Measurement of the <em>tt</em> production cross section in <em>pp</em> collisions at √s=1.96  TeV using events with large missing transverse energy and jets

Article

Reference

Measurement of the tt production cross section in pp collisions at

√s=1.96  TeV using events with large missing transverse energy and jets

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al .

Abstract

In this paper we report a measurement of the tt production cross section in pp collisions at s√=1.96  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 tt 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 tt production cross section of 7.99±0.55(stat)±0.76(syst)±0.46(lumi) pb, assuming a top mass mtop=172.5  GeV/c2, in agreement with previous measurements and standard model predictions.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of the tt production cross section in pp collisions at √s=1.96  TeV using events with large missing transverse energy and jets. Physical Review. D , 2011, vol. 84, no. 03, p. 032003

DOI : 10.1103/PhysRevD.84.032003

Available at:

http://archive-ouverte.unige.ch/unige:38708

Disclaimer: layout of this document may differ from the published version.

Measurement of the t t production cross section in p p collisions at ffiffiffi p s

¼ 1:96 TeV using events with large missing transverse energy and jets

T. Aaltonen,²¹B. A´ lvarez Gonza´lez,^9,wS. Amerio,^41aD. Amidei,³²A. Anastassov,³⁶A. Annovi,¹⁷J. Antos,¹² G. Apollinari,¹⁵J. A. Appel,¹⁵A. Apresyan,⁴⁶T. Arisawa,⁵⁶A. Artikov,¹³J. Asaadi,⁵¹W. Ashmanskas,¹⁵B. Auerbach,⁵⁹ A. Aurisano,⁵¹F. Azfar,⁴⁰W. Badgett,¹⁵A. Barbaro-Galtieri,²⁶V. E. Barnes,⁴⁶B. A. Barnett,²³P. Barria,^44c,44aP. Bartos,¹² M. Bauce,^41b,41aG. Bauer,³⁰F. Bedeschi,^44aD. Beecher,²⁸S. Behari,²³G. Bellettini,^44b,44aJ. Bellinger,⁵⁸D. Benjamin,¹⁴ A. Beretvas,¹⁵A. Bhatti,⁴⁸M. Binkley,^15,aD. Bisello,^41b,41aI. Bizjak,^28,aaK. R. Bland,⁵B. Blumenfeld,²³A. Bocci,¹⁴ A. Bodek,⁴⁷D. Bortoletto,⁴⁶J. Boudreau,⁴⁵A. Boveia,¹¹B. Brau,^15,bL. Brigliadori,^6b,6aA. Brisuda,¹²C. Bromberg,³³ E. Brucken,²¹M. Bucciantonio,^44b,44aJ. Budagov,¹³H. S. Budd,⁴⁷S. Budd,²²K. Burkett,¹⁵G. Busetto,^41b,41aP. Bussey,¹⁹

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Y. Kato,^39,oW. Ketchum,¹¹J. Keung,⁴³V. Khotilovich,⁵¹B. Kilminster,¹⁵D. H. Kim,²⁵H. S. Kim,²⁵H. W. Kim,²⁵ J. E. Kim,²⁵M. J. Kim,¹⁷S. B. Kim,²⁵S. H. Kim,⁵³Y. K. Kim,¹¹N. Kimura,⁵⁶M. Kirby,¹⁵S. Klimenko,¹⁶K. Kondo,⁵⁶

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P. Movilla Fernandez,¹⁵A. Mukherjee,¹⁵Th. Muller,²⁴P. Murat,¹⁵M. Mussini,^6b,6aJ. Nachtman,^15,nY. Nagai,⁵³ J. Naganoma,⁵⁶I. Nakano,³⁸A. Napier,⁵⁴J. Nett,⁵¹C. Neu,⁵⁵M. S. Neubauer,²²J. Nielsen,^26,fL. Nodulman,² O. Norniella,²²E. Nurse,²⁸L. Oakes,⁴⁰S. H. Oh,¹⁴Y. D. Oh,²⁵I. Oksuzian,⁵⁵T. Okusawa,³⁹R. Orava,²¹L. Ortolan,⁴

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

S. Rolli,⁵⁴R. Roser,¹⁵M. Rossi,^52aF. Rubbo,¹⁵F. Ruffini,^44c,44aA. Ruiz,⁹J. Russ,¹⁰V. Rusu,¹⁵A. Safonov,⁵¹ W. K. Sakumoto,⁴⁷Y. Sakurai,⁵⁶L. Santi,^52b,52aL. Sartori,^44aK. Sato,⁵³V. Saveliev,^42,uA. Savoy-Navarro,⁴² P. Schlabach,¹⁵A. Schmidt,²⁴E. E. Schmidt,¹⁵M. P. Schmidt,^59,aM. Schmitt,³⁶T. Schwarz,⁷L. Scodellaro,⁹ A. Scribano,^44c,44aF. Scuri,^44aA. Sedov,⁴⁶S. Seidel,³⁵Y. Seiya,³⁹A. Semenov,¹³F. Sforza,^44b,44aA. Sfyrla,²²

S. Z. Shalhout,⁷T. Shears,²⁷P. F. Shepard,⁴⁵M. Shimojima,^53,tS. Shiraishi,¹¹M. Shochet,¹¹I. Shreyber,³⁴ A. Simonenko,¹³P. Sinervo,³¹A. Sissakian,^13,aK. Sliwa,⁵⁴J. R. Smith,⁷F. D. Snider,¹⁵A. Soha,¹⁵S. Somalwar,⁵⁰ V. Sorin,⁴P. Squillacioti,¹⁵M. Stancari,¹⁵M. Stanitzki,⁵⁹R. St. Denis,¹⁹B. Stelzer,³¹O. Stelzer-Chilton,³¹D. Stentz,³⁶

J. Strologas,³⁵G. L. Strycker,³²Y. Sudo,⁵³A. Sukhanov,¹⁶I. Suslov,¹³K. Takemasa,⁵³Y. Takeuchi,⁵³J. Tang,¹¹ M. Tecchio,³²P. K. Teng,¹J. Thom,^15,hJ. Thome,¹⁰G. A. Thompson,²²E. Thomson,⁴³P. Ttito-Guzma´n,²⁹S. Tkaczyk,¹⁵

D. Toback,⁵¹S. Tokar,¹²K. Tollefson,³³T. Tomura,⁵³D. Tonelli,¹⁵S. Torre,¹⁷D. Torretta,¹⁵P. Totaro,^52b,52a M. Trovato,^44d,44aY. Tu,⁴³F. Ukegawa,⁵³S. Uozumi,²⁵A. Varganov,³²F. Va´zquez,^16,lG. Velev,¹⁵C. Vellidis,³M. Vidal,²⁹

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J. C. Yun,¹⁵A. Zanetti,^52aY. Zeng,¹⁴and S. Zucchelli^6b,6a (CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798, USA

6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy

7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA

9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

14Duke University, Durham, North Carolina 27708, USA

15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

16University of Florida, Gainesville, Florida 32611, USA

17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

18University of Geneva, CH-1211 Geneva 4, Switzerland

19Glasgow University, Glasgow G12 8QQ, United Kingdom

20Harvard University, Cambridge, Massachusetts 02138, USA

21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

22University of Illinois, Urbana, Illinois 61801, USA

23The Johns Hopkins University, Baltimore, Maryland 21218, USA

24Institut fu¨r 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, Korea

26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28University College London, London WC1E 6BT, United Kingdom

29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

31Institute of Particle Physics, McGill University, Montre´al, Que´bec, 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

32University of Michigan, Ann Arbor, Michigan 48109, USA

33Michigan State University, East Lansing, Michigan 48824, USA

34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

35University of New Mexico, Albuquerque, New Mexico 87131, USA

36Northwestern University, Evanston, Illinois 60208, USA

37The Ohio State University, Columbus, Ohio 43210, USA

38Okayama University, Okayama 700-8530, Japan

39Osaka City University, Osaka 588, Japan

40University of Oxford, Oxford OX1 3RH, United Kingdom

41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

41bUniversity of Padova, I-35131 Padova, Italy

42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

44bUniversity of Pisa, I-56127 Pisa, Italy

44cUniversity of Siena, I-56127 Pisa, Italy

44dScuola Normale Superiore, I-56127 Pisa, Italy

45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

46Purdue University, West Lafayette, Indiana 47907, USA

47University of Rochester, Rochester, New York 14627, USA

48The Rockefeller University, New York, New York 10065, USA

49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

49bSapienza Universita` di Roma, I-00185 Roma, Italy

50Rutgers University, Piscataway, New Jersey 08855, USA

51Texas A&M University, College Station, Texas 77843, USA

52aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, I-33100 Udine, Italy

52bUniversity of Trieste/Udine, I-33100 Udine, Italy

53University of Tsukuba, Tsukuba, Ibaraki 305, Japan

54Tufts University, Medford, Massachusetts 02155, USA

55University of Virginia, Charlottesville, Virginia 22906, USA

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

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MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D84,032003 (2011)

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 11 May 2011; published 9 August 2011)

In this paper we report a measurement of the ttproduction cross section inpp collisions at ffiffiffi ps

¼ 1:96 TeV using data corresponding to an integrated luminosity of 2:2 fb¹ 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 ofttdecays. 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 ttproduction cross section of 7:990:55ðstatÞ 0:76ðsystÞ 0:46ðlumiÞ pb, assuming a top mass mtop¼172:5 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 Inpp collisions at ffiffiffi

ps

¼1:96 TeVat the Tevatron, top quarks are produced mainly in pairs through quark- antiquark annihilation and gluon-gluon fusion processes.

In the standard model (SM), the calculated cross section for top pair production at the Tevatron center-of-mass energy is 7:46^þ0:66_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 new massive resonances [2], while the comparison of the top pair production cross section in different decay channels can be sensitive to the presence of top decays via a charged Higgs boson [3]. Thus, a precise measurement of the top pair production cross section is an important test of the SM. Both CDF and D0 Collaborations have performed many measurements of this quantity in different tt final states: the most recent published results, both measured in the decay channel with leptons and jets assumingmtop ¼ 172:5 GeV=c², are 7:700:52 pb for CDF [4] and 7:78^þ0:77_0:64pbfor D0 [5].

As the Cabibbo-Kobayashi-Maskawa matrix element V_tbis close to unity [6,7] and the top massmtop is larger than the sum of theWboson and bottom quark (b) masses, in the SM the t!Wb decay is dominant and has a branching ratio of about 100%. Since theW subsequently decays either to a quark-antiquark pair or to a lepton- neutrino pair, the resulting top pair production final states can be classified by the number of energetic charged leptons and the number of jets. When only oneW decays leptonically, thettevent is characterized by the presence of a charged lepton, missing energy due to the undetected neutrino, and four high energy jets, two of which originate frombquarks. In thislepton plus jetschannel, one selects events with an energetic electron or muon. For this paper we focus on an inclusive high-momentum neutrino signa- ture of large missing energy accompanied by jets. By not explicitly requiring leptons, our measurement is sensitive to allWleptonic decay modes includingdecays ofW’s:

about 40% of the signal sample obtained after the kine- matic selection contains events with a lepton in the final state. To ensure our measurement is statistically

independent from other CDF results [8], we veto events with high-momentum electrons or muons as well as multi- jet events with no leptons (all-hadronic ttdecays). This choice is expected to improve the final CDF combined cross section value: the previous 311 pb¹ 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 bandc jets (heavy flavor jets), which dominates the signal by 2 orders of magnitude before any selection. In order to improve the signal-to-background ratio (S=B), a neural network is trained to identify the kinematic and topological characteristics of SM ttevents and is applied to data to select a signal-rich sample. Top quarks are then identified by their distinctive decay into b quarks. Jets originating from b quarks (b jets) are selected (‘‘tagged’’) by their displaced vertex as defined by theSECVTXalgorithm [11].

After evaluating the average number ofb-tagged jets fortt events using a Monte Carlo (MC) simulation, the number of signal events in the sample and the corresponding cross section are measured by counting the number ofb-tagged jets in the sample selected by the neural network. The number of background b-tagged jets is estimated using per-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 between March 2002 and August 2007, corresponding to an inte- grated luminosity of 2:2 fb¹, 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 of the trigger requirements used for this analysis. The pre- liminary cleanup cuts applied to data are described in Sec. III, followed by the discussion of the data-driven background parametrization in Sec. IV. The kinematic variables characterizing the missing energy plus jets final state and the neural-network-based sample selection are described in Sec.Vand Sec.VI, respectively. We conclude the description of this measurement with a summary of the

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

II. THE CDF DETECTOR AND TRIGGER SYSTEM CDF II is a general-purpose, azimuthally and forward- backward symmetric detector located at the Tevatronpp collider 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 usesand as the polar and azimuthal angles, respectively, defined with re- spect to the proton beam axis direction,z. Thex-axis points toward the center of the accelerator while theyaxis points upward from the beam. The pseudorapidityis defined as ln½tanð=2Þ. The transverse momentum of a parti- cle isp_T ¼psinand its transverse energyE_T ¼Esin. The missing transverse energy6ET measures the transverse energy of the neutrinos via the imbalance of the energy detected in the calorimeters; it is defined by 6E_T ¼ j6E~_Tj where6E~T¼ P

iEⁱ_Tn^i, the indexiruns over the calorime- ter tower number and n^_i is a unit vector perpendicular to the beam axis and pointing at the i-th calorimeter tower.

The tracking system is composed of eight layers of silicon microstrip detectors, extending from 1.6 cm to 28 cm and covering up tojj<2:0, surrounded by a 3.1 m long open cell drift chamber, providingjjcoverage up to 1.0. Using information from the silicon detectors, the primary inter- action vertex is reconstructed with a precision of15m in the plane transverse to the beam [13]. The energy of the particles traversing the detector is measured by electro- magnetic and hadronic calorimeters segmented into pro- jective towers covering up to jj<3:6. In the central region (jj<1:1) the calorimetric towers are 15 wide inand 0.1 in; in the forward region (1:1<jj<3:6) the towers are 7.5 wide in azimuthal angle forjj<2:1 and 15forjj>2:1. The electromagnetic section is made of lead-scintillator plates, while the hadronic section uses iron-scintillator ones. The transverse profile of electromag- netic showers is measured by proportional chambers and scintillating strip detectors. Muons are detected up tojj<

0:6 by drift chambers located outside the hadronic calo- rimeters, behind a 60 cm iron shield. Additional drift chambers and scintillator detectors provide muon detection up tojj<1:5.

The CDF II trigger system [14] has a three-level archi- tecture designed to operate at 2.53 MHz and reduce the data rate to approximately 120 Hz to be written on tape.

The data used in this measurement are collected with a purely calorimetric trigger, described in Sec. IIA. At Level- 1 (L1) calorimetric towers are merged in pairs alongto define trigger towers: the L1 can take a decision on the energy contribution of individual trigger towers, on the sum of the energy of all the towers or on the missing

transverse energy of the event. At Level-2 (L2) trigger towers are merged into clusters by a simple clustering algorithm [15], while at Level-3 (L3) jets of particles are reconstructed by a fixed cone-based algorithm [16], the radius of the cone in theffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi plane (R¼

²þ²

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 multijet trigger. This trigger requires at L1 the presence of at least one central trigger tower withE_T 10 GeV, and at L2 at least four calorimetric clusters with E_T 15 GeV each and a total transverse energy greater than 175 GeV. The latter threshold was 125 GeV before February 2005 and was increased to reduce the trigger rate at higher instanta- neous luminosity. Finally, at L3, at least four jets with E_T 10 GeV (R¼0:4) are required. This trigger was specifically designed to collect all-hadronic tt events, where the final state nominally consists of six jets, but has a large acceptance also on final states characterized by 6ET and high jet multiplicity. Moreover the collected sample is uncorrelated with those used for top cross section measurements in the lepton plus jets final state, which are selected by requiring the presence of a high-momentum lepton. The choice of this trigger is also driven by the analysis strategy: the top cross section measurement is performed by counting the number of b-tagged jets from top decay in the final sample, and the multijet trigger provides a sample that is unbiased with respect to the b-tagging algorithm, as it does not apply any requirement on tracks.

III. PRELIMINARY REQUIREMENTS Events satisfying the trigger requirements are used in the analysis only if they were collected with fully operational tracking detectors, calorimeters and muon systems, and if their primary vertex is located within60 cmalongzfrom the center of the CDF II detector. Jets and6ETare corrected [17] for multiplepp interactions in the event, nonuniform- ities in the calorimeter response along, and any nonline- arity and energy loss in the uninstrumented regions of the calorimeters. The 6E_T is also corrected for the presence of high-p_Tmuons. We consider jets withR¼0:4, corrected transverse energy E_T 15 GeV andjj 2:0; the total transverse energy of the eventP

E_T is defined as the sum of all jetsE_T.

Events are required to have at least three jets and no central high-pT (pT>20 GeV=c) reconstructed electrons or muons to avoid overlaps with other top cross section measurements in lepton and jets final states [18]. In the same way, overlaps with top all-hadronic analyses are avoided by rejecting events with low 6ET significance 6E^sig_T , defined as 6E^sig_T ¼ 6E_T=pffiffiffiffiffiffiffiffiffiffiffiffiPE_T

, where 6E_T and PE_T MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D84,032003 (2011)

are measured in GeV, as the resolution on the 6E_T is observed to degrade as a function of the total transverse energy of the event. The 6E^sig_T is typically low when 6ET

arises from mismeasurements, so events are required to have6E^sig_T 3 GeV¹⁼².

Throughout the paper, the impact of analysis require- ments on signal is evaluated using inclusive tt samples generated withPYTHIAversion v6.216 [19] and processed through CDF II detector and full trigger simulation [20], assuming a top mass mtop¼172:5 GeV=c². (The most recent CDF and D0 combined result on top mass ismtop ¼ 173:31:1 GeV=c² [21].) After the preliminary cuts, there are 94 217 events remaining in the sample with at least four jets, with an expected signal-to-background ratio (S=B) of 1.4% and 44 310 events in the sample with exactly three jets, with an expected S=B lower than 0.1%. The latter sample, with a very lowttsignal content, will be used to derive the background parametrization in Sec.IV.

IV. BACKGROUND PARAMETRIZATION In this analysis, top quarks are identified by their decays into b quarks. However, many processes other than the decay of the top quark can give rise tobjets; therefore a procedure to estimate the number ofb-tagged jets yielded by background processes is needed.

The background-prediction method used in this analysis rests on the assumption that the probabilities of tagging ab jet inttsignal and background processes are different: the differences are due to the distinctive properties of b jets produced by the top quark decays, compared to b jets arising from QCD andW boson plus heavy flavor produc- tion processes. In this hypothesis, parametrizing theb-tag rates as a function of jet variables in events depleted of signal allows one to predict the number of b-tagged jets from background processes in any given sample. The parametrization is derived from a sample of pure back- ground: the data sample after the prerequisites requirement with exactly three jets, where thettsignal fraction is lower

than 0.1%. In this sample the per-jetb-tagging probability is found to depend mainly on jet E_T, the number of good quality tracks contained in the jet cone Ntrk, and the 6E_T projection along the jet direction 6E_T^prj, defined as6E_T^prj¼ 6E_Tcosð6E_T;jetÞ. These variables are chosen for the pa- rametrization, and their corresponding tag rate dependence is shown in Fig. 1. We expect the tagging probability to depend on jetE_TandNtrkdue to the implementation details of the b-tagging algorithm [11]. In more detail, the b-tagging probability decreases at high jetET due to the declining yield of tracks passing the quality cuts required by theb-tagging algorithm; it increases if a greater number of good quality tracks is associated to the jet cone. The6ET

projection along the jet direction is correlated with the heavy flavor component of the sample and the geometric properties of the event. Neutrinos from the b-quark semi- leptonic decays force 6E_T to be aligned with the jet direc- tion, while neutrinos fromWboson decays are more likely to be away from jets. For this reason, the b-tag rate is enhanced at high positive values of 6E_T^prj.

A three-dimensionalb-tagging matrixP is defined us- ing the per-jet b-tagging probabilities, and its binning is defined to avoid any entries with empty denominators. The matrix assigns the probability that a jet isb-tagged given its E_T, Ntrk and 6E_T^prj. The total number of expected back- ground b-tagged jetsNexp in a given data sample can be calculated by summing theb-tagging probabilities over all jets in the selected events:

Nexp¼^NX^evt

i¼1 NXjets;i

k¼1

PiðE^k_T; N_trk^k ;6E_T^prj;kÞ; (1)

where the indexkruns over the number of jetsNjetsin the i-th event and the indexiruns over all theNevtevents in the sample. 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 negligiblettsignal content.

For jet multiplicities greater than three, Nexp will over- estimate the number of b-tagged jets from background

[GeV]

ET

50 100 150 200 250

Tag Rate

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

(a)

Ntrk

2 4 6 8 10 12 14

Tag Rate

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

(b)

[GeV]

prj

ET

-100 -80 -60 -40 -20 0 20 40 60 80 100

Tag Rate

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

(c)

FIG. 1. btagging rates as a function of (a) jetE_T, (b)Ntrk and (c)6E_T^prj, for the data sample with exactly three jets in the event.

events,Nbkg, due to the presence ofttevents in the sample.

IfNobsis the number ofb-tagged jets observed in the data sample and we assume that the difference between Nobs

andNbkg is due to the presence ofttsignal, the number of top events in the sample ntop can be evaluated as ntop ¼ ðNobsNbkgÞ=^avetag, where ^avetag is the average number of b-tagged jets per top event, defined as the ratio between the number of b-tagged jets and the number ofttevents and calculated from MC simulation. If nevt is the number of events in the sample, we can estimate the number of b-tagged jets due to the backgroundNbkg by rescaling the valueNexp predicted by the b-tagging matrix as follows:

Nbkg ¼NexpðnevtntopÞ=nevt. Putting the expressions for Nbkgandntoptogether, we can evaluateNbkgas the limit of the following iterative formula:

Nbkg ¼lim

i!1Nexp;i (2)

with

N_exp;i¼N_exp;0nevtntop

nevt

¼Nexp;0nevt ðNobsNexp;i1Þ=^avetag

nevt ; (3)

whereN_exp;0¼Nexpis the number—fixed during the itera- tion—of expectedb-tagged jets coming from the tag rate parametrization before any correction. In our calculations the iterative procedure stops when^jNexp;i_N^Nexp;i1j

exp;i 1%. This

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

knowledge of the top production cross section, once we assume that the dependence of ^avetag from the top quark mass is negligible.

To ensure the correct behavior of theb-tagging parame- trization, an important check consists in calculating the predicted number ofb-tagged jets in data samples with jet multiplicities higher than three, and comparing it with the actual observed number ofb-tagged jets. The result of this check is shown in Fig.2. Taking into account the expected contribution to the number of observed b-tagged jets due to the presence of tt events in the sample (mtop¼ 172:5 GeV=c²), the agreement between the amount of ob- served and predicted b-tagged jets is good in all the jet multiplicity bins, being exactly the same by definition for three-jet events, on which the parametrization is calculated.

V. SIGNAL AND BACKGROUND CHARACTERIZATION

In the data sample under investigation,ttpairs are over- whelmed by multijet QCD andWþjets events. The main feature of thettdecay channel analyzed here is a consid- erable amount of 6E_T, the only observable signature of the presence of neutrinos from W leptonic decays. However, missing transverse energy can be also produced by jet energy mismeasurements, by semileptonic decays of b quarks in QCD events and by the leptonic decay of the W inWþjets events. To discriminate against the possible sources of missing transverse energy on a geometric basis we use the quantity min¼minð6ET;jetÞ, defined as the minimum angular difference between the6ET and each jet in the event. This quantity is expected to be large in W !ldecays and intt! 6ETþjets events. On the other hand, for QCD background events where the main source of 6E_T is due to jet energy mismeasurement, the 6E_T is expected to be aligned with the jet direction and the value ofminclose to zero.

Other kinematic variables related to the topology of the event characterize the ttproduction with respect to back- ground processes. Let Q_jðj¼1;3Þ be the eigenvalues of the normalized momentum tensor

M_ab¼

PjP_jaP_jb PjP²_j

[22], wherea,brun over the three space coordinates, and Pjis the momentum of the jetj. The sphericitySis defined asS¼³₂ð1Q3Þ.Sis zero in the limiting case of a pair of back-to-back jets, while it approaches 1 for events with a perfectly isotropic jet momenta distribution. The aplanar- ity A is defined as A¼³₂Q1 and lies in the range ½0;¹₂. Extremal values of A are reached in the case of two opposite jets and in the case of evenly distributed jets, respectively. Jets emerging from attpair are expected to be uniformly distributed and, as a consequence, they will Njets

3 4 5 6 7 8

0 1000 2000 3000 4000 5000 6000 7000

CDF Data L=2.2 fb-1

Background

uncertainty (stat) Background

=7.45 pb) σ (

Inclusive top

# of b-tagged jets

FIG. 2. Tagging matrix check on data after preliminary re- quirements and before any additional kinematic selection.

Observed and predicted number ofb-tagged jets as a function of the jet multiplicity are shown in the figure, statistical errors only. The expected contribution coming fromttevents based on the theoretical cross section of _tt¼7:45 pb is also shown.

Background error bands are centered on the inclusive top plus background prediction.

MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D84,032003 (2011)

hardly lie on the same plane: thus we expect high aplanar- ity and sphericity values for tt events. In addition to kinematic variables describing the topology of the event, distributions of energy-related variables can be useful to discriminatettevents over their background. The central- ityCis defined asC¼P

E_T= ffiffiffi s^

p , where ffiffiffi s^

p is the invariant mass of the jets system. In the case ofttpairs decaying hadronically, jets are emitted preferably in the transverse plane (rplane), so we expect to have a greater amount of energy emitted in this plane giving values ofCcloser to 1 with respect to background events. The variableP

3E_T is defined as the sum of all jetsE_Tin the event except the two leading ones. In QCD events, the two most energetic jets are produced by qq processes, while the least energetic ones come from gluon bremsstrahlung; on the contrary, in ttevents up to six jets can be produced by hard processes, and as a consequence P

3ET can help discriminating be- tween signal and background. All these variables will be used in the following section to train a neural network to discriminatettsignal from background.

VI. NEURAL-NETWORK-BASED EVENT SELECTION

In order to enhance the signal-to-background ratio in the data sample, we use a neural network (NN), trained to discriminate tt! 6ETþjets signal events from back- ground. The NN is built using the neural network imple- mentation inROOT[23].

We apply an additional kinematic requirement on data with at least four jets, removing events with low angle between jets and6ET with the cutminðET;jetsÞ>0:4. In the data these events come mostly from mismeasured jets and are difficult to simulate in MC. They are removed from the NN training to prevent it from converging on artificial differences between MC and data rather than on real physics effects. After this requirement, we are left with 20 043events in the sample with at least four jets, with an expectedS=Bof 3.5%: since this sample has lowttsignal fraction and no overlap with data used to determine the background parametrization, it will be used as background training sample. As signal training sample we use the same

[GeV]

1

ET

0 50 100 150 200 250 300

Fraction/(3 GeV)

0 0.01 0.02 0.03 0.04

0.05 Background

Signal (a)

[rad]

φmin

∆

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Fraction/(0.025 rad)

0 0.01 0.02 0.03 0.04 0.05 0.06

0.07 Background

Signal (b)

1/2] [GeV

sig

ET

3 4 5 6 7 8 9 10

1/2 Fraction/(0.1 GeV )

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0.18 Background

Signal (c)

[GeV]

ET

Σ

0 100 200 300 400 500 600

Fraction/(5 GeV)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Background Signal (d)

[GeV]

ET

Σ3

50 100 150 200 250

Fraction/(5 GeV)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Background Signal (e)

Centrality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction/(0.01)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Background Signal (f)

Sphericity

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction/(0.01)

0 0.005 0.01 0.015 0.02 0.025

Background Signal (g)

Aplanarity

0 0.05 0.1 0.15 0.2 0.25 0.3

Fraction/(0.005)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Background Signal (h)

FIG. 3. Distribution of neural network input variables for multijet data (background) andttMC (signal) samples: (a) the transverse energy of the leading jetE¹_T, (b)minð6E_T;jetÞ, (c)6E^sig_T , (d)P

E_T, (e)P

3E_T, (f ) the centralityC, and the topology-related variables (g) sphericitySand (h) aplanarityA.

amount of events passing the same event selection of data, taken randomly from thettsimulation. We use as inputs for the network the following kinematic variables, normalized with respect to their maximum values: the transverse en- ergy of the leading jet E¹_T, minð6ET;jetÞ, 6E^sig_T , P

ET, P3E_T, the centralityC, and the topology-related variables sphericitySand aplanarityA. The distributions of the input variables used in the NN for both the signal and the background training samples are shown in Fig.3.

After the training, theb-tagged data are processed by the NN: Fig. 4 shows the number of observed b-tagged jets versus the NN outputNN_out, along with the corresponding background prediction from the tag rate parametrization and the expected contribution from tt signal (mtop ¼ 172:5 GeV=c²), for events with at least four jets and with exactly three, four and five jets. The good agreement between data and the sum of expected background and tt-induced b-tagged jets in the high NN output region is both a confirmation of the effectiveness of the method we use to estimate the background and a demonstration of proper NN training and performance.

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

output value NN_out. The cut is chosen with the aim of minimizing the statistical uncertainty on the cross section measurement, maximizing S=B where S is the expected number of b-tagged jets from the signal and B is the predicted number of backgroundb-tagged jets. The former quantity is evaluated from an inclusive tt MC sample, while the latter is derived using the b-tagging matrix parametrization on data. The result of this optimization procedure is a cut onNN_out0:8, which gives the lowest expected statistical uncertainty on the cross section (8%) and an expected S=B4. The expected signal sample composition after this cut is shown in TableI.

VII. SYSTEMATIC UNCERTAINTIES The top quark pair production cross section is mea- sured as:

ðpp !ttÞ BRðtt! 6ETþjetsÞ ¼ NobsNexp

kin^avetag L; (4) where Nobs and Nexp are the number of observed and predicted tagged jets from background in the selected sample, respectively; kin is the kinematic efficiency of

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

# of b-tagged jets / 0.02

0 50 100 150 200 250

N. Jets>3 CDF Data L=2.2 fb-1

Background uncertainty (stat) Background

=7.45 pb) σ (

Inclusive top

(a)

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

10-2

10-1

1 10 102

N. Jets=3 CDF Data L=2.2 fb-1 Background uncertainty (stat) Background

=7.45 pb) σ ( Inclusive top

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

# of b-tagged jets / 0.04 _-2 10 10-1

1 10 102

(b)

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0 20 40 60 80 100 120 140 160 180

N. Jets=4 CDF Data L=2.2 fb-1

Background uncertainty (stat) Background

=7.45 pb) σ (

Inclusive top

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

# of b-tagged jets / 0.02

0 20 40 60 80 100 120 140 160 180 (c)

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0 10 20 30 40 50 60 70 80

N. Jets=5 CDF Data L=2.2 fb-1

Background uncertainty (stat) Background

=7.45 pb) σ (

Inclusive top

NNout

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

# of b-tagged jets / 0.02

0 10 20 30 40 50 60 70 80 (d)

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

MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D84,032003 (2011)