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Search for Anomalous Kinematics in t t Dilepton Events at CDF II

D. Acosta,16J. Adelman,12T. Affolder,9T. Akimoto,54M. G. Albrow,15D. Ambrose,43S. Amerio,42D. Amidei,33 A. Anastassov,50K. Anikeev,15A. Annovi,44J. Antos,1M. Aoki,54G. Apollinari,15T. Arisawa,56J.-F. Arguin,32 A. Artikov,13W. Ashmanskas,15A. Attal,7F. Azfar,41P. Azzi-Bacchetta,42N. Bacchetta,42H. Bachacou,28W. Badgett,15 A. Barbaro-Galtieri,28G. J. Barker,25V. E. Barnes,46B. A. Barnett,24S. Baroiant,6M. Barone,17G. Bauer,31F. Bedeschi,44

S. Behari,24S. Belforte,53G. Bellettini,44J. Bellinger,58E. Ben-Haim,15D. Benjamin,14A. Beretvas,15A. Bhatti,48 M. Binkley,15D. Bisello,42M. Bishai,15R. E. Blair,2C. Blocker,5K. Bloom,33B. Blumenfeld,24A. Bocci,48A. Bodek,47

G. Bolla,46A. Bolshov,31P. S. L. Booth,29D. Bortoletto,46J. Boudreau,45S. Bourov,15B. Brau,9C. Bromberg,34 E. Brubaker,12J. Budagov,13H. S. Budd,47K. Burkett,15G. Busetto,42P. Bussey,19K. L. Byrum,2S. Cabrera,14 M. Campanelli,18M. Campbell,33A. Canepa,46M. Casarsa,53D. Carlsmith,58S. Carron,14R. Carosi,14M. Cavalli-Sforza,3

A. Castro,4P. Catastini,44D. Cauz,53A. Cerri,28L. Cerrito,23J. Chapman,33C. Chen,43Y. C. Chen,1M. Chertok,6 G. Chiarelli,44G. Chlachidze,13F. Chlebana,15I. Cho,27K. Cho,27D. Chokheli,13J. P. Chou,20M. L. Chu,1S. Chuang,58

J. Y. Chung,38W.-H. Chung,58Y. S. Chung,47C. I. Ciobanu,23M. A. Ciocci,44A. G. Clark,18D. Clark,5M. Coca,47 A. Connolly,28M. Convery,48J. Conway,6B. Cooper,30M. Cordelli,17G. Cortiana,42J. Cranshaw,52J. Cuevas,10 R. Culbertson,15C. Currat,28D. Cyr,58D. Dagenhart,5S. Da Ronco,42S. D’Auria,19P. de Barbaro,47S. De Cecco,49

G. De Lentdecker,47S. Dell’Agnello,17M. Dell’Orso,44S. Demers,47L. Demortier,48M. Deninno,4D. De Pedis,49 P. F. Derwent,15C. Dionisi,49J. R. Dittmann,15C. Do¨rr,25P. Doksus,23A. Dominguez,28S. Donati,44M. Donega,18 J. Donini,42M. D’Onofrio,18T. Dorigo,42V. Drollinger,36K. Ebina,56N. Eddy,23J. Ehlers,18R. Ely,28R. Erbacher,6

M. Erdmann,25D. Errede,23S. Errede,23R. Eusebi,47H.-C. Fang,28S. Farrington,29I. Fedorko,44W. T. Fedorko,12 R. G. Feild,59M. Feindt,25J. P. Fernandez,46C. Ferretti,33R. D. Field,16G. Flanagan,34B. Flaugher,15

L. R. Flores-Castillo,45A. Foland,20S. Forrester,6G. W. Foster,15M. Franklin,20J. C. Freeman,28Y. Fujii,26I. Furic,12 A. Gajjar,29A. Gallas,37J. Galyardt,11M. Gallinaro,48M. Garcia-Sciveres,28A. F. Garfinkel,46C. Gay,59H. Gerberich,14

D. W. Gerdes,33E. Gerchtein,11S. Giagu,49P. Giannetti,44A. Gibson,28K. Gibson,11C. Ginsburg,58K. Giolo,46 M. Giordani,53M. Giunta,44G. Giurgiu,11V. Glagolev,13D. Glenzinski,15M. Gold,36N. Goldschmidt,33D. Goldstein,7

J. Goldstein,41G. Gomez,10G. Gomez-Ceballos,31M. Goncharov,51O. Gonza´lez,46I. Gorelov,36A. T. Goshaw,14 Y. Gotra,45K. Goulianos,48A. Gresele,4M. Griffiths,29C. Grosso-Pilcher,12U. Grundler,23M. Guenther,46 J. Guimaraes da Costa,20C. Haber,28K. Hahn,43S. R. Hahn,15E. Halkiadakis,47A. Hamilton,32B.-Y. Han,47R. Handler,58 F. Happacher,17K. Hara,54M. Hare,55R. F. Harr,57R. M. Harris,15F. Hartmann,25K. Hatakeyama,48J. Hauser,7C. Hays,14 H. Hayward,29E. Heider,55B. Heinemann,29J. Heinrich,43M. Hennecke,25M. Herndon,24C. Hill,9D. Hirschhbuehl,25 A. Hocker,47K. D. Hoffman,12A. Holloway,20S. Hou,1M. A. Houlden,29B. T. Huffman,41Y. Huang,14R. E. Hughes,38

J. Huston,34K. Ikado,56J. Incandela,9G. Introzzi,44M. Iori,49Y. Ishizawa,54C. Issever,9A. Ivanov,47Y. Iwata,22 B. Iyutin,31E. James,15D. Jang,50J. Jarrell,36D. Jeans,49H. Jensen,15E. J. Jeon,27M. Jones,46K. K. Joo,27S. Y. Jun,11 T. Junk,23T. Kamon,51J. Kang,33M. Karagoz Unel,37P. E. Karchin,57S. Kartal,15Y. Kato,40Y. Kemp,25R. Kephart,15

U. Kerzel,25V. Khotilovich,51B. Kilminster,38D. H. Kim,27H. S. Kim,23J. E. Kim,27M. J. Kim,11M. S. Kim,27 S. B. Kim,27S. H. Kim,54T. H. Kim,31Y. K. Kim,12B. T. King,29M. Kirby,14L. Kirsch,5S. Klimenko,16B. Knuteson,31 B. R. Ko,14H. Kobayashi,54P. Koehn,38D. J. Kong,27K. Kondo,56J. Konigsberg,16K. Kordas,32A. Korn,31A. Korytov,16

K. Kotelnikov,35A. V. Kotwal,14A. Kovalev,43J. Kraus,23I. Kravchenko,31A. Kreymer,15J. Kroll,43M. Kruse,14 V. Krutelyov,51S. E. Kuhlmann,2S. Kwang,12A. T. Laasanen,46S. Lai,32S. Lami,48S. Lammel,15J. Lancaster,14 M. Lancaster,30R. Lander,6K. Lannon,38A. Lath,50G. Latino,36R. Lauhakangas,21I. Lazzizzera,42Y. Le,24C. Lecci,25 T. LeCompte,2J. Lee,27J. Lee,47S. W. Lee,51R. Lefe`vre,3N. Leonardo,31S. Leone,44S. Levy,12J. D. Lewis,15K. Li,59 C. Lin,59C. S. Lin,15M. Lindgren,15T. M. Liss,23A. Lister,18D. O. Litvintsev,15T. Liu,15Y. Liu,18N. S. Lockyer,43 A. Loginov,35M. Loreti,42P. Loverre,49R.-S. Lu,1D. Lucchesi,42P. Lujan,28P. Lukens,15G. Lungu,16L. Lyons,41J. Lys,28 R. Lysak,1D. MacQueen,32R. Madrak,15K. Maeshima,15P. Maksimovic,24L. Malferrari,4G. Manca,29R. Marginean,38

C. Marino,23A. Martin,24M. Martin,59V. Martin,37M. Martı´nez,3T. Maruyama,54H. Matsunaga,54M. Mattson,57 P. Mazzanti,4K. S. McFarland,47D. McGivern,30P. M. McIntyre,51P. McNamara,50R. NcNulty,29A. Mehta,29 S. Menzemer,31A. Menzione,44P. Merkel,15C. Mesropian,48A. Messina,49T. Miao,15N. Miladinovic,5L. Miller,20 R. Miller,34J. S. Miller,33R. Miquel,28S. Miscetti,17G. Mitselmakher,16A. Miyamoto,26Y. Miyazaki,40N. Moggi,4

B. Mohr,7R. Moore,15M. Morello,44P. A. Movilla Fernandez,28A. Mukherjee,15M. Mulhearn,31T. Muller,25 R. Mumford,24A. Munar,43P. Murat,15J. Nachtman,15S. Nahn,59I. Nakamura,43I. Nakano,39A. Napier,55R. Napora,24

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D. Naumov,36V. Necula,16F. Niell,33J. Nielsen,28C. Nelson,15T. Nelson,15C. Neu,43M. S. Neubauer,8 C. Newman-Holmes,15T. Nigmanov,45L. Nodulman,2O. Norniella,3K. Oesterberg,21T. Ogawa,56S. H. Oh,14Y. D. Oh,27

T. Ohsugi,22T. Okusawa,40R. Oldeman,49R. Orava,21W. Orejudos,28C. Pagliarone,44E. Palencia,10R. Paoletti,44 V. Papadimitriou,15S. Pashapour,32J. Patrick,15G. Pauletta,53M. Paulini,11T. Pauly,41C. Paus,31D. Pellett,6A. Penzo,53 T. J. Phillips,14G. Piacentino,44J. Piedra,10K. T. Pitts,23C. Plager,7A. Pomposˇ,46L. Pondrom,58G. Pope,45X. Portell,3

O. Poukhov,13F. Prakoshyn,13T. Pratt,29A. Pronko,16J. Proudfoot,2F. Ptohos,17G. Punzi,44J. Rademachker,41 M. A. Rahaman,45A. Rakitine,31S. Rappoccio,20F. Ratnikov,50H. Ray,33B. Reisert,15V. Rekovic,36P. Renton,41

M. Rescigno,49F. Rimondi,4K. Rinnert,25L. Ristori,44W. J. Robertson,14A. Robson,41T. Rodrigo,10S. Rolli,55 L. Rosenson,31R. Roser,15R. Rossin,42C. Rott,46J. Russ,11V. Rusu,12A. Ruiz,10D. Ryan,55H. Saarikko,21S. Sabik,32

A. Safonov,6R. St. Denis,19W. K. Sakumoto,47G. Salamanna,49D. Saltzberg,7C. Sanchez,3A. Sansoni,17L. Santi,53 S. Sarkar,49K. Sato,54P. Savard,32A. Savoy-Navarro,15P. Schlabach,15E. E. Schmidt,15M. P. Schmidt,59M. Schmitt,37

L. Scodellaro,10A. Scribano,44F. Scuri,44A. Sedov,46S. Seidel,36Y. Seiya,40F. Semeria,4L. Sexton-Kennedy,15 I. Sfiligoi,17M. D. Shapiro,28T. Shears,29P. F. Shepard,45D. Sherman,20M. Shimojima,54M. Shochet,12Y. Shon,58 I. Shreyber,35A. Sidoti,44J. Siegrist,28M. Siket,1A. Sill,52P. Sinervo,32A. Sisakyan,13A. Skiba,25A. J. Slaughter,15

K. Sliwa,55D. Smirnov,36J. R. Smith,6F. D. Snider,15R. Snihur,32A. Soha,6S. V. Somalwar,50J. Spalding,15 M. Spezziga,52L. Spiegel,15F. Spinella,44M. Spiropulu,9P. Squillacioti,44H. Stadie,25B. Stelzer,32O. Stelzer-Chilton,32 J. Strologas,36D. Stuart,9A. Sukhanov,16K. Sumorok,31H. Sun,55T. Suzuki,54A. Taffard,23R. Tafirout,32S. F. Takach,57 H. Takano,54R. Takashima,22Y. Takeuchi,54K. Takikawa,54M. Tanaka,2R. Tanaka,39N. Tanimoto,39S. Tapprogge,21

M. Tecchio,33P. K. Teng,1K. Terashi,48R. J. Tesarek,15S. Tether,31J. Thom,15A. S. Thompson,19E. Thomson,43 P. Tipton,47V. Tiwari,11S. Trkaczyk,15D. Toback,51K. Tollefson,34T. Tomura,54D. Tonelli,44M. To¨nnesmann,34 S. Torre,44D. Torretta,15S. Tourneur,15W. Trischuk,32J. Tseng,41R. Tsuchiya,56S. Tsuno,39D. Tsybychev,16N. Turini,44

M. Turner,29F. Ukegawa,54T. Unverhau,19S. Uozumi,54D. Usynin,43L. Vacavant,28A. Vaiciulis,47A. Varganov,33 E. Vataga,44S. Vejcik III,15G. Velev,15V. Veszpremi,46G. Veramendi,23T. Vickey,23R. Vidal,15I. Vila,10R. Vilar,10 I. Vollrath,32I. Volobouev,28M. von der Mey,7P. Wagner,51R. G. Wagner,2R. L. Wagner,15W. Wagner,25R. Wallny,7

T. Walter,25T. Yamashita,39K. Yamamoto,40Z. Wan,50M. J. Wang,1S. M. Wang,16A. Warburton,32B. Ward,19 S. Waschke,19D. Waters,30T. Watts,50M. Weber,28W. C. Wester III,15B. Whitehouse,55A. B. Wicklund,2E. Wicklund,15

H. H. Williams,43P. Wilson,15B. L. Winer,38P. Wittich,43S. Wolbers,15M. Wolter,55M. Worcester,7S. Worm,50 T. Wright,33X. Wu,18F. Wu¨rthwein,8A. Wyatt,30A. Yagil,15C. Yang,59U. K. Yang,12W. Yao,28G. P. Yeh,15K. Yi,24 J. Yoh,15P. Yoon,47K. Yorita,56T. Yoshida,40I. Yu,27S. Yu,43Z. Yu,59J. C. Yun,15L. Zanello,49A. Zanetti,43I. Zaw,20

F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4 (CDF Collaboration)

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

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

5Brandeis University, Waltham, Massachusetts 02254, USA

6University of California at Davis, Davis, California 95616, USA

7University of California at Los Angeles, Los Angeles, California 90024, USA

8University of California at San Diego, La Jolla, California 92093, USA

9University of California at Santa Barbara, Santa Barbara, California 93106, USA

10Instituto de Fisica de Cantabria, CSIC –-University of Cantabria, 39005 Santander, Spain

11Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

12Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

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

14Duke University, Durham, North Carolina 27708

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

21The Helsinki Group: Helsinki Institute of Physics; and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00044, Helsinki, Finland

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22Hiroshima University, Higashi-Hiroshima 724, Japan

23University of Illinois, Urbana, Illinois 61801, USA

24The Johns Hopkins University, Baltimore, Maryland 21218, USA

25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

27Center for High Energy Physics: Kyungpook National University, Taegu 702-701; Seoul National University, Seoul 151-742;

and SungKyunKwan University, Suwon 440-746; Korea

28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

29University of Liverpool, Liverpool L69 7ZE, United Kingdom

30University College London, London WC1E 6BT, United Kingdom

31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

33University of Michigan, Ann Arbor, Michigan 48109, USA

34Michigan State University, East Lansing, Michigan 48824, USA

35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

36University of New Mexico, Albuquerque, New Mexico 87131, USA

37Northwestern University, Evanston, Illinois 60208, USA

38The Ohio State University, Columbus, Ohio 43210, USA

39Okayama University, Okayama 700-8530, Japan

40Osaka City University, Osaka 588, Japan

41University of Oxford, Oxford OX1 3RH, United Kingdom

42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova –Trento, I-35131 Padova, Italy

43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

44Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 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 10021, USA

49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University di Roma ‘‘La Sapienza,’’ I-00185 Roma, Italy

50Rutgers University, Piscataway, New Jersey 08855, USA

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

52Texas Tech University, Lubbock, Texas 79409, USA

53Istituto Nazionale di Fisica Nucleare, University of Trieste, Udine, Italy

54University of Tsukuba, Tsukuba, Ibaraki 305, Japan

55Tufts University, Medford, Massachusetts 02155, USA

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 10 December 2004; published 6 July 2005)

We report on a search for anomalous kinematics of tt dilepton events in pp collisions at ps

1:96 TeV using 193 pb1 of data collected with the CDF II detector. We developed a new a priori technique designed to isolate the subset in a data sample revealing the largest deviation from standard model (SM) expectations and to quantify the significance of this departure. In the four-variable space considered, no particular subset shows a significant discrepancy, and we find that the probability of obtaining a data sample less consistent with the SM than what is observed is 1.0%– 4.5%.

DOI:10.1103/PhysRevLett.95.022001 PACS numbers: 14.65.Ha, 13.85.Qk, 14.80.Ly

The discovery of the top quark during Run I of Fermilab’s Tevatron collider initiated an experimental pro- gram to characterize its production and decay properties in all possible decay channels. Within the standard model (SM) the top quark decays almost exclusively to aWboson and a bottom quark; the ‘‘dilepton’’ decay channel here denotes the case where the twoW bosons from a ttpair both decay into final states containing an electron or a muon, accounting for about 7% of all SM tt decays.

These events are characterized by two energetic leptons,

two jets from the hadronization of the bottom quarks, and large missing energy from the unobserved neutrinos. The measurements by the CDF and D0 Collaborations of thett production cross section in the dilepton channel in Run I [1] showed a slight excess over SM predictions [2].

Perhaps more interestingly, several of the events observed in the Run I data had missing transverse energy (6ET) and lepton pT’s [3] large enough to call into question their compatibility with SM top decay kinematics. In fact, it was suggested that the kinematics of these events could be

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better described by the cascade decays of heavy squarks [4], compelling us to subject the top dilepton sample to careful scrutiny in Run II.

In a previous Letter [5], we reported a measurement of the ttproduction cross section in the dilepton channel at Run II and found good agreement with the SM expectation.

Here we present the results of a detailed analysis of the kinematics of that data sample. Motivated by the possible anomalies in the top Run I dilepton sample, we devised a search for new physics based on the comparison of kine- matic features of observed events with those expected from the SM, assuming a175 GeV=c2 top mass [6]. The search is designed to be sensitive to any physical process that gives rise to events with specific kinematics different from those expected from SM top and backgrounds, especially processes that result in kinematics similar to the aforemen- tioned Run I events. The method seeks to isolate the subset of events in a data sample with the largest concentration of possible non-SM physics and to assign a probability that quantifies its departure from the SM.

Reference [5] provides a description of the CDF II detector, the event selection, and the data and simulation samples used for this analysis [7]. The basic selection requirements are (i) two oppositely charged, well- identified leptons (e or ) with pT>20 GeV=c, (ii) at least two jets withET>15 GeV, and (iii) 6ET >25 GeV.

Several other topological requirements are made to further purify the sample and are detailed in [5]. With this selec- tion, the SM predicts a yield of8:21:1ttevents (assum- ing attcross section of 6.7 pb [2]), and2:70:7events from other SM processes (mainly production of dibosons, Wassociated jets, and Drell-Yan events) in our sample.

Thirteen events are observed.

We consider a minimal set of assumptions about the nature of possible non-SM physics in order to make an a priorichoice of which kinematic quantities to investi- gate. The Tevatron provides us with the opportunity to look for phenomena beyond the presently known mass spec- trum. This together with the hints from the Run I data sample leads us to focus our search on events with large lepton pT and large 6ET resulting from the decay of an unknown heavy particle. In addition, two-body decays of massive particles (e.g., heavy chargino decay~!)~ tend to result in topologies where the charged lepton and the6ETdirection are back-to-back, whereas this tends not to be the case for the SM tt dilepton signature. Thus we expect the following variables to be sensitive to a wide range of new physics: the event’s 6ET, the transverse mo- mentum of the leading (i.e., highest-pT) leptonpT, and the angle‘mbetween the leading lepton and the direction of the6ET in the plane transverse to the beam.

We define an additional kinematic variable as follows.

The initial and intermediate state particles in thettdecay impose constraints on the final state product properties, m‘11 m‘22 mWandm‘11b1 m‘22b2

mt175 GeV=c2. These four constraints leave two of the six unknown neutrino momentum components unspecified when solving the system of kinematic equations. To fully reconstruct the event, we scan over these two remaining degrees of freedom and compare the resulting neutrino momentum sum (6E~predT ) with the6E~T measured in the event (6E~obsT ) by computing

T 6E~predT expfj6E~predT 6E~obsT j2=226E

Tg; (1)

where6ETparametrizes uncertainty on6ETdue to mismea- surement of the underlying event. When performing the scan, we assume detector resolutions to be Gaussian for the lepton and jet momenta and smear the observed values accordingly; the 6E~predT value is then recomputed according to the smeared jet and lepton energies. We define a variable T as the square root of the integral ofT over the possible values of6E~predT determined from the scan and summed over a twofold ambiguity in the lepton-b-jet pairing. This vari- able T represents how well an event’s kinematics satisfy the tt dilepton decay hypothesis; a non-tt dilepton event has on average a small value ofTcompared tottevents.

As mentioned before, we concentrate our search on events with large values of 6ET, pT, and ‘m and small values of T. We therefore assign the following weight to each event:

W w6E

Twp

Tw‘mwT 1=4; (2)

where w6ET, wp

T, w‘m, and wT represent probabilities (assuming the SM) for an event to have a 6ET, pT, ‘m larger than that observed and a T smaller than that ob- served, respectively. We then construct 13 subsets (‘‘K subsets’’) of the data; the first subset (K1) contains only the event with the lowest weightW, the second subset (K2) contains only the two events with the two lowest weights, and so on.

To quantify the departure of theKsubsets from the SM predictions, we do a shape comparison using the Kolmogorov-Smirnov (KS) statistic [8]. For each of the four variables i, the KS deviation K;i between the SM cumulative function and the cumulative function of theK subset is computed. To assess the probability of this devia- tion, we generate 100 000 pseudoexperiments by randomly drawing events from large Monte Carlo samples of ttand SM backgrounds. The number of events corresponding to each SM process is sampled from a Poisson distribution with mean equal to the number of events expected after event selection. Only pseudoexperiments with a total of 13 events are accepted. Further, in each pseudoexperiment, K subsets are formed and the respectiveK;ifor each are calculated. We thus build probability distribution functions for K;i from which the KS probability pK;i can be com- puted. Next we calculate the geometric mean K of the fourpK;i’s for each pseudoexperiment and form the proba-

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bility distribution functionsFK such that the quantity PKZobsK

0 FK d (3)

determines how well each K subset agrees with the SM expectation based on the combined information from the four variables. We define Q as the value of K with the smallestPK. By isolating this ‘‘unlikely’’ subsetQ(where

‘‘unlikely’’ here denotes having largepT,6ET,‘m, and/or small T), we minimize the dilution of a possible signal from the inclusion of SM events.

We use the quantityPQ as the test statistic to quantify the discrepancy of the data with the SM. Generating an- other set of 100 000 pseudoexperiments from SM Monte Carlo and repeating the above procedure, we deter- minePQ for each pseudoexperiment and build the proba- bility distribution function LPQ such that the significance of departure of the Q subset of events from the SM is

ZPdataQ

0 LPQ dPQ: (4)

is thepvalue of the test, representing the probability to obtain a data sample less consistent with the SM than what is actually observed. Sufficiently low values of would indicate the presence of new physics in the data sample, and theQevents would represent the subsample of the data with the largest concentration of new physics.

In order to evaluate the performance of the method, we simulated a sample of squark decays usingPYTHIA[9] and the supersymmetry (SUSY) parameters suggested in [4].

As a performance benchmark, we construct a 50%:50%

mixture of the SM and SUSY and ask how often we would observe apvalue () less than 0.3% (the equivalent of a 3 effect) when 13-event pseudoexperiments are drawn from this sample. We find that50%of these pseudoex- periments yield <0:3%. Moreover, the concentration of SUSY events in the most unlikely K subset found is on average 80%. By contrast, a KS test without using sub- samples finds <0:3%only 21% of the time and does not isolate a mostly SUSY subset.

We test our procedure as well as our ability to correctly simulate our kinematic variables in a high-statistics control sample of 973W 3jets events. We compare these data

FIG. 1. 6ET, leading leptonpT,‘m, and T distributions for the top dilepton sample. The hatched regions represent the Poisson uncertainty on the expectation in a given bin. The dashed histograms are the expected distributions from the SUSY MC calculation described in the text.

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with a Monte Carlo simulation of 6ET, pT and‘m using Wassociated jet, QCD, and tt production processes added in the amounts expected from the SM. We apply a three-dimensional version of our technique and observe that the data have a highpvalue (35:1%), indicating good modeling of the data by the simulation.

We test the modeling ofTin a control sample ofW4 jet events, treating the leading jet as a second lepton and the subleading jet as a second neutrino. We apply this reconstruction to the data and to an appropriately weighted sample of simulatedttandALPGENHERWIGW4par- ton Monte Carlo events [10]. We observe a KS probability of 0.97 for the respectiveT distributions, indicating good agreement between simulation and the data.

Having established that data are adequately modeled by the simulation, we apply the outlined technique to thett dilepton sample. The distributions of the selected variables forttdilepton events are presented in Fig. 1. We find the most unlikely subset of events to be the entire data set (i.e., Q13), with a pvalue1:6%. This result is entirely driven by the excess of leptons at lowpT (<40 GeV=c) seen in Fig. 1(b); since the method effectively orders the subsets from highpT to lowpT, thepvalue decreases as more of the low-pT excess is included, reaching a mini- mum when the entire data sample is considered.

A natural question to ask about the low-pT events is whether they can be attributed to underestimated non-tt SM backgrounds. To address this, we used a displaced secondary vertex ‘‘b-tag’’ algorithm [11] to look for long-lived b-hadron decays in the events; the fraction of non-tt SM dilepton events containing bottom quarks is expected to be negligible. We present the b-tag content of the sample as well as the distribution of events in the (pT,T) plane in Fig. 2. We note that six of the nine low-pT events contain at least one identifiedbjet. We also note that more than half of the low-pTevents are consistent with the ttkinematic hypothesis with large values ofT, as opposed to the small values ofT (<0:05) favored by non-ttSM

backgrounds [see Fig. 1(d)]. We thus conclude that the low-pTevents are not likely to have arisen from non-ttSM processes; details of the 13 events can be found elsewhere [12].

We next evaluate the effect of systematic uncertainties.

Uncertainties in the shapes of kinematic distributions from sources listed in Table I lead to an uncertainty in the probability distribution functionLPQ , and consequently to an uncertainty in the significance level of our measure- ment. We consider each source of systematic uncertainty and build a new probability distribution functionL0PQ . We then determine a newpvalue0 via

0 ZPdataQ

0 L0PQ dPQ: (5)

Table I shows the values of 0 obtained for different sources of uncertainty. Generating an L0PQ with the inclusion of all systematic effects that give a p value greater than that observed in the data (1.6%) results in a maximumpvalue of 4.5%; a minimumpvalue of 1.0% is obtained when a background estimate1lower than nomi- nal is used. All other combinations of systematic effects result inpvalues lying within this range.

In conclusion, we have assessed the consistency of thett dilepton sample with the SM in the four-variable space described and find apvalue of 1.0%– 4.5%. Our method is designed to be especially sensitive to data subsets that preferentially populate regions where new high-pTphysics can be expected. No such subset was found in our data. We have noted that the leptonpT distribution exhibits a mild excess at low pT; however, it can be concluded that new physics scenarios invoked to describe the high-pT=high-6ET events observed in Run I are not favored by the current Run II data.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.

This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research TABLE I. p values obtained upon inclusion of systematic effects. The last row shows the maximum range of p values resulting from various combinations of the individual system- atics.

Source of uncertainty 0 (%)

MC generator 1.6

Initial (final) state radiation 1.2 (1.6)

Parton distribution functions 1.9

Mtop170180 GeV 1.4 (2.1)

Jet energy scale, 1(1) 2.1 (2.6)

Background estimates, 1(1) 2.7 (1.0)

Combined 1.0 – 4.5

T

0 0.05 0.1 0.15 0.2 0.25

(GeV/c)

T

leading lepton p

20

40 60 80 100 120 140

httbar Entries 3332 Mean x 0.1054 Mean y 65.36 RMS x 0.04636 RMS y 25.96

httbar Entries 3332 Mean x 0.1054 Mean y 65.36 RMS x 0.04636 RMS y 25.96

CDF II

Ldt = 193 pb-1

double-b tag data

single-b tag data zero-b tag data

MC (arbitrary scale) t

t

FIG. 2. Top dilepton events in the (pT,T) plane withb-tagging information.

(7)

Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium fuer Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; the Comision Interministerial de Ciencia y Tecnologia, Spain; the Research Corporation; and in part by the European Community’s Human Potential Programme under Contract No. HPRN-CT-2002-00292, Probe for New Physics.

[1] F. Abe et al.(CDF Collaboration), Phys. Rev. Lett. 80, 2779 (1998); S. Abachiet al. (D0 Colloboration), Phys.

Rev. Lett.79, 1203 (1997).

[2] R. Bonciani et al., Nucl. Phys. B529, 424 (1998); M.

Cacciari et al., J. High Energy Phys. 04 (2004) 068; N.

Kidonakis and R. Vogt, Phys. Rev. D68, 114014 (2003).

[3] We use a cylindrical coordinate system about the beam axis in which is the polar angle. We define transverse momentumpTpsinand transverse energyET simi- larly. Missing transverse energy (6E~T) is defined as

*iEiTn^i, where n^i is the unit vector in the azimuthal plane that points from theppinteraction region to theith calorimeter tower. 6E~T is further corrected for the energy and momentum of identified muons.

[4] R. M. Barnett and L. J. Hall, Phys. Rev. Lett. 77, 3506 (1996).

[5] D. Acostaet al.(CDF Collaboration), Phys. Rev. Lett.93, 142001 (2004).

[6] L. Demortier et al., FERMILAB-TM-2084, 1999. It should be noted that the top mass measurements and their uncertainties assume the absence of new physics.

[7] Two selections are described in the cited reference. In order to minimize sensitivity to non-ttSM processes, we use the higher-purity selection referred to as ‘‘DIL’’

therein.

[8] W. H. Presset al., Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, England, 1993), 2nd ed.

[9] T. Sjostrand et al., Comput. Phys. Commun. 135, 238 (2001).

[10] M. L. Manganoet al., J. High Energy Phys. 07 (2003) 001;

G. Marchesini et al., Comput. Phys. Commun. 67, 465 (1992); G. Corcellaet al., J. High Energy Phys. 01 (2001) 010.

[11] D. Acosta et al.(CDF Collaboration), Phys. Rev. D71, 052003 (2005).

[12] A. Ivanov, Ph.D. thesis, University of Rochester, 2004.

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