Top Quark Mass Measurement in the Lepton + Jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration
TTop Quark Mass Measurement in the Lepton + Jets Channel Using a Matrix ElementMethod and in situ
Jet Energy Calibration
T. Aaltonen, B. ´Alvarez Gonz´alez v , S. Amerio, D. Amidei, A. Anastassov, A. Annovi, J. Antos, G. Apollinari, J.A. Appel, A. Apresyan, T. Arisawa, A. Artikov, J. Asaadi, W. Ashmanskas, B. Auerbach, A. Aurisano, F. Azfar, W. Badgett, A. Barbaro-Galtieri, V.E. Barnes, B.A. Barnett, P. Barria cc , P. Bartos, M. Bauce aa , G. Bauer, F. Bedeschi, D. Beecher, S. Behari, G. Bellettini bb , J. Bellinger, D. Benjamin, A. Beretvas, A. Bhatti, M. Binkley ∗ , D. Bisello aa , I. Bizjak gg , K.R. Bland, B. Blumenfeld, A. Bocci, A. Bodek, D. Bortoletto, J. Boudreau, A. Boveia, B. Brau a , L. Brigliadori z , A. Brisuda, C. Bromberg, E. Brucken, M. Bucciantonio bb , J. Budagov, H.S. Budd, S. Budd, K. Burkett, G. Busetto aa , P. Bussey, A. Buzatu, C. Calancha, S. Camarda, M. Campanelli, M. Campbell, F. Canelli , A. Canepa, B. Carls, D. Carlsmith, R. Carosi, S. Carrillo k , S. Carron, B. Casal, M. Casarsa, A. Castro z , P. Catastini, D. Cauz, V. Cavaliere cc , M. Cavalli-Sforza, A. Cerri f , L. Cerrito q , Y.C. Chen, M. Chertok, G. Chiarelli, G. Chlachidze, F. Chlebana, K. Cho, D. Chokheli, J.P. Chou, W.H. Chung, Y.S. Chung, C.I. Ciobanu, M.A. Ciocci cc , A. Clark, G. Compostella aa , M.E. Convery, J. Conway, M.Corbo, M. Cordelli, C.A. Cox, D.J. Cox, F. Crescioli bb , C. Cuenca Almenar, J. Cuevas v , R. Culbertson, D. Dagenhart, N. d’Ascenzo t , M. Datta, P. de Barbaro, S. De Cecco, G. De Lorenzo, M. Dell’Orso bb , C. Deluca, L. Demortier, J. Deng c , M. Deninno, F. Devoto, M. d’Errico aa , A. Di Canto bb , B. Di Ruzza, J.R. Dittmann, M. D’Onofrio, S. Donati bb , P. Dong, T. Dorigo, K. Ebina, A. Elagin, A. Eppig, R. Erbacher, D. Errede, S. Errede, N. Ershaidat y , R. Eusebi, H.C. Fang, S. Farrington, M. Feindt, J.P. Fernandez, C. Ferrazza dd , R. Field, G. Flanagan r , R. Forrest, M.J. Frank, M. Franklin, J.C. Freeman, I. Furic, M. Gallinaro, J. Galyardt, J.E. Garcia, A.F. Garfinkel, P. Garosi cc , H. Gerberich, E. Gerchtein, S. Giagu ee , V. Giakoumopoulou, P. Giannetti, K. Gibson, C.M. Ginsburg, N. Giokaris, P. Giromini, M. Giunta, G. Giurgiu, V. Glagolev, D. Glenzinski, M. Gold, D. Goldin, N. Goldschmidt, A. Golossanov, G. Gomez, G. Gomez-Ceballos, M. Goncharov, O. Gonz´alez, I. Gorelov, A.T. Goshaw, K. Goulianos, A. Gresele, S. Grinstein, C. Grosso-Pilcher, R.C. Group, J. Guimaraes da Costa, Z. Gunay-Unalan, C. Haber, S.R. Hahn, E. Halkiadakis, A. Hamaguchi, J.Y. Han, F. Happacher, K. Hara, D. Hare, M. Hare, R.F. Harr, K. Hatakeyama, C. Hays, M. Heck, J. Heinrich, M. Herndon, S. Hewamanage, D. Hidas, A. Hocker, W. Hopkins g , D. Horn, S. Hou, R.E. Hughes, M. Hurwitz, U. Husemann, N. Hussain, M. Hussein, J. Huston, G. Introzzi, M. Iori ee , A. Ivanov o , E. James, D. Jang, B. Jayatilaka, E.J. Jeon, M.K. Jha, S. Jindariani, W. Johnson, M. Jones, K.K. Joo, S.Y. Jun, T.R. Junk, T. Kamon, P.E. Karchin, Y. Kato n , W. Ketchum, J. Keung, V. Khotilovich, B. Kilminster, D.H. Kim, H.S. Kim, H.W. Kim, J.E. Kim, M.J. Kim, S.B. Kim, S.H. Kim, Y.K. Kim, N. Kimura, M. Kirby, S. Klimenko, K. Kondo, D.J. Kong, J. Konigsberg, A.V. Kotwal, M. Kreps, J. Kroll, D. Krop, N. Krumnack l , M. Kruse, V. Krutelyov d , T. Kuhr, M. Kurata, S. Kwang, A.T. Laasanen, S. Lami, S. Lammel, M. Lancaster, R.L. Lander, K. Lannon u , A. Lath, G. Latino cc , I. Lazzizzera, T. LeCompte, E. Lee, H.S. Lee, J.S. Lee, S.W. Lee w , S. Leo bb , S. Leone, J.D. Lewis, C.-J. Lin, J. Linacre, M. Lindgren, E. Lipeles, A. Lister, D.O. Litvintsev, C. Liu, Q. Liu, T. Liu, S. Lockwitz, N.S. Lockyer, A. Loginov, D. Lucchesi aa , J. Lueck, P. Lujan, P. Lukens, G. Lungu, J. Lys, R. Lysak, R. Madrak, K. Maeshima, K. Makhoul, P. Maksimovic, S. Malik, G. Manca b , A. Manousakis-Katsikakis, F. Margaroli, C. Marino, M. Mart´ınez, R. Mart´ınez-Ballar´ın, P. Mastrandrea, M. Mathis, M.E. Mattson, P. Mazzanti, K.S. McFarland, P. McIntyre, R. McNulty i , A. Mehta, P. Mehtala, A. Menzione, C. Mesropian, T. Miao, D. Mietlicki, A. Mitra, H. Miyake, S. Moed, N. Moggi, M.N. Mondragon k , C.S. Moon, R. Moore, M.J. Morello, J. Morlock, P. Movilla Fernandez, A. Mukherjee, Th. Muller, P. Murat, M. Mussini z , J. Nachtman m , Y. Nagai, J. Naganoma, I. Nakano, A. Napier, J. Nett, C. Neu, M.S. Neubauer, J. Nielsen e , L. Nodulman, O. Norniella, E. Nurse, L. Oakes, S.H. Oh, Y.D. Oh, I. Oksuzian, T. Okusawa, R. Orava, L. Ortolan, S. Pagan Griso aa , C. Pagliarone, E. Palencia f , V. Papadimitriou, A.A. Paramonov, J. Patrick, G. Pauletta ff , M. Paulini, C. Paus, D.E. Pellett, A. Penzo, T.J. Phillips, G. Piacentino, E. Pianori, J. Pilot, K. Pitts, C. Plager, L. Pondrom, K. Potamianos, O. Poukhov ∗ , a r X i v : . [ h e p - e x ] N ov F. Prokoshin x , A. Pronko, F. Ptohos h , E. Pueschel, G. Punzi bb , J. Pursley, A. Rahaman, V. Ramakrishnan, N. Ranjan, I. Redondo, P. Renton, M. Rescigno, F. Rimondi z , L. Ristori , A. Robson, T. Rodrigo, T. Rodriguez, E. Rogers, S. Rolli, R. Roser, M. Rossi, F. Rubbo, F. Ruffini cc , A. Ruiz, J. Russ, V. Rusu, A. Safonov, W.K. Sakumoto, L. Santi ff , L. Sartori, K. Sato, V. Saveliev t , A. Savoy-Navarro, P. Schlabach, A. Schmidt, E.E. Schmidt, M.P. Schmidt ∗ , M. Schmitt, T. Schwarz, L. Scodellaro, A. Scribano cc , F. Scuri, A. Sedov, S. Seidel, Y. Seiya, A. Semenov, F. Sforza bb , A. Sfyrla, S.Z. Shalhout, T. Shears, P.F. Shepard, M. Shimojima s , S. Shiraishi, M. Shochet, I. Shreyber, J. Siegrist, A. Simonenko, P. Sinervo, A. Sissakian ∗ , K. Sliwa, J.R. Smith, F.D. Snider, A. Soha, S. Somalwar, V. Sorin, P. Squillacioti, M. Stanitzki, R. St. Denis, B. Stelzer, O. Stelzer-Chilton, D. Stentz, J. Strologas, G.L. Strycker, Y. Sudo, A. Sukhanov, I. Suslov, K. Takemasa, Y. Takeuchi, J. Tang, M. Tecchio, P.K. Teng, J. Thom g , J. Thome, G.A. Thompson, E. Thomson, P. Ttito-Guzm´an, S. Tkaczyk, D. Toback, S. Tokar, K. Tollefson, T. Tomura, D. Tonelli, S. Torre, D. Torretta, P. Totaro ff , M. Trovato dd , Y. Tu, N. Turini cc , F. Ukegawa, S. Uozumi, A. Varganov, E. Vataga dd , F. V´azquez k , G. Velev, C. Vellidis, M. Vidal, I. Vila, R. Vilar, I. Volobouev, M. Vogel, G. Volpi bb , P. Wagner, R.L. Wagner, T. Wakisaka, R. Wallny, S.M. Wang, A. Warburton, D. Waters, M. Weinberger, W.C. Wester III, B. Whitehouse, D. Whiteson c , A.B. Wicklund, E. Wicklund, S. Wilbur, F. Wick, H.H. Williams, J.S. Wilson, P. Wilson, B.L. Winer, P. Wittich g , S. Wolbers, H. Wolfe, T. Wright, X. Wu, Z. Wu, K. Yamamoto, J. Yamaoka, T. Yang, U.K. Yang p , Y.C. Yang, W.-M. Yao, G.P. Yeh, K. Yi m , J. Yoh, K. Yorita, T. Yoshida j , G.B. Yu, I. Yu, S.S. Yu, J.C. Yun, A. Zanetti, Y. Zeng, and S. Zucchelli z (CDF Collaboration † ) Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China Argonne National Laboratory, Argonne, Illinois 60439, USA University of Athens, 157 71 Athens, Greece Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain Baylor University, Waco, Texas 76798, USA Istituto Nazionale di Fisica Nucleare Bologna, z University of Bologna, I-40127 Bologna, Italy University of California, Davis, Davis, California 95616, USA University of California, Los Angeles, Los Angeles, California 90024, USA Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia Joint Institute for Nuclear Research, RU-141980 Dubna, Russia Duke University, Durham, North Carolina 27708, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Florida, Gainesville, Florida 32611, USA Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy University of Geneva, CH-1211 Geneva 4, Switzerland Glasgow University, Glasgow G12 8QQ, United Kingdom Harvard University, Cambridge, Massachusetts 02138, USA Division of High Energy Physics, Department of Physics,University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland University of Illinois, Urbana, Illinois 61801, USA The Johns Hopkins University, Baltimore, Maryland 21218, USA Institut f¨ur Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany Center for High Energy Physics: Kyungpook National University,Daegu 702-701, Korea; Seoul National University, Seoul 151-742,Korea; Sungkyunkwan University, Suwon 440-746,Korea; Korea Institute of Science and Technology Information,Daejeon 305-806, Korea; Chonnam National University, Gwangju 500-757,Korea; Chonbuk National University, Jeonju 561-756, Korea Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA University of Liverpool, Liverpool L69 7ZE, United Kingdom University College London, London WC1E 6BT, United Kingdom Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Institute of Particle Physics: McGill University, Montr´eal, Qu´ebec,Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia,Canada V5A 1S6; University of Toronto, Toronto, Ontario,Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3 University of Michigan, Ann Arbor, Michigan 48109, USA Michigan State University, East Lansing, Michigan 48824, USA Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia University of New Mexico, Albuquerque, New Mexico 87131, USA Northwestern University, Evanston, Illinois 60208, USA The Ohio State University, Columbus, Ohio 43210, USA Okayama University, Okayama 700-8530, Japan Osaka City University, Osaka 588, Japan University of Oxford, Oxford OX1 3RH, United Kingdom Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, aa University of Padova, I-35131 Padova, Italy LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Istituto Nazionale di Fisica Nucleare Pisa, bb University of Pisa, cc University of Siena and dd Scuola Normale Superiore, I-56127 Pisa, Italy University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA Purdue University, West Lafayette, Indiana 47907, USA University of Rochester, Rochester, New York 14627, USA The Rockefeller University, New York, New York 10065, USA Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, ee Sapienza Universit`a di Roma, I-00185 Roma, Italy Rutgers University, Piscataway, New Jersey 08855, USA Texas A&M University, College Station, Texas 77843, USA Texas Tech University, Lubbock, TX 79609, USA Istituto Nazionale di Fisica Nucleare Trieste/Udine,I-34100 Trieste, ff University of Trieste/Udine, I-33100 Udine, Italy University of Tsukuba, Tsukuba, Ibaraki 305, Japan Tufts University, Medford, Massachusetts 02155, USA University of Virginia, Charlottesville, VA 22906, USA Waseda University, Tokyo 169, Japan Wayne State University, Detroit, Michigan 48201, USA University of Wisconsin, Madison, Wisconsin 53706, USA Yale University, New Haven, Connecticut 06520, USA (Dated: October 29, 2018)A precision measurement of the top quark mass m t is obtained using a sample of t ¯ t events from p ¯ p collisions at the Fermilab Tevatron with the CDF II detector. Selected events require an electronor muon, large missing transverse energy, and exactly four high-energy jets, at least one of which istagged as coming from a b quark. A likelihood is calculated using a matrix element method withquasi–Monte Carlo integration taking into account finite detector resolution and jet mass effects.The event likelihood is a function of m t and a parameter ∆ JES used to calibrate the jet energy scale in situ . Using a total of 1087 events in 5.6 fb − of integrated luminosity, a value of m t = 173 . ± . c is measured. PACS numbers: 14.65.Ha ∗ Deceased † With visitors from a University of Massachusetts Amherst,Amherst, Massachusetts 01003, b Istituto Nazionale di Fisica Nu-cleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy, c University of California Irvine, Irvine, CA 92697, d University ofCalifornia Santa Barbara, Santa Barbara, CA 93106 e Universityof California Santa Cruz, Santa Cruz, CA 95064, f CERN,CH-1211 Geneva, Switzerland, g Cornell University, Ithaca, NY 14853, h University of Cyprus, Nicosia CY-1678, Cyprus, i University Col-lege Dublin, Dublin 4, Ireland, j University of Fukui, Fukui City,Fukui Prefecture, Japan 910-0017, k Universidad Iberoamericana,Mexico D.F., Mexico, l Iowa State University, Ames, IA 50011, m University of Iowa, Iowa City, IA 52242, n Kinki University,Higashi-Osaka City, Japan 577-8502, o Kansas State University,Manhattan, KS 66506, p University of Manchester, Manchester M139PL, England, q Queen Mary, University of London, London, E14NS, England, r Muons, Inc., Batavia, IL 60510, s Nagasaki In-stitute of Applied Science, Nagasaki, Japan, t National ResearchNuclear University, Moscow, Russia, u University of Notre Dame,Notre Dame, IN 46556, v Universidad de Oviedo, E-33007 Oviedo,Spain, w Texas Tech University, Lubbock, TX 79609, x UniversidadTecnica Federico Santa Maria, 110v Valparaiso, Chile, y YarmoukUniversity, Irbid 211-63, Jordan, gg On leave from J. Stefan Insti-tute, Ljubljana, Slovenia
The top quark is the heaviest known fundamental par-ticle in the standard model of particle physics. Since the1995 discovery of the top quark at the Fermilab Teva-tron [1], both the CDF and D0 experiments have beenimproving the measurement of its mass m t , which is afundamental parameter in the standard model [2]. Loopcorrections in electroweak theory relate m t (along withthe W boson mass m W ) to the mass of the predictedHiggs boson. Thus, precision measurements of m t helpto constrain the value of the Higgs boson mass [3].This Letter describes the single most-precise measure-ment to date of the top quark mass. It is performedon data collected by the CDF II detector [4] duringRun II of the Fermilab Tevatron p ¯ p collider operatingat √ s = 1 .
96 TeV with a total integrated luminosity of5.6 fb − . The measurement is performed on candidate t ¯ t events containing a lepton and four jets [5]. For eachevent selected in this analysis, we calculate the probabil-ity of observing that event by integrating the matrix ele-ment for t ¯ t production and decay over phase-space vari-ables. We use a neural network discriminant to distin-guish between signal and background events to correctfor the contribution due to background, and employ acut on the peak likelihood for a given event for addi-tional rejection of background and poorly modeled sig-nal events. This analysis offers a gain of nearly 20% instatistical precision over our previous measurement [5]given an equal number of events; there, in order to makethe likelihood integration computationally tractable, weintroduced kinematic assumptions to reduce the dimen-sionality of the integral. In the present analysis, we use aquasi–Monte Carlo integration technique [6], which con-verges more rapidly than the typical O ( N − / ) conver-gence of standard Monte Carlo integration. This allowsus to integrate over a total of 19 dimensions in a com-putationally practical time, resulting in a more accuratemodeling of the event. Furthermore, in addition to theincreased data sample available with more integrated lu-minosity delivered by the Tevatron, we have expandedour muon selection ability, which increases the size ofour data sample by nearly 30%. In total, this measure-ment improves our statistical precision by a factor of twoover our previous analysis with 1.9 fb − [5].In this measurement, the largest uncertainty is due tothe uncertainty in the jet energy scale (JES) determina-tion. To reduce this uncertainty, we calculate the likeli-hood as a two-dimensional function of m t and a secondparameter, ∆ JES , which corrects the jet energies by afactor of 1 + ∆
JES · σ j , where σ j is the fractional system-atic uncertainty on the energy for a given jet [7, 8]. Theknown W boson mass is used to constrain the W → q ¯ q (cid:48) decay, which yields information on the ∆ JES parameter.We can thus optimally combine events to reduce the totaluncertainty on m t due to JES.Within the standard model, the top quark decays al- most exclusively into a W boson and a b quark. Wedefine a “lepton + jets” event as an event where oneof the W bosons produced by the t ¯ t pair decays into acharged lepton (in this analysis, an electron or a muon)and a neutrino, and the other into a q ¯ q (cid:48) pair. The two b quarks and two quarks from the W boson then producejets in the detector [9]. We thus require candidate eventsto have an electron with E T >
20 GeV or a muon with p T >
20 GeV/ c in the central detector ( | η | < p T >
20 GeV/ c obtained with a trigger [4] onmissing transverse energy, (cid:54) E T [10], instead of a centralmuon. As the neutrino energy is not detected, we require (cid:54) E T >
20 GeV in the event. We also require exactly fourjets with E T >
20 GeV within the region | η | < .
0, atleast one of which must be tagged as a b jet using a sec-ondary vertex tagging algorithm [11]. To model t ¯ t events,we use Monte Carlo–simulated events generated with the pythia [12] generator for 15 different m t values rangingfrom 162 to 184 GeV/ c .Background events contributing to the selected sam-ple are: a) events in which a W boson is produced inconjunction with heavy-flavor quarks ( b ¯ b , c ¯ c , or c ); b)events in which a W boson is produced along with lightquarks, at least one of which is mistagged as heavy fla-vor; c) QCD events that do not contain a true W bo-son; d) diboson ( W W , W Z , or ZZ ) or Z + jets events;e) single top events. We model the contribution from W +jets events using alpgen [13], single top events using madgraph [14], and diboson events with pythia . The Z +jets contributions are not modeled separately, but areincluded in the W +light flavor contribution. All MonteCarlo samples are processed with the CDF II detector re-sponse simulation package [15]. The non- W QCD back-ground is modeled using a sideband of data events se-lected to have a small contribution from heavy bosondecay. The numbers of background events are estimatedwith the method used for the t ¯ t cross section measure-ment [16], and are shown in Table I.For each event, we construct a likelihood as a functionof m t and ∆ JES using the following integral: L ( (cid:126)y | m t , ∆ JES ) = 1 N ( m t ) 1 A ( m t , ∆ JES ) × (cid:88) i =1 w i L i ( (cid:126)y | m t , ∆ JES ) L i ( (cid:126)y | m t , ∆ JES ) = (cid:90) f ( z ) f ( z ) F F
TF( (cid:126)y | (cid:126)x, ∆ JES ) ×| M ( m t , (cid:126)x ) | d Φ( (cid:126)x ) , (1)where (cid:126)y are the quantities measured in the detector(the momenta of the jets and charged lepton), (cid:126)x arethe parton-level quantities that define the kinematicsof the event, N ( m t ) is a global normalization factor, A ( m t , ∆ JES ) is the event acceptance as a function of
TABLE I: Expected sample composition for an integrated lu-minosity of 5.6 fb − . The t ¯ t contribution is estimated usinga cross-section of 7.4 pb [17] and m t = 172.5 GeV/ c .Event type 1 b tag ≥ b tags W +heavy flavor 129.5 ± ± W QCD 50.1 ± ± W +light flavor mistag 48.5 ± ± W W , W Z , ZZ ) 10.5 ± ± ± ± Z → (cid:96)(cid:96) + jets 9.9 ± ± ± ± t ¯ t signal 767.3 ± ± ± ± m t and ∆ JES , f ( z ) and f ( z ) are the parton distri-bution functions (PDFs) for incoming parton momen-tum fractions z and z , F F is the relativistic flux fac-tor, TF( (cid:126)y | (cid:126)x, ∆ JES ) are the transfer functions that de-scribe the measured jet-momentum distributions giventhe quark kinematics, d Φ( (cid:126)x ) the phase space for theeight particles in the t ¯ t production and decay process,and M ( m t , (cid:126)x ) is the matrix element for the process. Theintegral is calculated for each of the 24 possible permu-tations of jet-parton assignment and then summed withweights w i determined by the probability that a b or lightparton will result in a b -tagged or untagged jet.We use the Kleiss-Stirling matrix element [18], whichis a leading-order matrix element including both q ¯ q → t ¯ t and gg → t ¯ t production processes, as well as all spincorrelations. For the PDFs, we use the CTEQ5L func-tions [19] for the incoming q ¯ q and gluons. The normaliza-tion factor N ( m t ) is obtained by integrating the Kleiss-Stirling matrix element with the PDFs and the flux factorover the phase space formed by the two initial and thesix final-state particles. The acceptance A ( m t , ∆ JES ) isobtained from simulated events where the parton direc-tions and momenta are smeared to simulate final-statejets. The transfer functions connect the measured jets tothe partons. We construct the transfer functions by tak-ing simulated t ¯ t → lepton + jets events in a wide rangeof masses and matching the simulated jets to their parentpartons. The transfer functions are separated into mo-mentum and angular terms; both are constructed withdependence on the true jet p T and mass from the MonteCarlo simulation. The transfer functions are constructedseparately for b and light quarks, as well as for each offour bins of jet η . There are 32 phase space integrationvariables in Eq. (1) (for the two initial partons and sixfinal partons). Four of these are eliminated by energyand momentum conservation, and four more by takingthe charged lepton, neutrino, and initial parton masses as known. In addition, we assume that the lepton mo-mentum is perfectly measured, and we neglect the effectsof the individual transverse momenta of the initial par-tons so that we model only the transverse momentum ofthe total t ¯ t system, for which we use a prior derived fromMonte Carlo simulation. This leaves a total of 19 dimen-sions over which the integral must be evaluated, whichwe perform using a quasi–Monte Carlo technique.Handling of background events is unchanged from ourprevious publication [5]. We identify events likely tobe background using a jetnet 3.5 artificial neural net-work [20] with ten inputs. We construct distributions ofthe neural network output weight u for signal, S ( u ), andbackground, B ( u ), events, normalized to their overall ex-pected fractions, and calculate the expected backgroundfraction for a given event as f bg ( u ) = B ( u ) / ( B ( u ) + S ( u )).We calculate the likelihood for all candidate events un-der the assumption that they are signal, but the com-bined likelihood contains contributions from both signaland background events. However, only the signal eventscontain information about m t , so using Monte Carlo–simulated events we compute the average likelihood forbackground events and subtract it from the total likeli-hood:log L adj ( m t , ∆ JES )= (cid:88) i ∈ events [log L ( (cid:126)y i | m t , ∆ JES ) − f bg ( u i ) log L bg ( m t , ∆ JES )] , (2)where L adj is the adjusted total likelihood for a given setof events, L ( (cid:126)y i | m t , ∆ JES ) is the likelihood for an individ-ual event from Eq. (1), f bg ( u i ) is the background fractionfor a given event with a neural network output u i , and L bg ( m t , ∆ JES ) is the average likelihood for a backgroundevent.Besides background events, the sample includes eventswhich contain a real t ¯ t , but where one or more of the fourjets and/or the lepton observed in the detector do notcome directly from the t ¯ t decay, and are not well-modeledby the signal likelihood or handled by the backgroundsubtraction above. These events, which we refer to as“bad signal,” have a variety of sources (extra jets fromgluon radiation, t ¯ t events where both W bosons decayinto leptons or hadrons, W → τ ν decay, etc.) and makeup 36% of the simulated t ¯ t events for m t = 172.5 GeV/c .We suppress these events by requiring that the peak log-likelihood value for an event be at least 10. This cutretains 96.3% of the signal, while rejecting 30.8% of thebad signal and 37.3% of the background.We test and calibrate the method by constructing sim-ulated experiments using the Monte Carlo samples of t ¯ t events and background described earlier. For a given in-put m t and ∆ JES , we perform 2000 experiments using aPoisson distribution with mean of 1089 events (the num-ber of events expected to pass the likelihood cut), and usethese to calibrate the measurement as a function of theinput m t and ∆ JES . Figure 1 shows the output mass be-fore calibration and the calibrated expected uncertainty. ) ( G e V / c t O u t pu t m – Value at 173 = 172.46 0.01 – Slope = 0.97 ) (GeV/c t Input m155 160 165 170 175 180 185 ) ( G e V / c m s FIG. 1: Simulated experiment results using Monte Carlo sig-nal and background events. Top: output m t vs. input m t ,before calibration is applied. Bottom: expected uncertainty σ m vs. input m t , with calibration applied. The lines arelinear best fits. In the data we find a total of 1087 events which passall of the selection requirements (including the likelihoodpeak cut), of which 854 have 1 b tag and 233 have > b tag. Figure 2 shows the resulting 2-D likelihood contoursfor 1 σ , 2 σ , and 3 σ after all calibration. ) (GeV/c t m
170 171 172 173 174 175 ) s ( J ES D -0.6-0.4-0.2-00.20.40.60.8 -1 CDF Run II 5.6 fb (ln L) = -0.5 D (ln L) = -2.0 D (ln L) = -4.5 D -1 CDF Run II 5.6 fb
FIG. 2: Measured 2-D likelihood on the data events, withthe contours corresponding to a 1- σ , 2- σ , and 3- σ uncertaintyin the final m t measurement from the profile method. Themarker shows the point of maximum likelihood. To obtain a 1-D likelihood curve in m t only, we treat∆ JES as a nuisance parameter and eliminate it using theprofile likelihood method [21], where we take the maxi-mum value of the likelihood along the ∆
JES axis for each m t value. The top quark mass value extracted from theprofile likelihood after calibration is m t = 173 . ± . c . We can separate this uncertainty into the sta-tistical uncertainty on m t and the uncertainty due to ∆ JES by fixing the ∆
JES value to its maximum likeli-hood value. We find that the uncertainty from the re-sulting 1-D likelihood is 0 . c , so we assign theremaining uncertainty of 0 . c to ∆ JES and con-clude m t = 173 . ± . ± . /c .To validate the likelihood cut procedure, we comparethe peak values of the log-likelihood curves obtainedwith data to those obtained with Monte Carlo–simulatedevents at m t = 172 . c (the nearest available massvalue). The results are shown in Fig. 3. −2 0 2 4 6 8 10 12 14 16 18050100150200250 Log−likelihood value at peakNumber of eventsSignal + background MCBackground MC Data events FIG. 3: Comparison of the log-likelihood value of the peakof likelihood curves for data and Monte Carlo events. Thevertical line at 10 indicates the likelihood cut used in thisanalysis. A Kolmogorov-Smirnov test gives a confidence levelof 0.93, showing good agreement between the two.
The systematic uncertainties on m t , given in Table II,are derived using the methods described in Ref. [5]. Inbrief, we include uncertainties coming from: the calibra-tion method; signal Monte Carlo modeling, evaluated bycomparing events simulated with the pythia and her-wig [22] generators; variations of the parameters usedfor initial state radiation (ISR) and final state radiation(FSR); a residual JES uncertainty because the JES un-certainty contains several components with different p T and η dependence; additional uncertainties on the energyscale for b jets; uncertainty on the lepton p T scale; multi-ple hadron interactions, to take into account uncertaintyon the jet corrections as a function of the number of inter-actions in the event; uncertainties arising from the PDFsused in the integration; and the background modeling.This analysis includes a systematic uncertainty due tocolor reconnection effects, not considered in our previousanalysis. We use pythia version 6.4.20, which includes acolor reconnection model [23], and measure the differencebetween two tunes, Tune A, which is the tune used in thisanalysis, and Tune ACR, which adds color reconnectioneffects to Tune A. The individual systematic uncertain-ties are added in quadrature to obtain the final total of0.9 GeV/ c .In conclusion, the measured top quark mass in a sam-ple with 5.6 fb − of integrated luminosity, with 1087events passing all cuts, is m t = 173.0 ± ± ± c , for a total uncertaintyof 1.2 GeV/ c . The improved integration techniques andincreased data sample make this the best single measure-ment of the top quark mass to date, and it is comparablein precision to the most recent combination for the topquark mass at the Tevatron [2].We thank the Fermilab staff and the technical staffsof the participating institutions for their vital contribu-tions. This work was supported by the U.S. Departmentof Energy and National Science Foundation; the ItalianIstituto Nazionale di Fisica Nucleare; the Ministry ofEducation, Culture, Sports, Science and Technology ofJapan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A.P. Sloan Foundation; the Bundesministeriumf¨ur Bildung und Forschung, Germany; the World ClassUniversity Program, the National Research Foundationof Korea; the Science and Technology Facilities Coun-cil and the Royal Society, UK; the Institut National dePhysique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Minis-terio de Ciencia e Innovaci´on, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and theAcademy of Finland. [1] F. Abe et al. (CDF Collaboration), Phys. Rev Lett. ,2626 (1995); S. Abachi et al. (D0 Collaboration), ibid. , 2632 (1995).[2] The Tevatron Electroweak Working Group, FERMILAB-TM-2466-E, arXiv:1007.3178v1 (2010).[3] The LEP Collaboration, CERN-PH-EP/2007-039,TABLE II: List of systematic uncertainties on m t .Systematic source Uncertainty (GeV/ c )Calibration 0.10MC generator 0.37ISR and FSR 0.15Residual JES 0.49 b -JES 0.26Lepton p T et al. (CDF Collaboration), Phys. Rev. D ,052003 (2005).[5] T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D , 072001 (2009).[6] W. Morokoff and R. E. Caflisch, SIAM J. Sci. Stat.Comp. , 1251 (1994).[7] A. Abulencia et al. (CDF Collaboration), Phys. Rev.Lett. , 022004 (2006).[8] A. Bhatti et al. (CDF Collaboration), Nucl. Instrum.Meth. A , 375 (2006).[9] F. Abe et al. (CDF Collaboration), Phys. Rev. D ,1448 (1992).[10] A particle’s transverse momentum p T and tranverse en-ergy E T are given by | (cid:126)p | sin θ and E sin θ respectively,where θ is the polar angle with respect to the protondirection (z-axis). The pseudorapidity η of a particle’sthree-momentum is defined by η = − ln(tan( θ/ E T , (cid:54) E T , is defined by (cid:126) (cid:54) E T = −| (cid:80) i E T i ˆ n T i | ,where ˆ n T i is the unit vector in the x – y plane pointingfrom the primary vertex to a given calorimeter tower i ,and E T i is the E T measured in that tower.[11] D. Acosta et al. (CDF Collaboration), Phys. Rev. D ,052003 (2005).[12] T. Sj¨ostrand et al. , Comput. Phys. Commun. , 238(2001).[13] M. Mangano et al. , J. High Energy Phys. 07, 001 (2003).[14] F. Maltoni and T. Stelzer, J. High Energy Phys. 02, 027(2003).[15] E. Gerchtein, M. Paulini, arXiv:physics/0306031 (2003).[16] D. Acosta et al. (CDF Collaboration), Phys. Rev. D ,072005 (2005).[17] S. Moch and P. Uwer, Nucl. Phys. Proc. Suppl. , 75(2008).[18] R. Kleiss and W. J. Stirling, Z. Phys. C , 419 (1988).[19] H. L. Lai et al. , Eur. Phys. J. C , 375 (2000).[20] C. Peterson, T. R¨ognvaldsson, and L. L¨onnblad, Comput.Phys. Commun. , 185 (1994).[21] G. A. Young and R. L. Smith, Essentials of StatisticalInference (Cambridge University Press, 2005).[22] G. Corcella et al. , J. High Energy Phys. 01, 010 (2001).[23] P. Skands and D. Wicke, Eur. Phys. J. C52