, and P i is the four-momentum of the incoming parton i . For m t = m ¯ t ,the expression used for Q is identical to that in the standard PYTHIA . All other steps in the event simulation process asidefrom the generation of the hard-scattering process, e.g., themodeling of the detector response, are unchanged from thestandard
PYTHIA . We check our modified
PYTHIA version against the orig-inal by comparing large samples of simulated t ¯ t events for ( m t , m ¯ t ) = (
170 GeV ,
170 GeV ) , at both the parton and re-construction levels, and find full consistency.The t ¯ t samples are generated at fourteen combinations oftop and antitop quark masses ( m t , m ¯ t ) , which form a gridspaced at 5 GeV intervals between (165 GeV, 165 GeV) and(180 GeV, 180 GeV), excluding the two extreme points at(165 GeV, 180 GeV) and (180 GeV, 165 GeV). The fourpoints with m t = m ¯ t are generated with the standard PYTHIA ,whereas all others use our modified version of the generator.
B. Monte Carlo and other simulations of background
The dominant background to t ¯ t decays into ℓ + jets finalstates is from the electroweak production of a W boson inassociation with jets from gluon radiation. We simulate thehard scattering part of this process using the ALPGEN
MC pro-gram [34], which is capable of simulating up to five additionalparticles in the final state at leading order (LO) in a s . ALPGEN is coupled to
PYTHIA , which is used to model the hadroniza-tion of the partons and the evolution of the shower. TheMLM matching scheme is applied to avoid double-countingof partonic event configurations [35]. The W + jets contribu-tion is divided into two categories according to parton flavor: ( i ) W + b ¯ b + jets and W + c ¯ c + jets and (ii) all other contribu-tions, where “jets” generically denotes jets from u , d , s -quarksand gluons. The second category also includes the W + c + jetsfinal states. While the individual processes are generated with ALPGEN , the relative contributions of the two categories aredetermined using next-to-LO (NLO) calculations, with next-to-leading logarithmic (NLL) corrections based on the
MCFM
MC generator [36]. These NLO corrections increase the LOcross section of category ( i ) by a factor of k = . ± . k = ( ii ) . The resulting combined W + jets background contribution is then determined from a fitto data and predictions for other signal and background con-tributions, as described in Sec. V. Thus, the NLO k -factorsonly change the relative balance between ( i ) and ( ii ) .Additional background contributions arise from WW , W Z , ZZ , single top quark electroweak production, Z → tt , and Z → ee ( Z → mm ) production in the e + jets ( m + jets) chan-nel. The predictions for these backgrounds are taken fromMC simulations, and, with the exception of single top quarkelectroweak production, their production cross sections arenormalized to NLO + NLL calculations with
MCFM . Dibosonprocesses are simulated with
PYTHIA . The hard-scatteringpart of single top quark production is simulated with C OM - P HEP [37], while
ALPGEN is used for Z + jets boson produc-tion. For both backgrounds, PYTHIA is employed to modelhadronization and shower evolution. The CTEQ6L1 PDFsand the D0 Tune A underlying event model [38] are used inthe generation of all MC samples.Events from MJ production can pass our selection crite-ria, which typically happens when a jets mimics an electron,or a muon that arises from a semileptonic decay of a b or c quark appears to be isolated. The kinematic distributionsof the MJ background are modeled using events in data thatfail only the electron identification (muon isolation) criteria,but pass loosened versions of these criteria defined in [40].The absolute contribution of this background to each of thechannels is estimated using the method described in Ref. [40].This method uses the absolute numbers of events with promptleptons N t ¯ t + W loose and events from MJ production N MJloose in thesample with loosened lepton identification criteria, and relatesthem to the absolute contributions to the sample with standardlepton identification criteria via N = e t ¯ t + W N t ¯ t + W loose + e MJ N MJloose .Here, e t ¯ t + W and e MJ represent the efficiency of events whichpass the loosened lepton identification criteria to also pass thestandard identification criteria, and are measured in controlregions dominated by prompt leptons and MJ events, respec-tively. C. Event yields
We split the selected ℓ + jets events into subsamples accord-ing to lepton flavor ( e or m ), jet multiplicity, and the number of b -tagged jets in the event to verify an adequate description ofthe data with our signal and background model. In general, weobserve good agreement between data and simulations, andsystematic uncertainties on the final result explicitly accountfor moderate agreement observed in some kinematic distribu-tions (cf. Sec. VII).The numbers of events surviving the final stage of selectionwith at least one b -tag are summarized in Table 2. Here, forease of comparison, the contributions from t ¯ t events are scaledto 7 . + . − . pb, the NLO cross section including NNLO ap-proximations [41]. The total W + jets cross section is adjustedto bring the absolute yield from our signal and backgroundmodel into agreement with the number of events selected indata before applying b -jet identification criteria. The distri-butions in the transverse mass of the W boson, M WT [42], andin p / T are shown in Fig. 1 for data with at least one b -tag, to-gether with the predictions from our signal and backgroundmodels. V. GENERAL DESCRIPTION OF THE METHOD
In this section, we describe the measurement of D m usingthe ME method. The procedure is similar to the one usedin Ref. [13, 43] to measure the average top quark mass m top ,but instead of simultaneously determining m top and the jet en-ergy scale (JES), here we measure directly the masses of thetop and antitop quarks, m t and m ¯ t , which provides D m and m top . We review the ME approach in Sec. V A, the calcula-tion of signal and background event probabilities in Secs. V Band V C, respectively, as well as the parametrization of thedetector response and the use of b -tagging information inSec. V D. TABLE 2: Numbers of events selected in data, compared to yieldpredictions for individual processes using simulations, in the e + jetsand m + jets channels with exactly 4 jets and at least one b -tagged jet,split according to b -tag multiplicity. Uncertainties are purely statis-tical. See text for details. 1 b -tag > b -tags e + jets t ¯ t ± ± W + jets 39.9 ± ± ± ± Z + jets 7.6 ± ± ± ± ± ± m + jets t ¯ t ± ± W + jets 59.9 ± ± ± ± Z + jets 5.3 ± ± ± ± ± ± (GeV) TW M E ve n t s / G e V (a) Datat t W+jets MJ Other -1 DØ 2.6 fbe+jets (GeV) TW M E ve n t s / G e V (GeV) TW M E ve n t s / G e V (b) -1 DØ 2.6 fb+jets m (GeV) TW M E ve n t s / G e V (GeV) T p E ve n t s / G e V (c) -1 DØ 2.6 fbe+jets (GeV) T p E ve n t s / G e V (GeV) T p E ve n t s / G e V (d) -1 DØ 2.6 fb+jets m (GeV) T p E ve n t s / G e V FIG. 1: The transverse mass of the W boson M WT for events with atleast one b -tag is shown for the (a) e + jets and (b) m + jets channels.Similarly, p / T is shown for the (c) e + jets and (d) m + jets channels.The statistical uncertainties on the prediction from the t ¯ t signal andbackground models are indicated by the hatched area. A. Probability densities for events
To optimize the use of kinematic and topological informa-tion, each event is assigned a probability P evt to observe itas a function of the assumed top and antitop quark masses: P evt = P evt ( m t , m ¯ t ) . The individual probabilities for all eventsin a given sample are combined to form a likelihood, fromwhich the D m and m top parameters are extracted. Simplify-ing assumptions are made in the expression of the likelihoodabout, e.g., detector response or the sample composition, aremade to render the problem numerically solvable. It is there-fore necessary to calibrate the method using fully simulatedMC events, as detailed in Sec. VI B. Systematic uncertaintiesare estimated to account for possible effects of these assump-tions on the extracted value of D m .Assuming that the signal and background physics processesdo not interfere, the contribution to the overall probabilityfrom a single event can be formulated as P evt ( x ; m t , m ¯ t , f ) = A ( x ) { f · P sig ( x ; m t , m ¯ t )+ ( − f ) · P bkg ( x ) } , (1)where x denotes the set of measured kinematic variables forthe event observed in the detector, f is the fraction of sig-nal events in the sample, A ( x ) reflects the detector acceptanceand efficiencies for a given x , and P sig and P bkg are the prob-abilities for the event to arise from t ¯ t or W + jets production,respectively. The production of W bosons in association withjets is the dominant background, and we neglect all other con-tributions to P bkg . Kinematically similar contributions fromother background processes like MJ production are accountedfor in the analysis implicitly (cf. Sec. VII).Both signal and background probabilities depend on theJES, which is defined as the ratio of the calibrated energy of ajet over its uncalibrated energy. The standard calibration of jetenergies accounts for the energy response of the calorimeters,the energy that crosses the cone boundary due to the transverseshower size, and the additional energy from pileup of eventsand from multiple p ¯ p interactions in a single beam crossing.Although the D m observable is not expected to show a strongdependence on JES by construction, we apply an additionalabsolute calibration to the JES using a matrix element whichis a function of m top and JES from Refs. [13, 43]. The poten-tial systematic bias on D m from the uncertainty on the absolutevalue of the JES is estimated in Sec. VII.To extract the masses m t and m ¯ t from a set of n selectedevents, with sets of measured kinematic quantities x , ..., x n , alikelihood function is defined from the individual event prob-abilities according to Eq. (1): L ( x , ..., x n ; m t , m ¯ t , f ) = n (cid:213) i = P evt ( x i ; m t , m ¯ t , f ) . (2)For every assumed ( m t , m ¯ t ) pair, we first determine the valueof f ≡ f best that maximizes this likelihood. B. Calculation of signal probability P sig The probability density for the signal to yield a given set ofpartonic final state four-momenta y in p ¯ p collisions is propor-tional to the differential cross section d s for t ¯ t production:d s ( p ¯ p → t ¯ t → y ; m t , m ¯ t ) = Z q , q (cid:229) quarkflavors d q d q f ( q ) f ( q ) × ( p ) | M ( q ¯ q → t ¯ t → y ) | q q s d F , (3)where M denotes the matrix element for the q ¯ q → t ¯ t → b ( l n ) ¯ b ( q ¯ q ′ ) process, s is the square of the center-of-mass en-ergy, q i is the momentum fraction of the colliding parton i (as-sumed to be massless), and d F is an infinitesimal element ofsix-body phase space. The f ( q i ) denote the probability densi-ties for finding a parton of given flavor and momentum frac-tion q i in the proton or antiproton, and the sum runs over allpossible flavor configurations of the colliding quark and an-tiquark. In our definition of M , and therefore the t ¯ t signalprobability, only quark-antiquark annihilation at LO is takeninto account; in this sense, Eq. (3) does not represent the fulldifferential cross section for t ¯ t production in p ¯ p collisions.Effects from gluon-gluon and quark-gluon induced t ¯ t produc-tion are accounted for in the calibration procedure describedin Sec. VI B. We further test for an effect on D m from higher-order corrections in Sec. VII C.The differential cross section for observing a t ¯ t event witha set of kinematic quantities x measured in the detector can bewritten asd s ( p ¯ p → t ¯ t → x ; m t , m ¯ t , k JES )= A ( x ) Z y d y d s ( p ¯ p → t ¯ t → y ; m t , m ¯ t ) W ( x , y ; k JES ) , (4)where finite detector resolution and offline selections are takenexplicitly into account through the convolution over a transferfunction W ( x , y ; k JES ) that defines the probability for a par-tonic final state y to appear as x in the detector given an abso-lute JES correction k JES .With the above defintions, the differential probability to ob-serve a t ¯ t event with a set of kinematic quantities x measuredin the detector is given by P sig ( x ; m t , m ¯ t , k JES ) = d s ( p ¯ p → t ¯ t → x ; m t , m ¯ t , k JES ) s obs ( p ¯ p → t ¯ t ; m t , m ¯ t , k JES ) , (5)where s obs is the cross section for observing t ¯ t events in thedetector for the specific ME M defined in Eq. (3): s obs ( p ¯ p → t ¯ t ; m t , m ¯ t , k JES )= Z x , y d x d y d s ( p ¯ p → t ¯ t → y ; m t , m ¯ t ) W ( x , y ; k JES ) A ( x )= Z y d y d s ( p ¯ p → t ¯ t → y ; m t , m ¯ t ) Z x d x W ( x , y ; k JES ) A ( x ) . The normalization factor s obs is calculated using MC integra-tion techniques: s obs ( p ¯ p → t ¯ t ; m t , m ¯ t , k JES ) ≃ s tot ( m t , m ¯ t ) ×h A | m t , m ¯ t i , (6)where s tot ( m t , m ¯ t ) = Z y d y d s ( p ¯ p → t ¯ t → y ; m t , m ¯ t ) , (7)and h A | m t , m ¯ t i ≡ N gen (cid:229) acc w . (8)To calculate the h A | m t , m ¯ t i term, events are generated ac-cording to d s ( p ¯ p → t ¯ t ; m t , m ¯ t ) using PYTHIA and passedthrough the full simulation of the detector. Here, N gen is thetotal number of generated events, w are the MC event weightsthat account for trigger and identification efficiencies, and thesum runs over all accepted events.The formulae used to calculate the total cross section s tot and the matrix element M are described below in Secs. V B 1and V B 2. In all other respects, the calculation of the sig-nal probability proceeds identically to that in Refs. [13, 43],with the following exceptions: ( i ) CTEQ6L1 PDFs are usedthroughout, and ( ii ) the event probabilities are calculated on agrid in m t and m ¯ t spaced at 1 GeV intervals along each axis.As described in Sec. VI A, a transformation of variables to D m and m top is performed when defining the likelihood.
1. Calculation of the total cross section s tot Without the assumption of equal top and antitop quarkmasses, the total LO cross section for the q ¯ q → t ¯ t process inthe center of mass frame is given by s = pa s s | ~ p | (cid:2) E t E ¯ t + | ~ p | + m t m ¯ t (cid:3) , (9)where E t ( E ¯ t ) are the energies of the top and antitop quark,and ~ p is the three-momentum of the top quark. This reducesto the familiar form for m t = m ¯ t : s = pa s s b (cid:18) − b (cid:19) , where b = | ~ p t | / E t = | ~ p ¯ t | / E ¯ t represents the velocity of the t (or ¯ t ) quark in the q ¯ q rest frame.Integrating Eq. (9) over all incoming q ¯ q momenta and usingthe appropriate PDF yields s tot ( p ¯ p → t ¯ t ; m t , m ¯ t ) , as definedfor any values of m t and m ¯ t in Eq. (7). Figure 2 displays thedependence of s tot on D m for a given m top . The correspond-ing average acceptance term h A | m t , m ¯ t i , as defined in the sameequation, is shown in Fig. (3) for the e + jets and m + jets chan-nels.
2. Calculation of the matrix element M The LO matrix element for the q ¯ q → t ¯ t process we use inour analysis is | M | = g s F ¯ F · s × (cid:8) ( E t − | ~ p t | c qt ) + ( E ¯ t + | ~ p ¯ t | c qt ) + m t m ¯ t (cid:9) . (10)The form factors F ¯ F are identical to those given in Eqs. (24)and (25) of Ref. [13]. For the special case of m t = m ¯ t , theexpression in Eq. (10) reduces to | M | = g s F ¯ F · (cid:0) − b s qt (cid:1) , m (GeV) D -40 -20 0 20 40 ( pb ) t o t s
152 GeV188 GeV DØ FIG. 2: The total p ¯ p → t ¯ t production cross section s tot defined inEq. (7) as a function of D m and m top . Each line shows s tot as afunction of D m for a given value of m top displayed above the curve.The range from 152 GeV to 188 GeV is shown in 6 GeV increments,the broken line corresponds to 170 GeV. m (GeV) D -40 -20 0 20 40 - · æ t op m , m D A | Æ (a) DØe+jets m (GeV) D -40 -20 0 20 40 - · æ t op m , m D A | Æ (b) DØ+jets m FIG. 3: The dependence of the overall average acceptance h A | m t , m ¯ t i on D m and m top , as defined in Eq. (8), for the (a) e + jets and (b) m + jets signal MC samples. Each line shows h A | m t , m ¯ t i as a function of D m for a given value of m top displayed above the curve. The rangefrom 152 GeV to 188 GeV is shown in 6 GeV increments, the brokenlines correspond to 170 GeV. which is identical to Refs. [13, 44], where s qt is the sine ofthe angle between the incoming parton and the outgoing topquark in the q ¯ q rest frame. C. Calculation of the background probability P bkg The expression for the background probability P bkg is sim-ilar to that for P sig in Eq. (5), except that the ME M W + jets isfor W + jets production, and all jets are assumed to be lightquark or gluon jets. Clearly, M W + jets does not depend on m t or m ¯ t , and P bkg is therefore independent of either. We use aLO parameterization of M from the VECBOS [45] program.More details on the calculation of the background probabilitycan be found in Ref. [13].
D. Description of detector response
The transfer function W ( x , y , k JES ) , which relates the set ofvariables x characterizing the reconstructed final-state objectsto their partonic quantities y , is crucial for the calculationof the signal probability according to Eq. (5), and the cor-responding expression for P bkg . A full simulation of the de-tector would not be feasible for calculating event probabilitiesbecause of the overwhelming requirements for computing re-sources. Therefore, we parametrize the detector response andresolution through a transfer function.In constructing the transfer function, we assume that thefunctions for individual final-state particles are not correlated.We therefore factorize the transfer function into contributionsfrom each measured final-state object used in calculating P sig ,that is the isolated lepton and four jets. The poorly measuredimbalance in transverse momentum p / T , and consequently thetransverse momentum of the neutrino, is not used in definingevent probabilities. We assume that the directions of e , m ,and jets in ( h , f ) space are well-measured, and therefore de-fine the transfer functions for these quantities as d functions: d ( h , f ) ≡ d ( h y − h x ) d ( f y − f x ) . This reduces the number ofintegrations over the 6-particle phase space d F by 5 × = | ~ p | displaysignificant variations in resolution for leptons and jets and aretherefore parameterized by their corresponding resolutions.There is an inherent ambiguity in assigning jets recon-structed in the detector to specific partons from t ¯ t decay. Con-sequently, all 24 permutations of jet-quark assignments areconsidered in the analysis. The inclusion of b -tagging infor-mation provides improved identification of the correct per-mutation. This additional information enters the probabilitycalculation through a weight w i on a given permutation i ofjet-parton assignments. The w i are larger for those permu-tations that assign the b -tagged jets to b quarks and untaggedjets to light quarks. The sum of weights is normalized to unity: (cid:229) i = w i = W ( x , y ; k JES ) = W ℓ ( E x , E y ) d ℓ ( h , f ) × (cid:229) i = w i ( (cid:213) j = d i j ( h , f ) W jet ( E ix , E jy ; k JES ) ) , (11)where ℓ denotes the lepton flavor, with a term W e describingthe energy resolution for electrons and W m the resolution in thetransverse momentum for muons. Similarly, W jet describes theenergy resolution for jets. The sum in i is taken over the 24possible permutations of assigning jets to quarks in a givenevent. More details on W ℓ and W jet can be found in Ref. [43].The weight w i for a given permutation i is defined bya product of individual weights w ji for each jet j . For b -tagged jets, w ji is equal to the per-jet tagging efficiency e tag ( a k ; E jT , h j ) , where a k labels the three possible parton-flavor assignments of the jet: ( i ) b quark, ( ii ) c quark, and ( iii ) light ( u , d , s ) quark or gluon. For untagged jets, the w ji factors are equal to 1 − e tag ( a k ; E jT , h j ) .Because the contributions to W + jets are parameterized by M W + jets without regard to heavy-flavor content, the weights w i for each permutation in the background probability are allset equal. VI. MEASUREMENT OF THE TOP-ANTITOP QUARKMASS DIFFERENCEA. Fit to the top-antitop quark mass difference
For the set of selected events, the likelihood L ( m t , m ¯ t ) iscalculated from Eq. (2) (Sec. V A). The signal fraction f best that maximizes the likelihood is determined at each ( m t , m ¯ t ) point for grid spacings of 1 GeV. Subsequently, a trans-formation is made to the more appropriate set of variables ( D m , m top ) : L ( x , ..., x n ; D m , m top )= L [ x , ..., x n ; D m , m top , f best ( D m , m top )] . (12)To obtain the best estimate of D m in data, the two-dimensional likelihood in Eq. (12) is projected onto the D m axis, and the mean value h D m i , that maximizes it, as well asthe uncertainty d D m on h D m i are calculated. This procedureaccounts for any correlations between D m and m top . As a con-sistency check, we simultaneously extract the average mass m top by exchanging D m ↔ m top above. B. Calibration of the method
We calibrate the ME method by performing 1000 MCpseudo-experiments at each input point ( m t , m ¯ t ) . These areused to correlate the fitted parameters with their true inputvalues and to assure the correctness of the estimated un-certainties. Each pseudo-experiment is formed by drawing N sig signal and N bkg background events from a large pool offully simulated t ¯ t and W + jets MC events. We assume that W + jets events also represent the kinematic distributions ex-pected from MJ production and other background processeswith smaller contributions, and evaluate a systematic uncer-tainty from this assumption. Events are drawn randomly andcan be used more than once, and an “oversampling” correc-tion [46] is applied. The size of each pseudo-experiment, N = N sig + N bkg , is fixed by the total number of events ob-served in the data, i.e., N =
312 (303) events for the e + jets( m + jets) channel. The fraction of signal events is allowed tofluctuate relative to the signal fraction f determined from data(Sec. VI B 1), assuming binomial statistics. The same W + jetsbackground sample is used to form pseudo-experiments foreach ( m t , m ¯ t ) mass point.0
1. Determining the signal fraction in data
The signal fraction f is determined independently for the e + jets and m + jets channels directly from the selected datasample. The likelihood depends explicitly on three parame-ters: D m , m top , and f , as defined in Eq. (12). The uncalibratedsignal fraction f uncal is calculated in data as an average of f best determined at each point in the ( m t , m ¯ t ) grid and weighted bythe value of the likelihood at that point. To calibrate f uncal ,we form 1000 pseudo-experiments for each input signal frac-tion f true in the interval [ , ] in increments of 0.1, and extract f uncal for each one, following the same procedure as in data.Signal MC events with m t = m ¯ t = . f extr and f true , where f extr is the average of f uncal values extractedin 1000 pseudo-experiments for a given f true . We use the re-sults of a linear fit of f extr to f true to calibrate the fraction ofsignal events in data. The results are summarized in Table 3.Possible systematic biases on the measured value of D m fromthe uncertainty on f are discussed in Sec. VII. TABLE 3: Signal fractions determined from data for the assumptionthat m t = m ¯ t = . e + jets 0 . ± . m + jets 0 . ± .
2. Calibration of D m The dependence of the extracted D m on the generated D m is determined from the extracted values D m extr ( m t , m ¯ t ) , againobtained from averaging h D m i over 1000 pseudo-experimentsfor each ( m t , m ¯ t ) combination. The resulting distribution andfit to the 14 ( m t , m ¯ t ) points is shown in Fig. 4 (a) and (b) forthe e + jets and m + jets channels, respectively. This providesthe calibration of the extracted D m value: D m extr = x D m + x D m · D m gen . (13)The fit parameters x D mi are summarized in Table 4.For an unbiased estimate of D m and of the uncertainty d D m on the measured h D m i value, the distribution of the pullsshould be described by a Gaussian function with a standarddeviation (SD) of unity, and centered at zero. A SD of thepulls larger than unity would indicate an underestimation of d D m , which could be caused by the simplifying assumptionsof the ME technique discussed in Sec. V. For a given pseudo-experiment at ( m t , m ¯ t ) , we define the pull in D m as p D m = h D m i − D m extr ( m t , m ¯ t ) d D m . (14)The pull widths w p D m , defined by the SD in Gaussian fits to thepull distributions, are also shown for all 14 ( m t , m ¯ t ) points inFig. 4 (c) and (d) for the e + jets and m + jets channels, respec-tively. The average pull widths h w p D m i are taken from fits of TABLE 4: Fit parameters for the calibration of D m and m top , definedby Eq. (13), and average pull-widths h w p i for pulls in D m and m top ,defined in Eq. (14).Channel x (GeV) x h w p i D m e + jets 0 . ± ± ± m + jets − . ± ± ± m top e + jets 0 . ± ± ± m + jets 0 . ± ± ± the 14 pull widths in each channel to constant offsets and aresummarized in Table 4. We calibrate the estimated uncertaintyaccording to d cal D m ≡ h w p D m i × d D m .
3. Calibration of m top
Results from an analogous calibration of m top are displayedin Fig. 5 (a) and (b) for the e + jets and m + jets channel, respec-tively. The distributions in pull widths are given in parts (c)and (d) of the same figure. The corresponding fit parametersand average pull widths are also summarized in Table 4. (GeV) gen m D -10 -5 0 5 10 ( G e V ) ex t r m D -10-50510 (a) DØe+jets (GeV) gen m D -10 -5 0 5 10 ( G e V ) ex t r m D -10-50510 (b) DØ+jets m (GeV) gen m D -10 -5 0 5 10 æ m DpwÆ (c)
DØe+jets (GeV) gen m D -10 -5 0 5 10 æ m DpwÆ (d)
DØ+jets m FIG. 4: The calibration of the extracted D m value as a func-tion of generated D m is shown for the (a) e + jets and (b) m + jets channels. The points are fitted to a linear function. Eachpoint represents a set of 1000 pseudo-experiments for one ofthe fourteen ( m t , m ¯ t ) combinations. The circle, square, trian-gle, rhombus, cross, star, and “ × ” symbols stand for m top = , . , , . , , . , and 180 GeV, respectively. Sim-ilarly, the pull widths, as defined in the text, are given for the(c) e + jets and (d) m + jets channels. -172.5 (GeV) gentop m -5 0 5 10 - . ( G e V ) ex t r t op m -10-50510 (a) DØe+jets -172.5 (GeV) gentop m -5 0 5 10 - . ( G e V ) ex t r t op m -10-50510 (b) DØ+jets m -172.5 (GeV) gentop m -5 0 5 10 æpwÆ (c) DØe+jets -172.5 (GeV) gentop m -5 0 5 10 æpwÆ (d) DØ+jets m FIG. 5: The calibration of the extracted m top value as a function ofgenerated m top is shown for the (a) e + jets and (b) m + jets channels.The dependence is fitted to a linear function. Each point representsa set of 1000 pseudo-experiments for one of the fourteen ( m t , m ¯ t ) combinations. Similarly, the pull widths, as defined in the text, aregiven for the (c) e + jets and (d) m + jets channels. C. Results
With the calibration of D m and m top , we proceed to extract D m and, as a cross check, m top , from the data, as describedin Sec. V. As indicated previously, the probabilities for theselected events are calculated using the ME method, and thelikelihoods in D m and m top are constructed independently forthe e + jets and m + jets channels.The calibration of data involves a linear transformation ofthe uncalibrated axes of the likelihoods in D m and m top to theircorrected values, which we denote as D m cal and m caltop , accord-ing to: D m cal = D m − x D m x D m , (15) m caltop = m top − . − x m top x m top + . , (16)where the x i are summarized in Table 4. The resulting like-lihoods for data, as a function of D m and m top are shown inFigs. 6 and 7, respectively.After calibration, h D m i and h m top i with their respective un-certainties d D m and d m top , are extracted from the likelihoods asdescribed in Sec. VI A. The uncertainties are scaled up by theaverage pull widths given in Table 4. The resulting distribu-tions in expected uncertainties d cal D m are also shown in Fig. 6.The final measured results for D m and m top are summarized (GeV) cal m D -20-15-10 -5 0 5 10 15 20 m ax ) / L ca l m D L ( (a) -1 DØ 2.6 fbe+jets – = 0.05 cal m D (GeV) m D cal d o f e n se m b l es (b) -1 DØ 2.6 fbe+jets = 3.09 GeV m D cal d Data: (GeV) cal m D -20-15-10 -5 0 5 10 15 20 m ax ) / L ca l m D L ( (c) -1 DØ 2.6 fb+jets m – = -0.49 cal m D (GeV) m D cal d o f e n se m b l es (d) -1 DØ 2.6 fb+jets m = 2.91 GeV m D cal d Data:
FIG. 6: The normalized likelihood in D m cal after calibration viaEq. (15), together with a Gaussian fit, is shown for the (a) e + jetsand (c) m + jets events in data. The extracted D m cal values are indi-cated by arrows. The distributions in expected uncertainties d cal D m af-ter calibration via Eq. (15) and correction for the pull width, obtainedfrom ensemble studies using simulated MC events, is displayed forthe (b) e + jets and (d) m + jets channel. The observed d cal D m values areindicated by arrows. (GeV) topcal m
165 170 175 180 185 m ax ) / L t op ca l L ( m (a) -1 DØ 2.6 fbe+jets – = 173.94 topcal m (GeV) topcal m
165 170 175 180 185 m ax ) / L t op ca l L ( m (b) -1 DØ 2.6 fb+jets m – = 175.32 topcal m FIG. 7: The normalized likelihood in m caltop after calibration viaEq. (16) together with a Gaussian fit for the (a) e + jets and (b) m + jetschannel. Arrows indicate the extracted m caltop values. below according to channel, as well as combined: e + jets, 2.6 fb − : D m = . ± . m top = . ± . m + jets, 2.6 fb − : D m = − . ± . m top = . ± . ℓ + jets, 2.6 fb − : D m = − . ± . m top = . ± . . (17)The uncertainties given thus far are purely statistical. Thecombined ℓ + jets results are obtained by using the canonicalweighted average formulae assuming Gaussian uncertainties.We cross check the above values for m top with those obtainedfrom the absolute top quark mass analysis [43, 47] and findthem to be consistent.2 (GeV) t m
170 175 180 ( G e V ) t m (a) -1 DØ 2.6 fbe+jets (GeV) t m
170 175 180 ( G e V ) t m (b) -1 DØ 2.6 fb+jets m FIG. 8: Two-dimensional likelihood densities in m t and m ¯ t for the(a) e + jets and (b) m + jets channels. The bin contents are propor-tional to the area of the boxes. The solid, dashed, and dash-dottedlines represent the 1, 2, and 3 SD contours of two-dimensional Gaus-sian fits (corresponding to approximately 40%, 90% and 99% con-fidence level, respectively) to the distributions defined in Eq. (18),respectively. As an additional cross check, we independently extract themasses of the top and antitop quarks from the same data sam-ple. The two-dimensional likelihood densities, as functions of m t and m ¯ t , are displayed in Fig. 8. Also shown are contoursof equal probability for two-dimensional Gaussian fits to thelikelihood densities, where the Gaussian functions are of theform P ( x , y ) = A ps x s y p − r × exp n −
12 11 − r h ( x − ¯ x ) s x + ( y − y ) s y + r ( x − x )( y − y ) s x s y io , (18)with x ≡ m t and y ≡ m ¯ t . The fits to data yield e + jets, 2.6 fb − : m t = . ± . m ¯ t = . ± . r = − . m + jets, 2.6 fb − : m t = . ± . m ¯ t = . ± . r = − . . (19)The above uncertainties are again purely statistical; however,in contrast to Eq. (17), they are not corrected for pull widths in m t and m ¯ t . The correlation coefficients r are consistent withthe absence of correlations.In Sec. VIII, we will combine the results for D m summa-rized in Eq. (17) with the previous measurement using 1 fb − of integrated luminosity [12]. VII. SYSTEMATIC UNCERTAINTIES
For the measurement of m top we typically consider threemain types of sources of systematic uncertainties [43]:( i ) modeling of t ¯ t production and background processes, TABLE 5: Summary of systematic uncertainties on D m .Source Uncertaintyon D m (GeV)Modeling of detector:Jet energy scale 0 . . b and light quarks 0 . b and ¯ b quarks 0 . c and ¯ c quarks 0 . . . . . . . ( ii ) modeling of detector response, and ( iii ) limitations inher-ent in the measurement method. However, in the context of a D m measurement, many systematic uncertainties are reducedbecause of correlations between the measured properties oftop and antitop quarks, such as, the uncertainty from the ab-solute JES calibration. Given the small value of the upperlimit of O ( ) already observed for | D m | / m top , several othersources of systematic uncertainties relevant in the measure-ment of m top , such as modeling of hadronization, are not ex-pected to contribute to D m because they would affect t and ¯ t in a similar manner. Following [48], we check for any effectson D m that might arise from sources in the latter category inSec. VII C, and find them consistent with having no signif-icant impact. We therefore do not consider them further inthe context of this measurement. On the other hand, we esti-mate systematic uncertainties from additional sources whichare not considered in the m top measurement, for example fromthe asymmetry in calorimeter response to b and ¯ b quark jets.Typically, to propagate a systematic uncertainty on someparameter to the final result, that parameter is changed in thesimulation used to calibrate the ME method, and the D m re-sult is re-derived. If the change in a parameter can be takeninto account through a reweighting of events, a new calibra-tion is determined using those weights and applied directlyto data. When this procedure is not possible, a re-evaluationof event probabilities is performed for one sample of t ¯ t MCevents corresponding to a particular choice of m t and m ¯ t clos-est to the most likely value according to our measurement, i.e. m t = m ¯ t =
175 GeV, or, when no such sample of MC eventswith a changed parameter is available, m t = m ¯ t = . m t and m ¯ t .The systematic uncertainties are described below and sum-marized in Table 5. The total systematic uncertainty is ob-tained by adding all contributions in quadrature.3 A. Modeling of detector (i)
Jet energy scale:
As indicated in Sec. VI C, we use theabsolute JES calibration of k JES = . ± .
008 deter-mined from data. To propagate this uncertainty to D m ,we scale the jet energies in the selected data sample by k JES ± Remaining jet energy scale:
The systematic uncer-tainty on the absolute JES discussed above does not ac-count for possible effects from uncertainties on jet en-ergy corrections that depend on E jet and h jet . To esti-mate this effect on D m , we rescale the energies of jetsin the default t ¯ t MC sample by a differential scale fac-tor S ( E jet , h jet ) that is a function of the JES uncertain-ties, but conserves the magnitude of the absolute JEScorrection.(iii) Response to b and light quarks:
The difference inthe hadronic/electromagnetic response of the calorime-ter leads to differences in the response to b and lightquarks between data and simulation. This uncertaintyis evaluated by re-scaling the energies of jets matchedto b quarks in the default t ¯ t MC sample.(iv)
Response to b and ¯ b quarks: The measurement of D m can be affected by differences in the reconstruction ofthe transverse momenta of particles and antiparticles.A difference could in principle be caused by different p T scales for m + and m − . However, the data consistof an almost equal mix of events with opposite mag-net polarities, thereby minimizing such biases. We donot observe any difference in calorimeter response to e + and e − .A systematic bias to D m can also be caused by dif-ferences in calorimeter response to quarks and anti-quarks. In the case of t ¯ t events, this bias could ariseespecially from a different response to b and ¯ b -quarks.Several mechanisms could contribute to this, most no-tably a different content of K + / K − mesons, which havedifferent interaction cross sections. In our evaluation ofthis systematic uncertainty, we assume that, althoughdifferences in response to b / ¯ b quarks are present indata, they are not modeled in MC events. We measurethe difference of the calorimeter response to b quarksto that of ¯ b quarks, R b , ¯ b ≡ R b − R ¯ b , using a “tag-and-probe” method in data. Namely, we select back-to-backdijet events, and enhance the b ¯ b content by requiring b -tags for both jets. The tag jet is defined by the pres-ence of a muon within the jet cone, whose charge servesas an indication whether the probe jet is more likelyto be a b or a ¯ b -quark jet. By evaluating the | ~ p T | im-balance between tag and probe jets for positively andnegatively charged muon tags, we find an upper bound | R b , ¯ b | < . t ¯ t MC sample by re-scaling the momenta | ~ p | of b (¯ b )-quark jets by 1 ∓ · R b , ¯ b = . . Response to c and ¯ c quarks: A difference in calorime-ter response to c and ¯ c quarks can potentially bias D m ,since c quarks appear in decays of W + bosons from t quark decays, and vice versa for ¯ c and ¯ t . It is exper-mentally difficult to isolate a sufficiently clean sampleof c ¯ c dijet events, since it will suffer from considerablecontributions from b ¯ b dijet events. However, the ma-jor underlying mechanisms that could cause a responseassymetry, like, e.g., the different content of K + / K − mesons, are the same, but of roughly opposite magni-tude between c and b quark jets, which would result inan anticorrelation. Based on the above, we assume thesame upper bound | R c , ¯ c | ≤ R b , ¯ b < . R c , ¯ c and R b , ¯ b as uncorrelated. To propagate the sys-tematic uncertainty from R c , ¯ c to D m , we apply a simi-lar technique to that for the estimation of the systematicuncertainty due to different response to b and ¯ b quarks.(vi) Jet identification efficiency:
D0 uses scale factors toachieve data/MC agreement in jet identification effi-ciencies. To propagate to the D m measurement the ef-fect of uncertainties on these scale factors, we decreasethe jet identification efficiencies in the default t ¯ t sampleaccording to their uncertainties.(vii) Jet energy resolution:
An additional smearing of jetenergies derived by comparison of the p T balance in ( Z → ee ) + D m , we modifythe default t ¯ t MC sample by varying the jet energy res-olution within its uncertainty.(viii)
Determination of lepton charge:
This analysis uses thecharge of the lepton in t ¯ t candidate events to distinguishthe top quark from the antitop quark. Incorrectly recon-structed lepton charges can result in a systematic shiftin the measurement. The charge misidentification rateis found to be less than 1% in studies of Z → ee dataevents. To estimate the contribution of this uncertainty,we assume a charge misidentification rate of 1% forboth e + jets and m + jets final states and evaluate the ef-fects on D m resulting from a change in the mean valuesof the extracted m cal t and m cal¯ t . B. ME method (i)
Signal fraction:
The signal fractions f presented in Ta-ble 3 are changed by their respective uncertainties foreach decay channel, and ensemble studies are repeatedfor all MC samples to re-derive the calibration for D m .The new calibrations are applied to data and the resultscompared with those obtained using the default calibra-tion.4(ii) Background from multijet events:
In the calibration ofthis analysis, the background contribution to pseudo-experiments is formed using only W +jets events, asthey are also assumed to model the small MJ back-ground from QCD processes and smaller contributionsfrom other background processes present in the data.To estimate the systematic uncertainty from this as-sumption, we define a dedicated MJ-enriched sampleof events from data. The calibration is re-derived withthis background sample included in forming pseudo-experiments.(iii) Calibration of the ME method:
The statistical uncer-tainties associated with the offset ( x ) and slope ( x )parameters that define the mass calibration in Sec. VI Bcontribute to the uncertainty on D m . To quantify this,we calculate the uncertainty d D m due to d x and d x foreach channel according to the error propagation formula d D m = ((cid:18) D m − x x · d x (cid:19) + (cid:18) d x x (cid:19) ) − and then combine the resulting uncertainties for the e + jets and m + jets channels in quadrature. C. Additional checks
We check for effects on D m from sources of systematic un-certainties considered in the m top measurement [43] which arenot expected to contribute any bias in the context of the mea-surement of D m . For this, we follow the same approach asoutlined at the beginning of this Section. We find the resultsof our checks to be indeed consistent with no bias on D m .The additional checks are described below and summarizedin Table 6. Note that the numbers quoted merely reflect anupper bound on a possible bias, rather than any true effect.This limitation is statistical in nature and due to the number ofavailable simulated MC events. Furthermore, if the differencebetween the central result and the one obtained for a check issmaller than the statistical uncertainty on this difference, wequote the latter.
1. Modeling of physical processes (i)
Higher-order corrections:
To check the effect ofhigher-order corrections on D m , we perform ensemblestudies using t ¯ t events generated with ( i ) the NLO MCgenerator MC @ NLO [50], and ( ii ) the LO MC genera-tor ALPGEN , with H
ERWIG [51] for hadronization andshower evolution.(ii)
Initial and final-state radiation:
The modeling of extrajets from ISR/FSR is checked by comparing
PYTHIA samples with modified input parameters, such as the ± TABLE 6: Summary of additional checks for a possible bias on D m .None of those show any significant bias on D m . Note that the num-bers shown reflect an upper limit on a possible bias. This limitationis of statistical origin and due to the number of available simulatedMC events.Source Change in D m (GeV)Modeling of physical processes:Higher-order corrections 0 . . . . b -fragmentation 0 . . . . . . b -tagging efficiency 0 . e . m . (iii) Hadronization and underlying event:
To check a possi-ble effect of D m from the underlying event as well as thehadronization models, we compare samples hadronizedusing PYTHIA with those hadronized using H
ERWIG .(iv)
Color reconnection:
The default
PYTHIA tune used atD0 (tune A ), does not include explicit color reconnec-tion. For our check, we quantify the difference between D m values found in ensemble studies for t ¯ t MC sam-ples generated using tunes
Apro and
ACRpro , wherethe latter includes an explicit model of color reconnec-tion [53, 54].(v) b-fragmentation:
Uncertainties in the simulation of b -quark fragmentation can affect the measurement of m top in several phases of the analysis, such as in b -tagging and in the b -quark transfer functions used in theME calculations. Such effects are studied in the contextof D m by reweighting the simulated t ¯ t events used inthe calibration of the method from the default Bowlerscheme [55], which is tuned to LEP (ALEPH, OPAL,and DELPHI) data, to a tune that accounts for differ-ences between SLD and LEP data [56].(vi) Uncertainty on PDF:
The CTEQ6M [33] PDFs pro-vide a set of possible excursions in parameters fromtheir central values. To check the effect on D m fromPDFs, we change the default t ¯ t MC sample (generatedusing CTEQ6L1) by reweighting it to CTEQ6M, repeatthe ensemble studies for each of the parameter varia-tions, and evaluate the uncertainty using the prescribedformula [33]: d D m , PDF = (cid:26) (cid:229) i = [ D m ( S + i ) − D m ( S − i )] (cid:27) , S + i ) and negative ( S − i ) excursions.(vii) Multiple hadron interactions:
When calibrating theME method, we reweight the luminosity profiles of ourMC samples to the instantaneous luminosity profile forthat data-taking period. For our check, we re-derive thecalibration ignoring luminosity-dependent weights.(viii)
Modeling of background:
We check the effect of in-adequate modeling of background processes on our D m measurement by identifying distributions in thebackground-dominated ℓ + W + jets events that are reweighted to bring the iden-tified distributions of predicted signal and backgroundevents into better agreement with data.(ix) Heavy-flavor scale-factor:
As discussed in Sec. IV, aheavy-flavor scale-factor of 1 . ± .
22 is applied to the W + b ¯ b + jets and W + c ¯ c + jets production cross sectionsto increase the heavy-flavor content in the ALPGEN W +jets MC samples. Moreoever, a scale factor of1 . ± .
15 for the W + c + jets production cross sectionis obtained using MCFM . We re-derive the calibrationwith the heavy-flavor scale-factor changed by ±
30% tocheck the magnitude of the effect on D m .
2. Modeling of detector (i)
Trigger selection:
To check the magnitude the ef-fect from differential trigger efficiencies on D m , were-derive a new D m calibration ignoring the triggerweights.(ii) b-tagging efficiency: We check the possibility of a biasin our D m measurement from discrepancies in the b -tagging efficiency between data and MC events by us-ing absolute uncertainties on the b -tagging efficiencies,and account independently for possible discrepanciesthat are differential in h and p T of the jet by reweightingthe b -tagging rate in simulated t ¯ t MC events to that ob-served in data. The total magnitude of a possible effectis determined by combining in quadrature excursions of D m values obtained with the modified calibrations forboth absolute and differential changes.(iii) Momentum scale for electrons:
D0 calibrates the en-ergy of electrons based on studies of the Z → ee massfor data and MC events. We rescale the electron en-ergies in the default signal MC sample according to theuncertainties on the electron energy calibration to checkthe magnitude of the effect in the context of D m .(iv) Momentum scale for muons:
The absolute momen-tum scale for muons is obtained from J / y → mm and Z → mm data. However, both linear and quadratic in-terpolation between these two points can be employedfor the calibration. We check the effect of each extrap-olation on D m by applying the respective corrections tosimulated t ¯ t MC events in the default sample, and finda larger shift in D m for the linear parametrization. VIII. COMBINING THE 2.6 fb − AND 1 fb − ANALYSES
We use the BLUE method [58, 59] to combine our newmeasurement (Eq. 17) with the result of the analysis per-formed on data corresponding to 1 fb − [12]. The BLUEmethod assumes Gaussian uncertainties and accounts for cor-relations among measurements.For reference, we summarize the results obtained for 1 fb − : e + jets , − : D m = . ± . ( stat ) GeV , m + jets , − : D m = . ± . ( stat ) GeV ,ℓ + jets , − : D m = . ± . ( stat ) GeV . The 1 fb − analysis used a data-driven method to estimatesystematic uncertainties from modeling of signal processes.This method did not distinguish between different sourcesof systematic uncertainties such as: ( i ) higher-order correc-tions, ( ii ) initial and final state radiation, ( iii ) hadronizationand the underlying event, and ( iv ) color reconnection. Theabove sources are studied in the context of the m top measure-ment [43], but are not expected to contribute any bias to themeasurement of D m . We cross-check their impact on D m inSec. VII C, and find them consistent with no bias. Based onour findings, we do not consider any systematic uncertaintiesfrom modeling of signal and background processes.Two sources of systematic uncertainties from modeling ofdetector peformance (Table 5) are taken to be uncorrelatedbetween the two measurements: JES and remaining JES. Therest are taken to be fully correlated.In the 1 fb − analysis, a systematic uncertainty of 0.4 GeVfrom the difference in calorimeter response to b and ¯ b quarkswas estimated using MC studies and checks in data. Thissystematic uncertainty has been re-evaluated using an entirelydata-driven approach (item (iv) in Sec. VII A), and we there-fore use this new result for the analysis of the 1 fb − data.Furthermore, we now evaluated a systematic uncertainty fromthe difference in calorimeter response to c and ¯ c quarks, andpropagate our findings to the 1 fb − analysis.All other systematic uncertainties not explicitly mentionedabove are taken as uncorrelated.The combined result for D m corresponding to 3.6 fb − ofdata is D m = . ± . ( stat . ) ± . ( syst . ) GeV . (20)In this combination, BLUE determines a relative weight of72.8% (27.2%) for the 2.6 fb − (1 fb − ) measurement. The c / N DOF of the combination is 0.96. The combined likeli-hood densities for the two analyses are presented in Fig. 9 asfunctions of m t and m ¯ t , separately for the e + jets and m + jetschannels.6 (GeV) t m
170 175 180 ( G e V ) t m (a) -1 DØ 3.6 fbe+jets (GeV) t m
170 175 180 ( G e V ) t m (b) -1 DØ 3.6 fb+jets m FIG. 9: Combined likelihoods of the 2.6 fb − and 1 fb − measure-ments as functions of m t and m ¯ t in data for the (a) e + jets and(b) m + jets channel. The bin contents are proportional to the areaof the boxes. The solid, dashed, and dash-dotted lines represent the1, 2, and 3 SD contours of two-dimensional Gaussian fits defined inEq. (18) (corresponding to approximately 40%, 90% and 99% con-fidence level, respectively) to the distributions, respectively. No pullcorrections have been applied, and therefore the figures are for illus-trative purposes only. IX. CONCLUSION
We have applied the matrix element method to the mea-surement of the mass difference D m between top and an-titop quarks using t ¯ t candidate events in the lepton + jetschannel in data corresponding to an integrated luminosity ofabout 3.6 fb − . We find D m = . ± . ( stat . ) ± . ( syst . ) GeV , which is compatible with no mass difference at the level of ≈
1% of the mass of the top quark.
I. APPENDIX: GENERATION OF t ¯ t EVENTS WITH M t = M ¯ t We briefly describe below the modifications to the stan-dard
PYTHIA [32] code which were necessary to generate t ¯ t events with m t = m ¯ t . A new entry in the KF particle table iscreated for the ¯ t quark. The PYINPR subroutine is modifiedfor use cases in which one of the t ¯ t production subprocesses( ISUB = , , ,
85) is called. The ¯ t quark is assigned asthe second final-state particle whenever a t quark is selectedas the first final-state particle. Furthermore, the ordering of thefirst and second final-state particles are swapped, as needed,in the subroutine PYSCAT . Additional changes are made in thesubroutines
PYMAXI , PYRAND , and
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