Measurement of the t �t production cross section in p �p collisions atffiffiffis

p ¼ 1:96 TeV usingevents with large missing transverse energy and jets

T. Aaltonen,21 B. Alvarez Gonzalez,9,w S. Amerio,41a D. Amidei,32 A. Anastassov,36 A. Annovi,17 J. Antos,12

G. Apollinari,15 J. A. Appel,15 A. Apresyan,46 T. Arisawa,56 A. Artikov,13 J. Asaadi,51 W. Ashmanskas,15 B. Auerbach,59

A. Aurisano,51 F. Azfar,40 W. Badgett,15 A. Barbaro-Galtieri,26 V. E. Barnes,46 B.A. Barnett,23 P. Barria,44c,44a P. Bartos,12

M. Bauce,41b,41a G. Bauer,30 F. Bedeschi,44a D. Beecher,28 S. Behari,23 G. Bellettini,44b,44a J. Bellinger,58 D. Benjamin,14

A. Beretvas,15 A. Bhatti,48 M. Binkley,15,a D. Bisello,41b,41a I. Bizjak,28,aa K. R. Bland,5 B. Blumenfeld,23 A. Bocci,14

A. Bodek,47 D. Bortoletto,46 J. Boudreau,45 A. Boveia,11 B. Brau,15,b L. Brigliadori,6b,6a A. Brisuda,12 C. Bromberg,33

E. Brucken,21 M. Bucciantonio,44b,44a J. Budagov,13 H. S. Budd,47 S. Budd,22 K. Burkett,15 G. Busetto,41b,41a P. Bussey,19

A. Buzatu,31 C. Calancha,29 S. Camarda,4 M. Campanelli,33 M. Campbell,32 F. Canelli,12,15 A. Canepa,43 B. Carls,22

D. Carlsmith,58 R. Carosi,44a S. Carrillo,16,l S. Carron,15 B. Casal,9 M. Casarsa,15 A. Castro,6b,6a P. Catastini,15 D. Cauz,52a

V. Cavaliere,44c,44a M. Cavalli-Sforza,4 A. Cerri,26,g L. Cerrito,28,r Y. C. Chen,1 M. Chertok,7 G. Chiarelli,44a

G. Chlachidze,15 F. Chlebana,15 K. Cho,25 D. Chokheli,13 J. P. Chou,20 W.H. Chung,58 Y. S. Chung,47 C. I. Ciobanu,42

M.A. Ciocci,44c,44a A. Clark,18 G. Compostella,41b,41a M. E. Convery,15 J. Conway,7 M. Corbo,42 M. Cordelli,17

C. A. Cox,7 D. J. Cox,7 F. Crescioli,44b,44a C. Cuenca Almenar,59 J. Cuevas,9,w R. Culbertson,15 D. Dagenhart,15

N. d’Ascenzo,42,u M. Datta,15 P. de Barbaro,47 S. De Cecco,49a G. De Lorenzo,4 M. Dell’Orso,44b,44a C. Deluca,4

L. Demortier,48 J. Deng,14,d M. Deninno,6a F. Devoto,21 M. d’Errico,41b,41a A. Di Canto,44b,44a B. Di Ruzza,44a

J. R. Dittmann,5 M. D’Onofrio,27 S. Donati,44b,44a P. Dong,15 M. Dorigo,52a T. Dorigo,57 K. Ebina,56 A. Elagin,51

A. Eppig,32 R. Erbacher,7 D. Errede,22 S. Errede,22 N. Ershaidat,42,z R. Eusebi,51 H. C. Fang,26 S. Farrington,40

M. Feindt,24 J. P. Fernandez,29 C. Ferrazza,44d,44a R. Field,16 G. Flanagan,46,s R. Forrest,7 M. J. Frank,5 M. Franklin,20

J. C. Freeman,15 Y. Funakoshi,56 I. Furic,16 M. Gallinaro,48 J. Galyardt,10 J. E. Garcia,18 A. F. Garfinkel,46 P. Garosi,44c,44a

H. Gerberich,22 E. Gerchtein,15 S. Giagu,49b,49a V. Giakoumopoulou,3 P. Giannetti,44a K. Gibson,45 C.M. Ginsburg,15

N. Giokaris,3 P. Giromini,17 M. Giunta,44a G. Giurgiu,23 V. Glagolev,13 D. Glenzinski,15 M. Gold,35 D. Goldin,51

N. Goldschmidt,16 A. Golossanov,15 G. Gomez,9 G. Gomez-Ceballos,30 M. Goncharov,30 O. Gonzalez,29 I. Gorelov,35

A. T. Goshaw,14 K. Goulianos,48 A. Gresele,57 S. Grinstein,4 C. Grosso-Pilcher,11 R. C. Group,55 J. Guimaraes da Costa,20

Z. Gunay-Unalan,33 C. Haber,26 S. R. Hahn,15 E. Halkiadakis,50 A. Hamaguchi,39 J. Y. Han,47 F. Happacher,17 K. Hara,53

D. Hare,50 M. Hare,54 R. F. Harr,57 K. Hatakeyama,5 C. Hays,40 M. Heck,24 J. Heinrich,43 M. Herndon,58 S. Hewamanage,5

D. Hidas,50 A. Hocker,15W. Hopkins,15,h D. Horn,24 S. Hou,1 R. E. Hughes,37 M. Hurwitz,11 U. Husemann,59 N. Hussain,31

M. Hussein,33 J. Huston,33 G. Introzzi,44a M. Iori,49b,49a A. Ivanov,7,p E. James,15 D. Jang,10 B. Jayatilaka,14 E. J. Jeon,25

M.K. Jha,6a S. Jindariani,15 W. Johnson,7 M. Jones,46 K.K. Joo,25 S. Y. Jun,10 T. R. Junk,15 T. Kamon,51 P. E. Karchin,57

Y. Kato,39,o W. Ketchum,11 J. Keung,43 V. Khotilovich,51 B. Kilminster,15 D.H. Kim,25 H. S. Kim,25 H.W. Kim,25

J. E. Kim,25 M. J. Kim,17 S. B. Kim,25 S. H. Kim,53 Y.K. Kim,11 N. Kimura,56 M. Kirby,15 S. Klimenko,16 K. Kondo,56

D. J. Kong,25 J. Konigsberg,16 A.V. Kotwal,14 M. Kreps,24 J. Kroll,43 D. Krop,11 N. Krumnack,5,m M. Kruse,14

V. Krutelyov,51,e T. Kuhr,24 M. Kurata,53 S. Kwang,11 A. T. Laasanen,46 S. Lami,44a S. Lammel,15 M. Lancaster,28

R. L. Lander,7 K. Lannon,37,v A. Lath,50 G. Latino,44c,44a I. Lazzizzera,41a T. LeCompte,2 E. Lee,51 H. S. Lee,11 J. S. Lee,25

S.W. Lee,51,x S. Leo,44b,44a S. Leone,44a J. D. Lewis,15 C.-J. Lin,26 J. Linacre,40 M. Lindgren,15 E. Lipeles,43 A. Lister,18

D.O. Litvintsev,15 C. Liu,45 Q. Liu,46 T. Liu,15 S. Lockwitz,59 N. S. Lockyer,43 A. Loginov,59 D. Lucchesi,41b,41a

J. Lueck,24 P. Lujan,26 P. Lukens,15 G. Lungu,48 J. Lys,26 R. Lysak,12 R. Madrak,15 K. Maeshima,15 K. Makhoul,30

P. Maksimovic,23 S. Malik,48 G. Manca,27,c A. Manousakis-Katsikakis,3 F. Margaroli,46 C. Marino,24 M. Martınez,4

R. Martınez-Balların,29 P. Mastrandrea,49a M. Mathis,23 M. E. Mattson,57 P. Mazzanti,6a K. S. McFarland,47 P. McIntyre,51

R. McNulty,27,j A. Mehta,27 P. Mehtala,21 A. Menzione,44a C. Mesropian,48 T. Miao,15 D. Mietlicki,32 A. Mitra,1

H. Miyake,53 S. Moed,20 N. Moggi,6a M.N. Mondragon,15,l C. S. Moon,25 R. Moore,15 M. J. Morello,15 J. Morlock,24

P. Movilla Fernandez,15 A. Mukherjee,15 Th. Muller,24 P. Murat,15 M. Mussini,6b,6a J. Nachtman,15,n Y. Nagai,53

J. Naganoma,56 I. Nakano,38 A. Napier,54 J. Nett,51 C. Neu,55 M. S. Neubauer,22 J. Nielsen,26,f L. Nodulman,2

O. Norniella,22 E. Nurse,28 L. Oakes,40 S. H. Oh,14 Y.D. Oh,25 I. Oksuzian,55 T. Okusawa,39 R. Orava,21 L. Ortolan,4

S. Pagan Griso,41b,41a C. Pagliarone,52a E. Palencia,9,g V. Papadimitriou,15 A.A. Paramonov,2 J. Patrick,15

G. Pauletta,52b,52a M. Paulini,10 C. Paus,30 D. E. Pellett,7 A. Penzo,52a T. J. Phillips,14 G. Piacentino,44a E. Pianori,43

J. Pilot,37 K. Pitts,22 C. Plager,8 L. Pondrom,58 K. Potamianos,46 O. Poukhov,13,a F. Prokoshin,13,y A. Pronko,15

F. Ptohos,17,i E. Pueschel,10 G. Punzi,44b,44a J. Pursley,58 A. Rahaman,45 V. Ramakrishnan,58 N. Ranjan,46 I. Redondo,29

P. Renton,40 M. Rescigno,49a F. Rimondi,6b,6a L. Ristori,44a,15 A. Robson,19 T. Rodrigo,9 T. Rodriguez,43 E. Rogers,22

PHYSICAL REVIEW D 84, 032003 (2011)

1550-7998=2011=84(3)=032003(12) 032003-1 � 2011 American Physical Society

S. Rolli,54 R. Roser,15 M. Rossi,52a F. Rubbo,15 F. Ruffini,44c,44a A. Ruiz,9 J. Russ,10 V. Rusu,15 A. Safonov,51

W.K. Sakumoto,47 Y. Sakurai,56 L. Santi,52b,52a L. Sartori,44a K. Sato,53 V. Saveliev,42,u A. Savoy-Navarro,42

P. Schlabach,15 A. Schmidt,24 E. E. Schmidt,15 M. P. Schmidt,59,a M. Schmitt,36 T. Schwarz,7 L. Scodellaro,9

A. Scribano,44c,44a F. Scuri,44a A. Sedov,46 S. Seidel,35 Y. Seiya,39 A. Semenov,13 F. Sforza,44b,44a A. Sfyrla,22

S. Z. Shalhout,7 T. Shears,27 P. F. Shepard,45 M. Shimojima,53,t S. Shiraishi,11 M. Shochet,11 I. Shreyber,34

A. Simonenko,13 P. Sinervo,31 A. Sissakian,13,a K. Sliwa,54 J. R. Smith,7 F. D. Snider,15 A. Soha,15 S. Somalwar,50

V. Sorin,4 P. Squillacioti,15 M. Stancari,15 M. Stanitzki,59 R. St. Denis,19 B. Stelzer,31 O. Stelzer-Chilton,31 D. Stentz,36

J. Strologas,35 G. L. Strycker,32 Y. Sudo,53 A. Sukhanov,16 I. Suslov,13 K. Takemasa,53 Y. Takeuchi,53 J. Tang,11

M. Tecchio,32 P. K. Teng,1 J. Thom,15,h J. Thome,10 G.A. Thompson,22 E. Thomson,43 P. Ttito-Guzman,29 S. Tkaczyk,15

D. Toback,51 S. Tokar,12 K. Tollefson,33 T. Tomura,53 D. Tonelli,15 S. Torre,17 D. Torretta,15 P. Totaro,52b,52a

M. Trovato,44d,44a Y. Tu,43 F. Ukegawa,53 S. Uozumi,25 A. Varganov,32 F. Vazquez,16,l G. Velev,15 C. Vellidis,3 M. Vidal,29

I. Vila,9 R. Vilar,9 M. Vogel,35 G. Volpi,44b,44a P. Wagner,43 R. L. Wagner,15 T. Wakisaka,39 R. Wallny,8 S.M. Wang,1

A. Warburton,31 D. Waters,28 M. Weinberger,51 W.C. Wester III,15 B. Whitehouse,54 D. Whiteson,43,d A. B. Wicklund,2

E. Wicklund,15 S. Wilbur,11 F. Wick,24 H.H. Williams,43 J. S. Wilson,37 P. Wilson,15 B. L. Winer,37 P. Wittich,15,h

S. Wolbers,15 H. Wolfe,37 T. Wright,32 X. Wu,18 Z. Wu,5 K. Yamamoto,39 J. Yamaoka,14 T. Yang,15 U.K. Yang,11,q

Y. C. Yang,25 W.-M. Yao,26 G. P. Yeh,15 K. Yi,15,n J. Yoh,15 K. Yorita,56 T. Yoshida,39,k G. B. Yu,14 I. Yu,25 S. S. Yu,15

J. C. Yun,15 A. Zanetti,52a Y. Zeng,14 and S. Zucchelli6b,6a

(CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China2Argonne National Laboratory, Argonne, Illinois 60439, USA

3University of Athens, 157 71 Athens, Greece4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798, USA6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

14Duke University, Durham, North Carolina 27708, USA15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

16University of Florida, Gainesville, Florida 32611, USA17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

18University of Geneva, CH-1211 Geneva 4, Switzerland19Glasgow University, Glasgow G12 8QQ, United Kingdom

20Harvard University, Cambridge, Massachusetts 02138, USA21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics,

FIN-00014, Helsinki, Finland22University of Illinois, Urbana, Illinois 61801, USA

23The Johns Hopkins University, Baltimore, Maryland 21218, USA24Institut fur Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

25Center 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, Korea26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

27University of Liverpool, Liverpool L69 7ZE, United Kingdom28University College London, London WC1E 6BT, United Kingdom

29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

31Institute of Particle Physics, McGill University, Montreal, Quebec, 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

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32University of Michigan, Ann Arbor, Michigan 48109, USA33Michigan State University, East Lansing, Michigan 48824, USA

34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia35University of New Mexico, Albuquerque, New Mexico 87131, USA

36Northwestern University, Evanston, Illinois 60208, USA37The Ohio State University, Columbus, Ohio 43210, USA

38Okayama University, Okayama 700-8530, Japan39Osaka City University, Osaka 588, Japan

40University of Oxford, Oxford OX1 3RH, United Kingdom41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

41bUniversity of Padova, I-35131 Padova, Italy42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

44bUniversity of Pisa, I-56127 Pisa, Italy44cUniversity of Siena, I-56127 Pisa, Italy

44dScuola Normale Superiore, I-56127 Pisa, Italy45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

46Purdue University, West Lafayette, Indiana 47907, USA47University of Rochester, Rochester, New York 14627, USA

48The Rockefeller University, New York, New York 10065, USA49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

49bSapienza Universita di Roma, I-00185 Roma, Italy50Rutgers University, Piscataway, New Jersey 08855, USA

51Texas A&M University, College Station, Texas 77843, USA52aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, I-33100 Udine, Italy

52bUniversity of Trieste/Udine, I-33100 Udine, Italy53University of Tsukuba, Tsukuba, Ibaraki 305, Japan54Tufts University, Medford, Massachusetts 02155, USA

55University of Virginia, Charlottesville, Virginia 22906, USA56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

aDeceasedbVisitor from University of Massachusetts, Amherst, Amherst, Massachusetts 01003, USAcVisitor from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), ItalydVisitor from University of California Irvine, Irvine, CA 92697, USAeVisitor from University of California Santa Barbara, Santa Barbara, CA 93106, USAfVisitor from University of California Santa Cruz, Santa Cruz, CA 95064, USAgVisitor from CERN, CH-1211 Geneva, SwitzerlandhVisitor from Cornell University, Ithaca, NY 14853, USAiVisitor from University of Cyprus, Nicosia CY-1678, CyprusjVisitor from University College Dublin, Dublin 4, IrelandkVisitor from University of Fukui, Fukui City, Fukui Prefecture, 910-0017, JapanlVisitor from Universidad Iberoamericana, Mexico D.F., Mexico

mVisitor from Iowa State University, Ames, IA 50011, USAnVisitor from University of Iowa, Iowa City, IA 52242, USAoVisitor from Kinki University, Higashi-Osaka City 577-8502, JapanpVisitor from Kansas State University, Manhattan, KS 66506, USAqVisitor from University of Manchester, Manchester M13 9PL, EnglandrVisitor from Queen Mary, University of London, London, E1 4NS, EnglandsVisitor from Muons, Inc., Batavia, IL 60510, USAtVisitor from Nagasaki Institute of Applied Science, Nagasaki, JapanuVisitor from National Research Nuclear University, Moscow, RussiavVisitor from University of Notre Dame, Notre Dame, IN 46556, USAwVisitor from Universidad de Oviedo, E-33007 Oviedo, SpainxVisitor from Texas Tech University, Lubbock, TX 79609, USAyVisitor from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, ChilezVisitor from Yarmouk University, Irbid 211-63, JordanaaOn leave from J. Stefan Institute, Ljubljana, Slovenia

MEASUREMENT OF THE t�t PRODUCTION CROSS . . . PHYSICAL REVIEW D 84, 032003 (2011)

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58University of Wisconsin, Madison, Wisconsin 53706, USA59Yale University, New Haven, Connecticut 06520, USA(Received 11 May 2011; published 9 August 2011)

In this paper we report a measurement of the t�t production cross section in p �p collisions atffiffiffis

p ¼1:96 TeV using data corresponding to an integrated luminosity of 2:2 fb�1 collected with the CDF II

detector at the Tevatron accelerator. We select events with significant missing transverse energy and high

jet multiplicity. This measurement vetoes the presence of explicitly identified electrons and muons, thus

enhancing the tau contribution of t�t decays. Signal events are discriminated from the background using a

neural network, and heavy flavor jets are identified by a secondary-vertex tagging algorithm. We measure

a t�t production cross section of 7:99� 0:55ðstatÞ � 0:76ðsystÞ � 0:46ðlumiÞ pb, assuming a top mass

mtop ¼ 172:5 GeV=c2, in agreement with previous measurements and standard model predictions.

DOI: 10.1103/PhysRevD.84.032003 PACS numbers: 14.65.Ha, 13.60.Hb

I. INTRODUCTION

In p �p collisions atffiffiffis

p ¼ 1:96 TeV at the Tevatron, topquarks are produced mainly in pairs through quark-antiquark annihilation and gluon-gluon fusion processes.In the standard model (SM), the calculated cross sectionfor top pair production at the Tevatron center-of-massenergy is 7:46þ0:66

�0:80 pb [1] for a top mass of

172:5 GeV=c2. This value can be enhanced by new pro-cesses beyond the SM such as top pair production via newmassive resonances [2], while the comparison of the toppair production cross section in different decay channelscan be sensitive to the presence of top decays via a chargedHiggs boson [3]. Thus, a precise measurement of the toppair production cross section is an important test of theSM. Both CDF and D0 Collaborations have performedmany measurements of this quantity in different t�t finalstates: the most recent published results, both measured inthe decay channel with leptons and jets assuming mtop ¼172:5 GeV=c2, are 7:70� 0:52 pb for CDF [4] and7:78þ0:77

�0:64pb for D0 [5].

As the Cabibbo-Kobayashi-Maskawa matrix elementVtb is close to unity [6,7] and the top mass mtop is larger

than the sum of theW boson and bottom quark (b) masses,in the SM the t ! Wb decay is dominant and has abranching ratio of about 100%. Since the W subsequentlydecays either to a quark-antiquark pair or to a lepton-neutrino pair, the resulting top pair production final statescan be classified by the number of energetic chargedleptons and the number of jets. When only one W decaysleptonically, the t�t event is characterized by the presence ofa charged lepton, missing energy due to the undetectedneutrino, and four high energy jets, two of which originatefrom b quarks. In this lepton plus jets channel, one selectsevents with an energetic electron or muon. For this paperwe focus on an inclusive high-momentum neutrino signa-ture of large missing energy accompanied by jets. By notexplicitly requiring leptons, our measurement is sensitiveto all W leptonic decay modes including � decays of W ’s:about 40% of the signal sample obtained after the kine-matic selection contains events with a � lepton in thefinal state. To ensure our measurement is statistically

independent from other CDF results [8], we veto eventswith high-momentum electrons or muons as well as multi-jet events with no leptons (all-hadronic t�t decays). Thischoice is expected to improve the final CDF combinedcross section value: the previous 311 pb�1 result [9] car-ried a weight of about 17% in the combination [10].One of the major challenges of this measurement is the

large background from QCD multijet processes and elec-troweak production of W bosons associated with b and cjets (heavy flavor jets), which dominates the signal by 2orders of magnitude before any selection. In order toimprove the signal-to-background ratio (S=B), a neuralnetwork is trained to identify the kinematic and topologicalcharacteristics of SM t�t events and is applied to data toselect a signal-rich sample. Top quarks are then identifiedby their distinctive decay into b quarks. Jets originatingfrom b quarks (b jets) are selected (‘‘tagged’’) by theirdisplaced vertex as defined by the SECVTX algorithm [11].After evaluating the average number of b-tagged jets for t�tevents using a Monte Carlo (MC) simulation, the numberof signal events in the sample and the corresponding crosssection are measured by counting the number of b-taggedjets in the sample selected by the neural network. Thenumber of background b-tagged jets is estimated usingper-jet parametrized probabilities of b-jet identification,measured directly from data, rather than relying on theo-retical prediction of cross sections and MC simulations.The results reported here are based on data taken betweenMarch 2002 and August 2007, corresponding to an inte-grated luminosity of 2:2 fb�1, recorded by the CDF ex-periment at Fermilab.The organization of the paper is the following: Sec. II

contains a brief description of the CDF II detector and ofthe trigger requirements used for this analysis. The pre-liminary cleanup cuts applied to data are described inSec. III, followed by the discussion of the data-drivenbackground parametrization in Sec. IV. The kinematicvariables characterizing the missing energy plus jets finalstate and the neural-network-based sample selection aredescribed in Sec. Vand Sec. VI, respectively. We concludethe description of this measurement with a summary of the

T. AALTONEN et al. PHYSICAL REVIEW D 84, 032003 (2011)

032003-4

different sources of systematic uncertainties in Sec. VII,while the cross section measurement is presented inSec. VIII. Section IX gives our conclusions.

II. THE CDF DETECTOR AND TRIGGER SYSTEM

CDF II is a general-purpose, azimuthally and forward-backward symmetric detector located at the Tevatron p �pcollider at Fermilab. It consists of a charged-particle track-ing system immersed in a 1.4 T magnetic field. The sole-noid is surrounded by calorimeters and muon detectors[12]. The CDF II coordinate system uses � and � as thepolar and azimuthal angles, respectively, defined with re-spect to the proton beam axis direction, z. The x-axis pointstoward the center of the accelerator while the y axis pointsupward from the beam. The pseudorapidity � is defined as� � � ln½tanð�=2Þ�. The transverse momentum of a parti-cle is pT ¼ p sin� and its transverse energy ET ¼ E sin�.The missing transverse energy 6ET measures the transverseenergy of the neutrinos via the imbalance of the energy

detected in the calorimeters; it is defined by 6ET ¼ j ~6ETjwhere ~6ET¼ �P

iEiTni, the index i runs over the calorime-

ter tower number and ni is a unit vector perpendicular tothe beam axis and pointing at the i-th calorimeter tower.The tracking system is composed of eight layers of siliconmicrostrip detectors, extending from 1.6 cm to 28 cm andcovering up to j�j< 2:0, surrounded by a 3.1 m long opencell drift chamber, providing j�j coverage up to 1.0. Usinginformation from the silicon detectors, the primary inter-action vertex is reconstructed with a precision of �15 �min the plane transverse to the beam [13]. The energy of theparticles traversing the detector is measured by electro-magnetic and hadronic calorimeters segmented into pro-jective towers covering up to j�j< 3:6. In the centralregion (j�j< 1:1) the calorimetric towers are 15� widein � and 0.1 in �; in the forward region (1:1< j�j< 3:6)the towers are 7.5� wide in azimuthal angle for j�j< 2:1and 15� for j�j> 2:1. The electromagnetic section is madeof lead-scintillator plates, while the hadronic section usesiron-scintillator ones. The transverse profile of electromag-netic showers is measured by proportional chambers andscintillating strip detectors. Muons are detected up to j�j<0:6 by drift chambers located outside the hadronic calo-rimeters, behind a 60 cm iron shield. Additional driftchambers and scintillator detectors provide muon detectionup to j�j< 1:5.

The CDF II trigger system [14] has a three-level archi-tecture designed to operate at 2.53 MHz and reduce thedata rate to approximately 120 Hz to be written on tape.The data used in this measurement are collected with apurely calorimetric trigger, described in Sec. IIA. At Level-1 (L1) calorimetric towers are merged in pairs along � todefine trigger towers: the L1 can take a decision on theenergy contribution of individual trigger towers, on thesum of the energy of all the towers or on the missing

transverse energy of the event. At Level-2 (L2) triggertowers are merged into clusters by a simple clusteringalgorithm [15], while at Level-3 (L3) jets of particlesare reconstructed by a fixed cone-based algorithm [16],

the radius of the cone in the ��� plane (�R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��2 þ��2

p) being 0.4, 0.7 or 1 depending on the specific

trigger.

A. The multijet trigger

The data used in this analysis are collected by a multijettrigger. This trigger requires at L1 the presence of at leastone central trigger tower with ET � 10 GeV, and at L2 atleast four calorimetric clusters with ET � 15 GeV eachand a total transverse energy greater than 175 GeV. Thelatter threshold was 125 GeV before February 2005 andwas increased to reduce the trigger rate at higher instanta-neous luminosity. Finally, at L3, at least four jets withET � 10 GeV (�R ¼ 0:4) are required. This trigger wasspecifically designed to collect all-hadronic t�t events,where the final state nominally consists of six jets, buthas a large acceptance also on final states characterizedby 6ET and high jet multiplicity. Moreover the collectedsample is uncorrelated with those used for top cross sectionmeasurements in the lepton plus jets final state, which areselected by requiring the presence of a high-momentumlepton. The choice of this trigger is also driven by theanalysis strategy: the top cross section measurement isperformed by counting the number of b-tagged jets fromtop decay in the final sample, and the multijet triggerprovides a sample that is unbiased with respect to theb-tagging algorithm, as it does not apply any requirementon tracks.

III. PRELIMINARY REQUIREMENTS

Events satisfying the trigger requirements are used in theanalysis only if they were collected with fully operationaltracking detectors, calorimeters and muon systems, and iftheir primary vertex is located within�60 cm along z fromthe center of the CDF II detector. Jets and 6ET are corrected[17] for multiple p �p interactions in the event, nonuniform-ities in the calorimeter response along �, and any nonline-arity and energy loss in the uninstrumented regions of thecalorimeters. The 6ET is also corrected for the presence ofhigh-pT muons.We consider jets with�R ¼ 0:4, correctedtransverse energy ET � 15 GeV and j�j � 2:0; the totaltransverse energy of the event

PET is defined as the sum

of all jets ET .Events are required to have at least three jets and no

central high-pT (pT > 20 GeV=c) reconstructed electronsor muons to avoid overlaps with other top cross sectionmeasurements in lepton and jets final states [18]. In thesame way, overlaps with top all-hadronic analyses areavoided by rejecting events with low 6ET significance

6EsigT , defined as 6Esig

T ¼ 6ET=ffiffiffiffiffiffiffiffiffiffiffiffiP

ET

p, where 6ET and

PET

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are measured in GeV, as the resolution on the 6ET isobserved to degrade as a function of the total transverse

energy of the event. The 6EsigT is typically low when 6ET

arises from mismeasurements, so events are required to

have 6EsigT � 3 GeV1=2.

Throughout the paper, the impact of analysis require-ments on signal is evaluated using inclusive t�t samplesgenerated with PYTHIA version v6.216 [19] and processedthrough CDF II detector and full trigger simulation [20],assuming a top mass mtop ¼ 172:5 GeV=c2. (The most

recent CDF and D0 combined result on top mass is mtop ¼173:3� 1:1 GeV=c2 [21].) After the preliminary cuts,there are 94 217 events remaining in the sample with atleast four jets, with an expected signal-to-background ratio(S=B) of 1.4% and 44 310 events in the sample with exactlythree jets, with an expected S=B lower than 0.1%. Thelatter sample, with a very low t�t signal content, will be usedto derive the background parametrization in Sec. IV.

IV. BACKGROUND PARAMETRIZATION

In this analysis, top quarks are identified by their decaysinto b quarks. However, many processes other than thedecay of the top quark can give rise to b jets; therefore aprocedure to estimate the number of b-tagged jets yieldedby background processes is needed.

The background-prediction method used in this analysisrests on the assumption that the probabilities of tagging a bjet in t�t signal and background processes are different: thedifferences are due to the distinctive properties of b jetsproduced by the top quark decays, compared to b jetsarising from QCD and W boson plus heavy flavor produc-tion processes. In this hypothesis, parametrizing the b-tagrates as a function of jet variables in events depleted ofsignal allows one to predict the number of b-tagged jetsfrom background processes in any given sample. Theparametrization is derived from a sample of pure back-ground: the data sample after the prerequisites requirementwith exactly three jets, where the t�t signal fraction is lower

than 0.1%. In this sample the per-jet b-tagging probabilityis found to depend mainly on jet ET , the number of goodquality tracks contained in the jet cone Ntrk, and the 6ET

projection along the jet direction 6ETprj, defined as 6ET

prj ¼6ET cos��ð6ET; jetÞ. These variables are chosen for the pa-rametrization, and their corresponding tag rate dependenceis shown in Fig. 1. We expect the tagging probability todepend on jet ET andNtrk due to the implementation detailsof the b-tagging algorithm [11]. In more detail, theb-tagging probability decreases at high jet ET due to thedeclining yield of tracks passing the quality cuts requiredby the b-tagging algorithm; it increases if a greater numberof good quality tracks is associated to the jet cone. The 6ET

projection along the jet direction is correlated with theheavy flavor component of the sample and the geometricproperties of the event. Neutrinos from the b-quark semi-leptonic decays force 6ET to be aligned with the jet direc-tion, while neutrinos fromW boson decays are more likelyto be away from jets. For this reason, the b-tag rate isenhanced at high positive values of 6ET

prj.A three-dimensional b-tagging matrix P is defined us-

ing the per-jet b-tagging probabilities, and its binning isdefined to avoid any entries with empty denominators. Thematrix assigns the probability that a jet is b-tagged given itsET , Ntrk and 6ET

prj. The total number of expected back-ground b-tagged jets Nexp in a given data sample can be

calculated by summing the b-tagging probabilities over alljets in the selected events:

Nexp ¼XNevt

i¼1

XNjets;i

k¼1

P iðEkT; N

ktrk; 6ET

prj;kÞ; (1)

where the index k runs over the number of jets Njets in the

i-th event and the index i runs over all theNevt events in thesample. Because of the method we used, Nexp is obtained

under the same assumption that allowed the parametriza-tion of the tagging rate, i.e. a negligible t�t signal content.For jet multiplicities greater than three, Nexp will over-

estimate the number of b-tagged jets from background

[GeV]TE

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FIG. 1. b tagging rates as a function of (a) jet ET , (b) Ntrk and (c) 6ETprj, for the data sample with exactly three jets in the event.

T. AALTONEN et al. PHYSICAL REVIEW D 84, 032003 (2011)

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events, Nbkg, due to the presence of t�t events in the sample.

If Nobs is the number of b-tagged jets observed in the datasample and we assume that the difference between Nobs

and Nbkg is due to the presence of t�t signal, the number of

top events in the sample ntop can be evaluated as ntop ¼ðNobs � NbkgÞ=�avetag , where �avetag is the average number of

b-tagged jets per top event, defined as the ratio between thenumber of b-tagged jets and the number of t�t events andcalculated from MC simulation. If nevt is the number ofevents in the sample, we can estimate the number ofb-tagged jets due to the background Nbkg by rescaling the

value Nexp predicted by the b-tagging matrix as follows:

Nbkg ¼ Nexpðnevt � ntopÞ=nevt. Putting the expressions for

Nbkg and ntop together, we can evaluate Nbkg as the limit of

the following iterative formula:

Nbkg ¼ limi!1Nexp;i (2)

with

Nexp;i ¼ Nexp;0

nevt � ntop

nevt

¼ Nexp;0

nevt � ðNobs � Nexp;i�1Þ=�avetag

nevt; (3)

where Nexp;0 ¼ Nexp is the number—fixed during the itera-

tion—of expected b-tagged jets coming from the tag rateparametrization before any correction. In our calculations

the iterative procedure stops whenjNexp;i�Nexp;i�1j

Nexp;i� 1%. This

correction procedure is used in all samples with more thanthree jets to remove the t�t contribution from the back-ground estimation. This method does not require

knowledge of the top production cross section, once weassume that the dependence of �avetag from the top quark

mass is negligible.To ensure the correct behavior of the b-tagging parame-

trization, an important check consists in calculating thepredicted number of b-tagged jets in data samples with jetmultiplicities higher than three, and comparing it with theactual observed number of b-tagged jets. The result of thischeck is shown in Fig. 2. Taking into account the expectedcontribution to the number of observed b-tagged jetsdue to the presence of t�t events in the sample (mtop ¼172:5 GeV=c2), the agreement between the amount of ob-served and predicted b-tagged jets is good in all the jetmultiplicity bins, being exactly the same by definition forthree-jet events, on which the parametrization is calculated.

V. SIGNAL AND BACKGROUNDCHARACTERIZATION

In the data sample under investigation, t�t pairs are over-whelmed by multijet QCD and W þ jets events. The mainfeature of the t�t decay channel analyzed here is a consid-erable amount of 6ET , the only observable signature of thepresence of neutrinos from W leptonic decays. However,missing transverse energy can be also produced by jetenergy mismeasurements, by semileptonic decays of bquarks in QCD events and by the leptonic decay of theW in W þ jets events. To discriminate against the possiblesources of missing transverse energy on a geometric basiswe use the quantity ��min ¼ min��ð6ET; jetÞ, defined asthe minimum angular difference between the 6ET and eachjet in the event. This quantity is expected to be large inW ! l� decays and in t�t ! 6ET þ jets events. On the otherhand, for QCD background events where the main sourceof 6ET is due to jet energy mismeasurement, the 6ET isexpected to be aligned with the jet direction and the valueof ��min close to zero.Other kinematic variables related to the topology of the

event characterize the t�t production with respect to back-ground processes. Let Qjðj¼1;3Þ be the eigenvalues of the

normalized momentum tensor

Mab ¼P

j PjaPjbPj P

2j

[22], where a, b run over the three space coordinates, andPj is the momentum of the jet j. The sphericity S is defined

as S ¼ 32 ð1�Q3Þ. S is zero in the limiting case of a pair of

back-to-back jets, while it approaches 1 for events with aperfectly isotropic jet momenta distribution. The aplanar-ity A is defined as A ¼ 3

2Q1 and lies in the range ½0; 12�.Extremal values of A are reached in the case of twoopposite jets and in the case of evenly distributed jets,respectively. Jets emerging from a t�t pair are expected tobe uniformly distributed and, as a consequence, they will

jetsN3 4 5 6 7 8

0

1000

2000

3000

4000

5000

6000

7000-1CDF Data L=2.2 fb

Background

uncertainty (stat)Background

=7.45 pb)σ(Inclusive top

# o

f b

-tag

ged

jets

FIG. 2. Tagging matrix check on data after preliminary re-quirements and before any additional kinematic selection.Observed and predicted number of b-tagged jets as a functionof the jet multiplicity are shown in the figure, statistical errorsonly. The expected contribution coming from t�t events based onthe theoretical cross section of �t�t ¼ 7:45 pb is also shown.Background error bands are centered on the inclusive top plusbackground prediction.

MEASUREMENT OF THE t�t PRODUCTION CROSS . . . PHYSICAL REVIEW D 84, 032003 (2011)

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hardly lie on the same plane: thus we expect high aplanar-ity and sphericity values for t�t events. In addition tokinematic variables describing the topology of the event,distributions of energy-related variables can be useful todiscriminate t�t events over their background. The central-

ity C is defined asC ¼ PET=

ffiffiffis

p, where

ffiffiffis

pis the invariant

mass of the jets system. In the case of t�t pairs decayinghadronically, jets are emitted preferably in the transverseplane (r�� plane), so we expect to have a greater amountof energy emitted in this plane giving values of C closer to1 with respect to background events. The variable

P3ET is

defined as the sum of all jets ET in the event except the twoleading ones. In QCD events, the two most energetic jetsare produced by q �q processes, while the least energeticones come from gluon bremsstrahlung; on the contrary, int�t events up to six jets can be produced by hard processes,and as a consequence

P3ET can help discriminating be-

tween signal and background. All these variables will beused in the following section to train a neural network todiscriminate t�t signal from background.

VI. NEURAL-NETWORK-BASEDEVENT SELECTION

In order to enhance the signal-to-background ratio in thedata sample, we use a neural network (NN), trained todiscriminate t�t ! 6ET þ jets signal events from back-ground. The NN is built using the neural network imple-mentation in ROOT [23].We apply an additional kinematic requirement on data

with at least four jets, removing events with low anglebetween jets and 6ET with the cut ��minðET; jetsÞ> 0:4. Inthe data these events come mostly from mismeasured jetsand are difficult to simulate in MC. They are removed fromthe NN training to prevent it from converging on artificialdifferences between MC and data rather than on realphysics effects. After this requirement, we are left with20 043 events in the sample with at least four jets, with anexpected S=B of 3.5%: since this sample has low t�t signalfraction and no overlap with data used to determine thebackground parametrization, it will be used as backgroundtraining sample. As signal training sample we use the same

[GeV]1TE

0 50 100 150 200 250 300

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ctio

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3 G

eV)

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]1/2 [GeV sigTE

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)

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5 G

eV)

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ctio

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ctio

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)

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Background

Signal

(h)

FIG. 3. Distribution of neural network input variables for multijet data (background) and t�t MC (signal) samples: (a) the transverse

energy of the leading jet E1T , (b) ��minð6ET; jetÞ, (c) 6Esig

T , (d)P

ET , (e)P

3ET , (f) the centrality C, and the topology-related variables

(g) sphericity S and (h) aplanarity A.

T. AALTONEN et al. PHYSICAL REVIEW D 84, 032003 (2011)

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amount of events passing the same event selection of data,taken randomly from the t�t simulation. We use as inputs forthe network the following kinematic variables, normalizedwith respect to their maximum values: the transverse en-

ergy of the leading jet E1T , ��minð6ET; jetÞ, 6Esig

T ,P

ET ,P3ET , the centrality C, and the topology-related variables

sphericity S and aplanarity A. The distributions of the inputvariables used in the NN for both the signal and thebackground training samples are shown in Fig. 3.

After the training, the b-tagged data are processed by theNN: Fig. 4 shows the number of observed b-tagged jetsversus the NN output NNout, along with the correspondingbackground prediction from the tag rate parametrizationand the expected contribution from t�t signal (mtop ¼172:5 GeV=c2), for events with at least four jets and withexactly three, four and five jets. The good agreementbetween data and the sum of expected background andt�t-induced b-tagged jets in the high NN output region isboth a confirmation of the effectiveness of the method weuse to estimate the background and a demonstration ofproper NN training and performance.

In order to select a signal-rich sample to perform thecross section measurement, we choose to cut on the NN

output value NNout. The cut is chosen with the aim ofminimizing the statistical uncertainty on the cross sectionmeasurement, maximizing S=B where S is the expectednumber of b-tagged jets from the signal and B is thepredicted number of background b-tagged jets. The formerquantity is evaluated from an inclusive t�t MC sample,while the latter is derived using the b-tagging matrixparametrization on data. The result of this optimizationprocedure is a cut on NNout � 0:8, which gives the lowestexpected statistical uncertainty on the cross section(�8%) and an expected S=B� 4. The expected signalsample composition after this cut is shown in Table I.

VII. SYSTEMATIC UNCERTAINTIES

The top quark pair production cross section is mea-sured as:

�ðp �p ! t�tÞ BRðt�t ! 6ET þ jetsÞ ¼ Nobs � Nexp

�kin �avetag L ; (4)

where Nobs and Nexp are the number of observed and

predicted tagged jets from background in the selectedsample, respectively; �kin is the kinematic efficiency of

outNN

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

# o

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ged

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uncertainty (stat)Background

=7.45 pb)σ(Inclusive top

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=7.45 pb)σ(Inclusive top

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ged

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/ 0.

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180N. Jets=4

-1CDF Data L=2.2 fb

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=7.45 pb)σ(Inclusive top

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# o

f b

-tag

ged

jets

/ 0.

02

0

10

20

30

40

50

60

70

80(d)

FIG. 4. Observed and matrix-predicted number of b-tagged jets versus neural network output in the multijet data for (a) all eventswith at least four jets, and for events with exactly (b) three, (c) four and (d) five jets, along with the expected contribution due to t�tsignal events. Background error bands are centered on the inclusive top plus background prediction.

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trigger, preliminary requirements and neural network se-lection determined using inclusive MC t�t events; �avetag ,

defined as the ratio of the number of b-tagged jets to thenumber of events in the inclusive t�t Monte Carlo sample,gives the average number of b-tagged jets per t�t event.Finally, L is the integrated luminosity of the data set used.All quantities in the denominator of Eq. (4), as well as thenumber of expected b-tagged jets, are subject to differentsources of systematic uncertainties.

The kinematic efficiency �kin is evaluated on inclusive t�tsamples generated with PYTHIA, and its uncertainty arisesfrom the particular choice of the MC generator, the set ofparton density functions used in the generator, as well asthe modeling of color reconnection effects and of the initialand final state radiation.

The MC generators differ in their hadronizationschemes and in their description of the underlying eventand multiple interactions: in order to evaluate the genera-tor dependence of the kinematic efficiency, we comparethe value of �kin obtained using PYTHIA with the valueobtained on a sample of events generated with HERWIG

v6.510 [24] and take the relative difference as the system-atic uncertainty.

The choice of parton distribution function (PDF) affectsthe kinematics of t�t events, and thus the acceptance forsignal events. We estimate this uncertainty comparing the�kin value derived from MC samples based on the defaultPDF CTEQ5L [25] with the one obtained using samplesbased on MRST72 and MRST75 [26], which differ by thevalue of the strong coupling constant s used to computethe PDF; we also consider the difference in the value of �kinobtained with the leading order (LO) and next to leadingorder (NLO) calculations of PDFs, evaluated using defaultCTEQ5L (LO) and CTEQ6M (NLO) PDFs, and derive thecorresponding uncertainty. We add these two contributionsin quadrature to obtain the systematic uncertainty due toour choice of PDF.

Uncertainties arising from the modeling of color recon-nection effects are estimated by evaluating the shift in thekinematic efficiency using two samples of events generatedby PYTHIA, corresponding to different models of colorreconnection [27].

Additional jets coming from initial and final state radia-tion might change the sample composition and affect theefficiency of the kinematic selection. The systematic un-certainty related to these effects is evaluated by calculatingthe shift in �kin using inclusive t�t samples with differentamounts of initial and final state radiation.The systematic uncertainty due to the calorimeter

response is accounted for by varying the corrected jetenergies within �1� of their corresponding systematicuncertainty and recalculating �kin after these variations.Finally, �kin is also affected by the simulation of the

trigger requirements on MC events, and a trigger accep-tance uncertainty is determined by comparing trigger turn-on curves between MC and data events.The average number of b-tagged jets per t�t event is

affected by the uncertainty on the scale factor used toaccount for the different efficiency of the b-tagging algo-rithm in data and inMC. The systematic uncertainty on �avetag

is obtained varying the scale factor within the �1� rangefrom its central value and determining, on the MC sample,the difference in terms of average number of b-tagged jetsper event with respect to the standard �avetag value.

The uncertainty on the number Nexp of matrix-predicted

b-tagged jets is calculated by comparing the number ofb-tagged jets yielded by the tagging matrix to the actualnumber of observed SECVTX-tagged jets in a control sam-ple depleted of signal (events with NN output lower than0.6). The relative difference between the expected andobserved number of tagged jets is taken as an estimate ofthe uncertainty of our background prediction.The luminosity measurement is affected by two sources

of uncertainty: the acceptance of the luminosity monitorand the total inelastic p �p cross section (60:7� 2:4 mb).The uncertainties on these quantities are 4.2% and 4.0%,respectively, giving a total uncertainty of 5.8% on theintegrated luminosity calculated for any given CDF dataset.

TABLE I. Expected signal sample composition (in %) after theNNout > 0:8 cut.

Number of jets 3 4 5 6 7 8 9 Total

All-hadronic 0.1 0.5 1.7 4.9 7.8 10.2 9.9 2.3

eþ jets 26.7 25.2 35.5 36.2 35.1 33.6 33.8 32.1

�þ jets 32.2 32.5 19.1 15.8 14.5 16.1 12.9 22.7

Dileptonic 6.5 2.3 1.1 0.7 0.5 0.6 0.0 1.4

Hadronic �þ jets 15.8 21.9 30.5 31.5 31.8 29.9 34.4 27.7

Leptonic �þ jets 11.7 13.2 9.9 9.1 8.9 8.1 8.4 10.8

�� 1.1 1.1 0.6 0.5 0.4 0.4 0.3 0.8

e=�þ � 6.0 3.4 1.6 1.3 0.9 1.1 0.3 2.2

TABLE II. Summary of relative systematic uncertainties onthe signal efficiency, and other uncertainties related to the crosssection evaluation.

Source Uncertainty

�kin systematics

Generator dependence 3.9%

PDFs 1.2%

Initial state radiation/final state radiation 2.7%

Color reconnection 4.3%

Jet energy scale 4.2%

Trigger simulation 3.0%

Other systematics

�avetag (b-tag scale factor) 3.9%

Background parametrization 2.5%

Luminosity measurement 5.8%

T. AALTONEN et al. PHYSICAL REVIEW D 84, 032003 (2011)

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The summary of all sources of systematic uncertaintiesto the cross section evaluation is listed in Table II.

VIII. CROSS SECTION MEASUREMENT

After the neural network selection, we are left with 1420events with at least four jets, of which 636 are b-tagged.Inserting in Eq. (4) the input parameters quoted inTable III, the measured cross section value is

�t�t ¼ 7:99� 0:55ðstatÞ � 0:76ðsystÞ � 0:46ðlumiÞ pb¼ 7:99� 1:05 pb:

Observed and expected b-tagged jets after selection fordifferent jet multiplicities are shown in Fig. 5, along withthe expected contribution of inclusive t�t signal, normalizedto the measured cross section.

IX. CONCLUSIONS

We presented a measurement of the t�t production crosssection in a final state with large missing transverse energyand multiple jets. We explicitly vetoed well-identifiedhigh-pT electrons or muons from W boson decay andrejected events with low missing transverse energy, toavoid overlaps with other cross section measurementsperformed by the CDF Collaboration. Using an optimizedneural-network-based kinematic selection and a bjet iden-tification technique on a sample of data corresponding toan integrated luminosity of 2:2 fb�1, we obtain a produc-tion cross section value of 7:99� 1:05 pb, in good agree-ment with the reference theoretical value of 7:46þ0:66

�0:80 pb[1] and with other next-to-next-to-leading-order calcula-tions [28] for a top mass of 172:5 GeV=c2. The agreementwith the most recent experimental determinations isalso good. Given the high precision of the result, this

independent cross section measurement will have a signifi-cant impact on a future CDF combined value. The same6ET þ jets selection can be used for top quark mass mea-surement to obtain a result statistically uncorrelated withthose of other methods.

ACKNOWLEDGMENTS

We thank the Fermilab staff and the technical staffs ofthe participating institutions for their vital contributions.This work was supported by the U.S. Department of Energyand National Science Foundation; the Italian IstitutoNazionale di Fisica Nucleare; the Ministry of Education,Culture, Sports, Science and Technology of Japan; theNatural Sciences and Engineering Research Council ofCanada; the National Science Council of the Republic ofChina; the Swiss National Science Foundation; theA. P. Sloan Foundation; the Bundesministerium fuerBildung und Forschung, Germany; the Korean Scienceand Engineering Foundation and the Korean ResearchFoundation; the Particle Physics and Astronomy ResearchCouncil and theRoyal Society, UK; theRussian Foundationfor Basic Research; the Comision Interministerial deCiencia y Tecnologia, Spain; and in part by the EuropeanCommunity’s Human Potential Programme under ContractNo. HPRN-CT-2002-00292, Probe for New Physics.

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TABLE III. Input values for the cross section measurement.�avetag is the average number of b-tagged jets per top event.

Variable Symbol Value

Integrated luminosity (pb�1) L 2207:5� 128Observed b-tagged jets Nobs 636

Background b-tagged jets Nbkg 131� 9:6Kinematic efficiency (%) �kin 3:53� 0:29b-tagged jets per t�t event �avetag 0:81� 0:03

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