arX

iv:0

810.

3522

v1 [

hep-

ex]

20

Oct

200

8

Search for new physics in the µµ + e/µ + ET/ channel with a low-pT lepton threshold

at the Collider Detector at Fermilab

T. Aaltonen,24 J. Adelman,14 T. Akimoto,56 M.G. Albrow,18 B. Alvarez Gonzalez,12 S. Ameriow,44 D. Amidei,35

A. Anastassov,39 A. Annovi,20 J. Antos,15 G. Apollinari,18 A. Apresyan,49 T. Arisawa,58 A. Artikov,16

W. Ashmanskas,18 A. Attal,4 A. Aurisano,54 F. Azfar,43 P. Azzurriz,47 W. Badgett,18 A. Barbaro-Galtieri,29

V.E. Barnes,49 B.A. Barnett,26 V. Bartsch,31 G. Bauer,33 P.-H. Beauchemin,34 F. Bedeschi,47 D. Beecher,31

S. Behari,26 G. Bellettinix,47 J. Bellinger,60 D. Benjamin,17 A. Beretvas,18 J. Beringer,29 A. Bhatti,51 M. Binkley,18

D. Bisellow,44 I. Bizjakcc,31 R.E. Blair,2 C. Blocker,7 B. Blumenfeld,26 A. Bocci,17 A. Bodek,50 V. Boisvert,50

G. Bolla,49 D. Bortoletto,49 J. Boudreau,48 A. Boveia,11 B. Braua,11 A. Bridgeman,25 L. Brigliadori,44

C. Bromberg,36 E. Brubaker,14 J. Budagov,16 H.S. Budd,50 S. Budd,25 S. Burke,18 K. Burkett,18 G. Busettow,44

P. Busseyk,22 A. Buzatu,34 K. L. Byrum,2 S. Cabrerau,17 C. Calancha,32 M. Campanelli,36 M. Campbell,35

F. Canelli,18 A. Canepa,46 B. Carls,25 D. Carlsmith,60 R. Carosi,47 S. Carrillom,19 S. Carron,34 B. Casal,12

M. Casarsa,18 A. Castrov,6 P. Catastiniy,47 D. Cauzbb,55 V. Cavalierey,47 M. Cavalli-Sforza,4 A. Cerri,29

L. Cerriton,31 S.H. Chang,28 Y.C. Chen,1 M. Chertok,8 G. Chiarelli,47 G. Chlachidze,18 F. Chlebana,18 K. Cho,28

D. Chokheli,16 J.P. Chou,23 G. Choudalakis,33 S.H. Chuang,53 K. Chung,13 W.H. Chung,60 Y.S. Chung,50

T. Chwalek,27 C.I. Ciobanu,45 M.A. Ciocciy,47 A. Clark,21 D. Clark,7 G. Compostella,44 M.E. Convery,18

J. Conway,8 M. Cordelli,20 G. Cortianaw,44 C.A. Cox,8 D.J. Cox,8 F. Cresciolix,47 C. Cuenca Almenaru,8

J. Cuevasr,12 R. Culbertson,18 J.C. Cully,35 D. Dagenhart,18 M. Datta,18 T. Davies,22 P. de Barbaro,50

S. De Cecco,52 A. Deisher,29 G. De Lorenzo,4 M. Dell’Orsox,47 C. Deluca,4 L. Demortier,51 J. Deng,17 M. Deninno,6

P.F. Derwent,18 G.P. di Giovanni,45 C. Dionisiaa,52 B. Di Ruzzabb,55 J.R. Dittmann,5 M. D’Onofrio,4 S. Donatix,47

P. Dong,9 J. Donini,44 T. Dorigo,44 S. Dube,53 J. Efron,40 A. Elagin,54 R. Erbacher,8 D. Errede,25 S. Errede,25

R. Eusebi,18 H.C. Fang,29 S. Farrington,43 W.T. Fedorko,14 R.G. Feild,61 M. Feindt,27 J.P. Fernandez,32

C. Ferrazzaz,47 R. Field,19 G. Flanagan,49 R. Forrest,8 M.J. Frank,5 M. Franklin,23 J.C. Freeman,18 I. Furic,19

M. Gallinaro,52 J. Galyardt,13 F. Garberson,11 J.E. Garcia,21 A.F. Garfinkel,49 K. Genser,18 H. Gerberich,25

D. Gerdes,35 A. Gessler,27 S. Giaguaa,52 V. Giakoumopoulou,3 P. Giannetti,47 K. Gibson,48 J.L. Gimmell,50

C.M. Ginsburg,18 N. Giokaris,3 M. Giordanibb,55 P. Giromini,20 M. Giuntax,47 G. Giurgiu,26 V. Glagolev,16

D. Glenzinski,18 M. Gold,38 N. Goldschmidt,19 A. Golossanov,18 G. Gomez,12 G. Gomez-Ceballos,33

M. Goncharov,54 O. Gonzalez,32 I. Gorelov,38 A.T. Goshaw,17 K. Goulianos,51 A. Greselew,44 S. Grinstein,23

C. Grosso-Pilcher,14 R.C. Group,18 U. Grundler,25 J. Guimaraes da Costa,23 Z. Gunay-Unalan,36 C. Haber,29

K. Hahn,33 S.R. Hahn,18 E. Halkiadakis,53 B.-Y. Han,50 J.Y. Han,50 F. Happacher,20 K. Hara,56 D. Hare,53

M. Hare,57 S. Harper,43 R.F. Harr,59 R.M. Harris,18 M. Hartz,48 K. Hatakeyama,51 C. Hays,43 M. Heck,27

A. Heijboer,46 J. Heinrich,46 C. Henderson,33 M. Herndon,60 J. Heuser,27 S. Hewamanage,5 D. Hidas,17

C.S. Hillc,11 D. Hirschbuehl,27 A. Hocker,18 S. Hou,1 M. Houlden,30 S.-C. Hsu,29 B.T. Huffman,43 R.E. Hughes,40

U. Husemann,36 M. Hussein,36 U. Husemann,61 J. Huston,36 J. Incandela,11 G. Introzzi,47 M. Ioriaa,52 A. Ivanov,8

E. James,18 B. Jayatilaka,17 E.J. Jeon,28 M.K. Jha,6 S. Jindariani,18 W. Johnson,8 M. Jones,49 K.K. Joo,28

S.Y. Jun,13 J.E. Jung,28 T.R. Junk,18 T. Kamon,54 D. Kar,19 P.E. Karchin,59 Y. Kato,42 R. Kephart,18 J. Keung,46

V. Khotilovich,54 B. Kilminster,18 D.H. Kim,28 H.S. Kim,28 H.W. Kim,28 J.E. Kim,28 M.J. Kim,20 S.B. Kim,28

S.H. Kim,56 Y.K. Kim,14 N. Kimura,56 L. Kirsch,7 S. Klimenko,19 B. Knuteson,33 B.R. Ko,17 K. Kondo,58

D.J. Kong,28 J. Konigsberg,19 A. Korytov,19 A.V. Kotwal,17 M. Kreps,27 J. Kroll,46 D. Krop,14 N. Krumnack,5

M. Kruse,17 V. Krutelyov,11 T. Kubo,56 T. Kuhr,27 N.P. Kulkarni,59 M. Kurata,56 Y. Kusakabe,58 S. Kwang,14

A.T. Laasanen,49 S. Lami,47 S. Lammel,18 M. Lancaster,31 R.L. Lander,8 K. Lannonq,40 A. Lath,53 G. Latinoy,47

I. Lazzizzeraw,44 T. LeCompte,2 E. Lee,54 H.S. Lee,14 S.W. Leet,54 S. Leone,47 J.D. Lewis,18 C.-S. Lin,29

J. Linacre,43 M. Lindgren,18 E. Lipeles,46 A. Lister,8 D.O. Litvintsev,18 C. Liu,48 T. Liu,18 N.S. Lockyer,46

A. Loginov,61 M. Loretiw,44 L. Lovas,15 D. Lucchesiw,44 C. Luciaa,52 J. Lueck,27 P. Lujan,29 P. Lukens,18

G. Lungu,51 L. Lyons,43 J. Lys,29 R. Lysak,15 D. MacQueen,34 R. Madrak,18 K. Maeshima,18 K. Makhoul,33

T. Maki,24 P. Maksimovic,26 S. Malde,43 S. Malik,31 G. Mancae,30 A. Manousakis-Katsikakis,3 F. Margaroli,49

C. Marino,27 C.P. Marino,25 A. Martin,61 V. Martinl,22 M. Martınez,4 R. Martınez-Balların,32 T. Maruyama,56

P. Mastrandrea,52 T. Masubuchi,56 M. Mathis,26 M.E. Mattson,59 P. Mazzanti,6 K.S. McFarland,50 P. McIntyre,54

R. McNultyj ,30 A. Mehta,30 P. Mehtala,24 A. Menzione,47 P. Merkel,49 C. Mesropian,51 T. Miao,18 N. Miladinovic,7

R. Miller,36 C. Mills,23 M. Milnik,27 A. Mitra,1 G. Mitselmakher,19 H. Miyake,56 N. Moggi,6 C.S. Moon,28

R. Moore,18 M.J. Morellox,47 J. Morlok,27 P. Movilla Fernandez,18 J. Mulmenstadt,29 A. Mukherjee,18 Th. Muller,27

R. Mumford,26 P. Murat,18 M. Mussiniv,6 J. Nachtman,18 Y. Nagai,56 A. Nagano,56 J. Naganoma,56 K. Nakamura,56

2

I. Nakano,41 A. Napier,57 V. Necula,17 J. Nett,60 C. Neuv,46 M.S. Neubauer,25 S. Neubauer,27 J. Nielseng,29

L. Nodulman,2 M. Norman,10 O. Norniella,25 E. Nurse,31 L. Oakes,43 S.H. Oh,17 Y.D. Oh,28 I. Oksuzian,19

T. Okusawa,42 R. Orava,24 S. Pagan Grisow,44 E. Palencia,18 V. Papadimitriou,18 A. Papaikonomou,27

A.A. Paramonov,14 B. Parks,40 S. Pashapour,34 J. Patrick,18 G. Paulettabb,55 M. Paulini,13 C. Paus,33 T. Peiffer,27

D.E. Pellett,8 A. Penzo,55 T.J. Phillips,17 G. Piacentino,47 E. Pianori,46 L. Pinera,19 K. Pitts,25 C. Plager,9

L. Pondrom,60 O. Poukhov∗,16 N. Pounder,43 F. Prakoshyn,16 A. Pronko,18 J. Proudfoot,2 F. Ptohosi,18

E. Pueschel,13 G. Punzix,47 J. Pursley,60 J. Rademackerc,43 A. Rahaman,48 V. Ramakrishnan,60 N. Ranjan,49

I. Redondo,32 P. Renton,43 M. Renz,27 M. Rescigno,52 S. Richter,27 F. Rimondiv,6 L. Ristori,47 A. Robson,22

T. Rodrigo,12 T. Rodriguez,46 E. Rogers,25 S. Rolli,57 R. Roser,18 M. Rossi,55 R. Rossin,11 P. Roy,34 A. Ruiz,12

J. Russ,13 V. Rusu,18 A. Safonov,54 W.K. Sakumoto,50 O. Salto,4 L. Santibb,55 S. Sarkaraa,52 L. Sartori,47 K. Sato,18

A. Savoy-Navarro,45 P. Schlabach,18 A. Schmidt,27 E.E. Schmidt,18 M.A. Schmidt,14 M.P. Schmidt∗,61 M. Schmitt,39

T. Schwarz,8 L. Scodellaro,12 A. Scribanoy,47 F. Scuri,47 A. Sedov,49 S. Seidel,38 Y. Seiya,42 A. Semenov,16

L. Sexton-Kennedy,18 F. Sforza,47 A. Sfyrla,25 S.Z. Shalhout,59 T. Shears,30 P.F. Shepard,48 M. Shimojimap,56

S. Shiraishi,14 M. Shochet,14 Y. Shon,60 I. Shreyber,37 A. Sidoti,47 P. Sinervo,34 A. Sisakyan,16 A.J. Slaughter,18

J. Slaunwhite,40 K. Sliwa,57 J.R. Smith,8 F.D. Snider,18 R. Snihur,34 A. Soha,8 S. Somalwar,53 V. Sorin,36

J. Spalding,18 T. Spreitzer,34 P. Squillaciotiy,47 M. Stanitzki,61 R. St. Denis,22 B. Stelzer,34 O. Stelzer-Chilton,34

D. Stentz,39 J. Strologas,38 G.L. Strycker,35 D. Stuart,11 J.S. Suh,28 A. Sukhanov,19 I. Suslov,16 T. Suzuki,56

A. Taffardf ,25 R. Takashima,41 Y. Takeuchi,56 R. Tanaka,41 M. Tecchio,35 P.K. Teng,1 K. Terashi,51 J. Thomh,18

A.S. Thompson,22 G.A. Thompson,25 E. Thomson,46 P. Tipton,61 P. Ttito-Guzman,32 S. Tkaczyk,18 D. Toback,54

S. Tokar,15 K. Tollefson,36 T. Tomura,56 D. Tonelli,18 S. Torre,20 D. Torretta,18 P. Totarobb,55 S. Tourneur,45

M. Trovato,47 S.-Y. Tsai,1 Y. Tu,46 N. Turiniy,47 F. Ukegawa,56 S. Vallecorsa,21 N. van Remortelb,24 A. Varganov,35

E. Vatagaz,47 F. Vazquezm,19 G. Velev,18 C. Vellidis,3 V. Veszpremi,49 M. Vidal,32 R. Vidal,18 I. Vila,12 R. Vilar,12

T. Vine,31 M. Vogel,38 I. Volobouevt,29 G. Volpix,47 P. Wagner,46 R.G. Wagner,2 R.L. Wagner,18 W. Wagner,27

J. Wagner-Kuhr,27 T. Wakisaka,42 R. Wallny,9 S.M. Wang,1 A. Warburton,34 D. Waters,31 M. Weinberger,54

J. Weinelt,27 W.C. Wester III,18 B. Whitehouse,57 D. Whitesonf ,46 A.B. Wicklund,2 E. Wicklund,18 S. Wilbur,14

G. Williams,34 H.H. Williams,46 P. Wilson,18 B.L. Winer,40 P. Wittichh,18 S. Wolbers,18 C. Wolfe,14

T. Wright,35 X. Wu,21 F. Wurthwein,10 S.M. Wynne,30 S. Xie,33 A. Yagil,10 K. Yamamoto,42 J. Yamaoka,53

U.K. Yango,14 Y.C. Yang,28 W.M. Yao,29 G.P. Yeh,18 J. Yoh,18 K. Yorita,14 T. Yoshida,42 G.B. Yu,50

I. Yu,28 S.S. Yu,18 J.C. Yun,18 L. Zanelloaa,52 A. Zanetti,55 X. Zhang,25 Y. Zhengd,9 and S. Zucchelliv,6

(CDF Collaboration†)1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 604393University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain5Baylor University, Waco, Texas 76798

6Istituto Nazionale di Fisica Nucleare Bologna, vUniversity of Bologna, I-40127 Bologna, Italy7Brandeis University, Waltham, Massachusetts 02254

8University of California, Davis, Davis, California 956169University of California, Los Angeles, Los Angeles, California 90024

10University of California, San Diego, La Jolla, California 9209311University of California, Santa Barbara, Santa Barbara, California 93106

12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain13Carnegie Mellon University, Pittsburgh, PA 15213

14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 6063715Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia17Duke University, Durham, North Carolina 27708

18Fermi National Accelerator Laboratory, Batavia, Illinois 6051019University of Florida, Gainesville, Florida 32611

20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy21University of Geneva, CH-1211 Geneva 4, Switzerland

22Glasgow University, Glasgow G12 8QQ, United Kingdom23Harvard University, Cambridge, Massachusetts 02138

24Division of High Energy Physics, Department of Physics,University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

25University of Illinois, Urbana, Illinois 6180126The Johns Hopkins University, Baltimore, Maryland 21218

27Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, 76128 Karlsruhe, Germany

3

28Center 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

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 9472030University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 0213934Institute 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 2A335University of Michigan, Ann Arbor, Michigan 48109

36Michigan State University, East Lansing, Michigan 4882437Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 8713139Northwestern University, Evanston, Illinois 6020840The Ohio State University, Columbus, Ohio 43210

41Okayama University, Okayama 700-8530, Japan42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom44Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, wUniversity of Padova, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France46University of Pennsylvania, Philadelphia, Pennsylvania 19104

47Istituto Nazionale di Fisica Nucleare Pisa, xUniversity of Pisa,yUniversity of Siena and zScuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 1526049Purdue University, West Lafayette, Indiana 47907

50University of Rochester, Rochester, New York 1462751The Rockefeller University, New York, New York 10021

52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,aaSapienza Universita di Roma, I-00185 Roma, Italy53Rutgers University, Piscataway, New Jersey 08855

54Texas A&M University, College Station, Texas 7784355Istituto Nazionale di Fisica Nucleare Trieste/Udine, bbUniversity of Trieste/Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan57Tufts University, Medford, Massachusetts 02155

58Waseda University, Tokyo 169, Japan59Wayne State University, Detroit, Michigan 48201

60University of Wisconsin, Madison, Wisconsin 5370661Yale University, New Haven, Connecticut 06520

A search for new physics using three-lepton (trilepton) data collected with the CDF II detector andcorresponding to an integrated luminosity of 976 pb−1 is presented. The standard model predictsa low rate of trilepton events, which makes some supersymmetric processes, such as chargino-neutralino production, measurable in this channel. The µµ + ℓ signature is investigated, whereℓ is an electron or a muon, with the additional requirement of large missing transverse energy. Inthis analysis, the lepton transverse momenta with respect to the beam direction (pT ) are as lowas 5 GeV/c, a selection that improves the sensitivity to particles which are light as well as to oneswhich result in leptonically decaying tau leptons. At the same time, this low-pT selection presentsadditional challenges due to the non-negligible heavy-quark background at low lepton momenta.This background is measured with an innovative technique using experimental data. Several dimuonand trilepton control regions are investigated, and good agreement between experimental results andstandard-model predictions is observed. In the signal region, we observe one three-muon event andexpect 0.4 ± 0.1 µµ + ℓ events from standard-model processes.

PACS numbers: 11.30.Pb, 12.60.Jv, 13.85.Hd, 13.85.Rm, 14.80.Ly.

∗Deceased †With visitors from aUniversity of Massachusetts Amherst,

4

I. INTRODUCTION

The standard model (SM) of particle physics is enor-mously successful in describing the known particles andtheir interactions. However, strong motivation from ex-perimental data as well as important theoretical consid-erations point to new physics beyond the SM. Astrophys-ical observations that have resulted in the “concordance”model of cosmology [1] require a source of dark matterthat does not exist in the SM. Theoretically, the SM haswell-known limitations in explaining the origin of massand solving the hierarchy problem. Moreover, it doesnot satisfy our desire for the unification of the strong andelectroweak interactions and the integration of gravity ina unique theory [2].

A powerful strategy for discovering new physics is tosearch in event topologies where the SM predicts ex-tremely low production rates. One of these topologiesis three leptons (trileptons) in hadronic collisions. Thelepton candidates we observe at the Tevatron collider re-sult mainly from QCD processes or the decays of massivegauge bosons (W or Z), or photon conversions. The lep-tons rarely appear in multiplicity greater than two. Thetrilepton signature is favored by a large class of modelsof supersymmety (SUSY) [3, 4], in which the lightest su-persymmetric particles are the gauginos, the supersym-metric partners of the gauge bosons. The correspondingobservable SUSY particles are two charginos (χ±

1,2) and

four neutralinos (χ01,2,3,4), which result from the mixing

of the gauginos and the supersymmetric partners of theHiggs bosons, the higgsinos. The associated productionof charginos and neutralinos may have a detectable crosssection [5] at the Tevatron and may give rise to trileptonevents as shown in Figs. 1 and 2. The most common de-cays are through off-shell vector bosons or scalar leptons(sleptons), with branching fractions that depend on the

Amherst, Massachusetts 01003, bUniversiteit Antwerpen, B-2610Antwerp, Belgium, cUniversity of Bristol, Bristol BS8 1TL,United Kingdom, dChinese Academy of Sciences, Beijing 100864,China, eIstituto Nazionale di Fisica Nucleare, Sezione di Cagliari,09042 Monserrato (Cagliari), Italy, f University of CaliforniaIrvine, Irvine, CA 92697, gUniversity of California Santa Cruz,Santa Cruz, CA 95064, hCornell University, Ithaca, NY 14853,iUniversity of Cyprus, Nicosia CY-1678, Cyprus, jUniversityCollege Dublin, Dublin 4, Ireland, kRoyal Society of Edin-burgh/Scottish Executive Support Research Fellow, lUniversity ofEdinburgh, Edinburgh EH9 3JZ, United Kingdom, mUniversidadIberoamericana, Mexico D.F., Mexico, nQueen Mary, Universityof London, London, E1 4NS, England, oUniversity of Manchester,Manchester M13 9PL, England, pNagasaki Institute of Applied Sci-ence, Nagasaki, Japan, qUniversity of Notre Dame, Notre Dame,IN 46556, rUniversity de Oviedo, E-33007 Oviedo, Spain, sTexasTech University, Lubbock, TX 79409, tIFIC(CSIC-Universitat deValencia), 46071 Valencia, Spain, uUniversity of Virginia, Char-lottesville, VA 22904, ccOn leave from J. Stefan Institute, Ljubl-jana, Slovenia,

a)W ∗±

q

q′ χ02

χ±1

b)

χ±1q

q∗q′ χ0

2

FIG. 1: Chargino-neutralino production through an s-channelW boson (a) and a t-channel squark propagator (b). The t-channel is suppressed in scenarios with very massive squarks.

a) c)

χ±1

χ01

W ∗±

ℓ±

ν

χ02

χ01

Z∗

ℓ−

ℓ+ χ02

ℓ±

χ01

ℓ∓

ℓ±

χ±1

χ01

ℓ±(ν) ℓ±(ν)

ν(ℓ±)

b) d)

FIG. 2: Chargino and neutralino decays through gauge bosons(a,b) and through sleptons (c,d). The branching fractionsdepend on the masses of the sleptons, which always decayto charged leptons, unlike the gauge bosons. The leptonicsignature consists of three leptons in both cases.

chargino, neutralino, and slepton masses.

Under the assumption of R-parity [6] conservation,SUSY particles cannot yield only SM particles in theirdecay; the lightest SUSY particle (LSP) will be stableand escape detection. Therefore, SUSY events would becharacterized by large transverse momentum imbalance(“missing transverse energy”, or ET/ ). In many SUSYscenarios the lightest neutralino is either the LSP or it de-cays to the LSP resulting in ET/ in both cases. AdditionalET/ results from the undetected final-state neutrinos, asshown in Fig. 2. The trilepton+ET/ topology investigatedhere is the “golden” signature for the discovery of SUSYat the Tevatron [7, 8, 9, 10, 11].

The LSP is a candidate for the cold dark matter of theuniverse [12, 13]. In addition, SUSY offers a solution tothe hierarchy problem [14, 15, 16] and the possibility for

5

unification of interactions at high energies [17].Searches for chargino and neutralino production have

been previously performed by the LEP [18, 19] and Teva-tron experiments [20, 21]. In this paper we presenta trilepton analysis that utilizes increased luminosityand improved kinematic acceptance. We search for newphysics in the final state with two muons and an ad-ditional electron or muon using data collected with theCDF II detector from March 2002 to February 2006 fromproton-antiproton collisions at

√s = 1.96 TeV. The inte-

grated luminosity of our sample is 976 pb−1. To increasethe sensitivity to new light particles and tau leptons thatdecay leptonically, we use a very low pT threshold (5GeV/c) for the identified leptons, where pT is the trans-verse momentum with respect to the beam direction.

We define several dimuon and trilepton SM-dominatedcontrol regions, in which we verify our understanding ofthe backgrounds. In order to avoid bias, we completethe validation of the background – both in event yieldsand kinematic shapes – in the control regions before in-vestigating the events in the signal region. Finally, ourresult is combined with other trilepton searches at CDF[22] to set a stronger limit on chargino-neutralino produc-tion. Although this search is inspired by SUSY-predictedchargino-neutralino production, the analysis is genericenough to be sensitive to any new physics that wouldenhance the production of prompt trileptons and ET/ .

This paper is organized as follows. In Section II we de-scribe the CDF II detector. In Section III we define theexperimental dataset and present an event selection thatreduces the SM background expectation while acceptingevents from possible new-physics signals. Section IV de-scribes how the SM background rates are estimated, andSection V discusses two SUSY-model scenarios we con-sider. In Section VI we present the determination of thesystematic uncertainties on the signal and backgroundevent-yield predictions. In Section VII we present theevent yields and kinematic distributions in our controlregions that increase the confidence in our understand-ing of the SM background. Finally, in Section VIII wepresent the results in the signal region.

II. THE CDF II DETECTOR

The CDF II detector [23] is a multi-purpose cylindri-cal detector with projective-tower calorimeter geometryand excellent lepton identification capability. It oper-ates at the Tevatron collider where protons and antipro-tons collide with a center-of-mass energy of 1.96 TeV. Inour coordinate system the positive z-axis is defined bythe proton beam direction and the positive y-axis by thevertical upward direction. The detector is approximatelysymmetric in the η and φ coordinates, where the pseudo-rapidity η is defined as η = − ln(tan(θ/2)), θ is the polarangle with respect to ~z, and φ is the azimuthal angle. Webriefly present here the CDF components that are mostcritical to this analysis.

In the center of the apparatus, near the beam collisionpoint, a silicon detector of inner radius of 1.35 cm andouter radius of 25.6 cm provides detailed tracking in the|η| < 2 region, necessary for the accurate determinationof the proton-antiproton interaction points (primary ver-tices) and impact parameters of particle trajectories withrespect to these points.

A cylindrical 96-layer open-cell argon-ethane (50%-50%) drift chamber (COT) of inner radius of 44 cm andouter radius of 132 cm provides tracking for chargedparticles with ∼ 100% detection efficiency in the cen-tral (|η| < 1.1) region. The central tracking systemis located in a magnetic field of 1.4 T provided by asuperconducting solenoidal magnet. The relative reso-lution in tracking momentum provided by the COT isδpT /pT = 0.0017pT (GeV/c)−1.

Surrounding the central tracker, and outside thesolenoid, a central electromagnetic calorimeter (CEM)and a central hadronic calorimeter (CHA) measure theenergy of electrons, photons, and hadrons. The CEMis composed of layers of lead and scintillator whereasthe CHA is composed of layers of steel and scintilla-tor. The relative energy resolution is 13.5%/

√ET ⊕ 2%

for the CEM and 75%/√ET ⊕ 3% for the CHA, where

the transverse energy ET = E sin θ is quoted in GeVunits. A strip chamber (CES), placed inside the elec-tromagnetic calorimeter at the position of maximum de-velopment of the electromagnetic shower (six radiationlengths), is used for shower shape determination and formatching the calorimeter energy depositions with COTtracks. In the forward region, a plug electromagneticcalorimeter (1.1 < |η| < 2.4) has a relative resolutionof 16%/

√ET ⊕ 0.7% and a plug hadronic calorimeter

(1.3 < |η| < 2.4) a resolution of 130%/√ET ⊕ 4%.

The raw missing transverse energy vector is defined as

−(∑

i~EiT ), where ~EiT has magnitude equal to the en-

ergy deposited in the ith calorimeter tower and direc-tion perpendicular to the beam axis and pointing to thatcalorimeter tower.

Outside the calorimeters, the central muon systemconsists of drift chambers. The central muon cham-bers (CMU) detect muons in the pseudorapidity range|η| < 0.6, while the central muon extension (CMX) cham-bers detect muons in the 0.6 < |η| < 1.0 range, both witha detection efficiency of almost 100% for muons above 3GeV/c. To reduce the hadron punch-through contami-nation, extra chambers (CMP) are installed outside theCMU chambers, with extra steel absorber added betweenthem. The muons that are detected by both CMU andCMP chambers are labeled “CMUP muons”, and theirdetector signatures cannot be easily caused by hadrons.

The instantaneous luminosity is measured withCherenkov counters located close to the beam line at3.7 < |η| < 4.7.

The CDF trigger system [24] has a three-level pipelinedand buffered architecture; each level provides a rate re-duction sufficient to allow for processing at the next levelwith minimal deadtime. The first level consists of special-

6

purpose processors that accept events at rate of 25 kHz,with an average event size of 170 kB, counts main trig-gering objects and feeds the second level with an eventrate of 350 Hz. The second level is also based on hard-ware and performs a partial event reconstruction beforepassing the events to the next level. Finally a software-based third level uses a fast version of the offline eventreconstruction to reduce the event rate to 75 Hz, ap-propriate for writing to tape. The track-based triggersaccount for approximately 75% of the trigger bandwidthand are used in this analysis. For a muon trigger, themain requirement is that a COT track is geometricallymatched to a track segment in a muon detector.

III. THE CDF DATASET AND

SIGNAL-REGION EVENT SELECTION

In order to include in our analysis muons and elec-trons that come from tau decays, we use a low trans-verse momentum requirement (pT > 5 GeV/c) for theseleptons. For this reason we analyze data collected withthe CDF low-pT dimuon triggers (pT nominally above4 GeV/c for both muons). These muons are central inthe detector (CMUP or CMX). We measure the trig-ger efficiency using J/ψ, Υ and Z-boson events collectedwith single-muon triggers. In these samples, we removehadronic backgrounds using the mass-spectra sidebands,and count the frequency that a second muon fired thetrigger of interest. The plateau value of the trigger effi-ciency’s pT dependence for single muons is ∼ 0.95 and itis reached at pT ∼ 5 GeV/c.

After the collected events are processed by the offlinereconstruction software, additional requirements are ap-plied for the definition of the dimuon sample. We re-quire that each event has a primary vertex within 60 cmfrom the nominal center of the detector in the z directionand that at least two muons with transverse momentaabove 5 GeV/c originate from that primary vertex andpass the CDF standard muon tracking and calorimetryrequirements and track-chamber matching requirements[25]. In events with more than one reconstructed pri-mary vertex, we use the primary vertex that is closest tothe tracks of the two highest-pT muons that satisfy allother event requirements. We specifically require thattwo good-quality COT tracks are geometrically matchedwith respective reconstructed track segments in the CMXor CMU+CMP detectors, that the energies deposited inthe electromagnetic and hadronic calorimeters are con-sistent with that expected from minimum ionizing par-ticles, and that the two muons are isolated. We definethe isolation I as the energy deposited in the calorime-ters in a cone of ∆R =

√

(∆φ)2 + (∆η)2 = 0.4 aroundthe muon without counting the energy deposited by themuon. We require that I < 0.1 × pT c if pT > 20 GeV/cor I < 2 GeV otherwise, where pT is the transverse mo-mentum of the muon. The selected two muons are also∆R > 0.4 apart. A critical requirement is that the muons

are prompt as measured by the impact parameter (d0),defined as the distance of closest approach of a track tothe primary vertex in the transverse plane. We requirethat |d0| < 0.02 cm if the the muon leaves tracking signalsin the silicon detector (silicon hits) and that |d0| < 0.2 cmif the muon leaves no silicon hits. We expect that mostmuons with large impact parameters come from heavyflavor (bottom- or charm-hadron semileptonic decays),fake muons (light-flavor hadrons such as pions and kaonsthat decay in flight or punch-through to the muon de-tectors), and cosmic rays. The heavy flavor (HF) andfake-muon backgrounds dominate at low dimuon masses.Residual cosmic-ray background, not removed by the cos-mic filters described in [25], is reduced by requiring thatthe three-dimensional angular separation (∆ϕ) of the twohighest-pT muons is less than 178 degrees. After includ-ing the selection criteria discussed above, the total muonidentification efficiency, as measured with J/ψ and Z bo-son CDF data, is (90-96)%, rising with increasing muonpT .

For the trilepton selection, we require the presenceof a third muon satisfying the same selection require-ments as the first two, or an electron satisfying theCDF standard electron calorimeter, tracking, and track-calorimeter matching identification requirements [25].The transverse energy and momentum of an electron isrequired to exceed 5 GeV. Tracks associated with elec-trons should match hits in the CES wires. We requirethat I < 0.1 × ET if ET > 20 GeV or I < 2 GeV oth-erwise, where I is now the energy-based isolation of theelectron, and ET is its transverse energy. Electrons orig-inating from photons that convert into e+e− pairs areidentified with an algorithm [25] that seeks nearby trackswith a common vertex and direction. These electronsare removed from the observed data sample. The elec-tron identification efficiency is (75-83)% [25], rising withincreasing electron transverse energy, as measured withDrell-Yan [26] electrons. The third lepton is required tobe ∆R > 0.4 away from the leading two muons.

We define the signal region by the following additionalrequirements: the dimuon mass (constructed using thetwo highest-pT muons) is greater than 15 GeV/c2, forremoval of low-mass resonances, and outside a Z masswindow of 76 < Mµµ < 106 GeV/c2. In addition, werequire the missing transverse energy (ET/ ) to exceed 15GeV, in order to select events with undetected new parti-cles while rejecting Drell-Yan, HF, and fake-muon back-grounds. Finally, we count the number of jets Njets withenergy above 15 GeV and we require that Njets ≤ 1, inorder to reduce the tt background. In this analysis weuse jets defined by a fixed-cone algorithm [25] with acone size of ∆R = 0.4. We require that jets deposit lessthan 90% of their measured energy in the electromag-netic calorimeter, in order to avoid counting electrons orphotons as jets. Jet energies are corrected [27] to repre-sent better the energy of the final-state hadrons. Globaland local corrections are applied as well as inclusion ofcorrections for the effects of multiple interactions. These

7

corrections are also applied to the raw missing transverseenergy for the calculation of ET/ , which is also correctedfor the presence of muons in our events. We check theconsistency of the observed data compared to the SMpredictions in the control regions that are described inSection VII.

IV. STANDARD-MODEL BACKGROUNDS

To determine the significance of any incompatibilitybetween prediction and observation, and also to set lim-its on production cross sections and masses of new parti-cles, we need a reliable background estimation. The ma-jor SM source of dimuons is the Drell-Yan (DY) processand, in events with low dimuon mass, HF production andthe fake-lepton background. In the trilepton regions, thedominant backgrounds are DY (accompanied by a fakelepton), dibosons (WW , ZZ, andWZ), and HF. BecauseHF and fake leptons are difficult to model with MonteCarlo (MC) simulations due to sizable higher-order QCDeffects and the imperfect modeling of the lepton isolationin a high particle-multiplicity hadronic environment, weestimate these backgrounds using CDF data. All otherbackgrounds are estimated with MC simulation.

A. MC-estimated backgrounds

We use the pythia [28] generator to model the DY,WW , ZZ, and tt background, and madevent [29] forthe WZ background [30]. The DY background includesthe decays to tau leptons that subsequently decay tomuons [31]. We use the cteq5l [32] parton distributionfunctions (PDF) throughout. For the trilepton predic-tions we require the reconstructed electrons and muonsto be kinematically matched with the generator-level lep-tons, in order not to double-count some of the fake-leptoncontribution. To estimate the trilepton background fromDY+γ, we relax this matching requirement, demand thatthe electron is identified at the event-simulation level as aphoton-conversion product, and normalize the survivingevent using a scale factor [33]. This scale factor accountsfor the difference in conversion-removal inefficiency be-tween the observed data and the MC simulation. In theremainder of the paper we add the DY+γ backgroundto the rest of the diboson contribution (WW , ZZ, andWZ). We process each generated event with the CDFdetector simulation, based on geant [34]. We normal-ize all samples using the leading-order theoretical crosssections multiplied by the appropriate scale (“K-factor”)to correct for next-to-leading order effects [35, 36]. Scalefactors that correct for the known differences in leptonidentification and reconstruction efficiencies between theobserved data and the MC simulation are also applied.

B. Data-estimated backgrounds

We first estimate the fake-lepton background, usingan independent CDF data sample. Subsequently, we usethis fake-lepton background and the MC-estimated DYcontribution in our HF-estimation method.

1. Fake leptons

“Fake” leptons are reconstructed lepton candidatesthat are either not real leptons or are real leptons but areneither prompt nor do they originate from semileptonicdecays of HF quarks. In the case of muons, the fakes canbe light-flavored hadrons, such as pions and kaons or partof hadronic showers, that penetrate (“punch through”)the calorimeters and reach the muon detectors or decayto muons in flight. In the case of electrons, fakes arejets that are misreconstructed as electrons, often due toneutral pions that decay to photons, which shower inthe electromagnetic calorimeter. We can thus associatethe fake leptons with light-flavor partons. Using multijetCDF datasets collected with jet-based triggers, we mea-sure the “fake rate”, i.e., the probability for an isolatedtrack to be misreconstructed as a muon or the probabil-ity for a jet to be misreconstructed as an electron. Thefake-rate is measured as a function of the track’s (jet’s)transverse momentum (energy) and pseudorapidity. Thefake rate is of the order of 10−2 for isolated tracks to beincorrectly reconstructed as muons and increases with thepT of the muon candidate’s track. The fake rate of a jetbeing reconstructed as an electron is of the order of 10−4

and falls with increasing ET . The fake rates increase forhigher pseudorapidity leptons [33].

To determine the background coming from a realmuon and a misidentified hadron (i.e., fake dimuon back-ground), we use single-muon low-pT -triggered CDF data.For each event, we require one good muon candidate thatpasses the requirements of our analysis. We then applythe fake rate on all other tracks in the event, except onthe track of a second muon (to remove DY contamina-tion of the fake background). We remove events in whichthe “muon+track” mass is within the Z boson window(76 < Mµµ < 106 GeV/c2) and also 35 < ET/ < 55GeV. These events are associated with decays of real Zbosons produced at rest, where one decay muon is notdetected, resulting in ET/ equal to about half the mass ofthe Z boson. We investigate the heavy flavor contami-nation in this light-flavor-dominated background, causedby a real muon coming from a heavy-quark semileptonicdecay, which is misreconstructed as an isolated track in-stead of a muon. This contamination is negligible (ap-proximately 0.2% of the background), mainly because ofthe background-rejection power of our muon isolation re-quirement. Because the single-muon low-pT trigger wasnot always present during data taking, the dimuon fakesextracted using this trigger are normalized to the defaultdimuon CDF data luminosity, in order to represent the

8

size of fake dimuon contamination in our analysis CDFdataset. In CDF data with no ET/ or jet multiplicity cutsapplied (“inclusive” dataset), ∼ (9± 5)% of the dimuonsare fake. In the signal region, the dimuon fake contami-nation is ∼ (16 ± 8)%.

For the determination of the background comingfrom a real muon pair and a misidentified hadron (i.e.,fake trilepton background), we use our dimuon low-pT -triggered CDF dataset, require two good muons, andmodel the fake third lepton by applying the fake rate tothe extra tracks. We assume that the number of eventswith two fake leptons is negligible, given the low value ofthe fake rates. In order not to over-count the trileptonfakes, we require the three leptons in our signal MC andbackground MC samples to be kinematically matchedwith the generated ones. The fake trilepton backgroundis determined to be ∼ (50±25)% of the total backgroundin both the inclusive dataset and the signal region.

2. Heavy flavor

One of the most significant challenges of this analysisis the consideration of muons with transverse momentumas low as 5 GeV/c. This low pT requirement increasesour acceptance, but at the same time contaminates oursample with HF and fake-lepton events.

We present here an innovative technique for the de-termination of the amount of this background using theobserved data. We construct an HF-rich (HFR) CDFdataset by reversing the impact parameter requirementfor at least one of the observed muons, so that the abso-lute value of the muon impact parameter is above 0.02 cmif there are silicon hits associated with the muon track, orabove 0.2 cm if there are no silicon hits. We also requirethe dimuon mass to be less than 35 GeV/c2. Monte Carlostudies show that above that value we expect mainly DYand a negligible HF background. We investigated the ex-pected dimuon mass spectrum of DY and fake-lepton inthe HFR sample and we determined that the effect of thecontamination is negligible.

We subsequently use the HFR dimuon mass shapecombined with the absolute fake dimuon mass distribu-tion plus the absolute DY dimuon mass distribution fromMC simulation in order to fit the observed data. Alldata samples other than HFR include the low impactparameter requirement. Because we observe negligibleDY in the same-charge dimuon channel, we perform thefit for same-charge and opposite-charge dimuons sepa-rately. This helps us validate our HF-estimation methodin the HF-rich same-charge dimuon environment. Theonly free parameter of the fits is the HF normalization– the DY contribution is fixed based on the theoreticalcross section and the integrated luminosity of the ob-served data, and the fake-lepton background distributionis fixed based on the absolute expectation, as described inSection IVB 1. The results of the fits can be seen in Figs.3 and 4, for opposite-charge and same-charge muons, re-

spectively. From the two fits, we extract two HF normal-ization factors that are applied as weights to the origi-nal unweighted same-charge and opposite-charge dimuonHFR events, in order to describe the HF background inthe observed data. The same weights are used in allkinematic control regions. The weight for the opposite-charge HF dimuons is 1.94±0.04 and for the same-chargeHF dimuons is 1.12± 0.05, where the uncertainties comefrom the fits. This tells us that we expect almost twice asmany opposite-charge HF events in the low-impact pa-rameter region compared to the high-impact parameterone. Overall, the ratio of opposite-charge HF to same-charge HF events in the inclusive observed data afterthe normalization is ∼ 4:1, a value that is also verifiedwith bb/cc MC simulation and is a result of the conservedcharge in the underlying quark-pair production and therates of cascade semileptonic decays of b-hadrons and c-hadrons. In regions with no HFR events, we estimate thesize of this background by extrapolating the HF predic-tion from neighboring dimuon control regions that con-tain sufficient numbers of events.

The trilepton HF background is estimated by requiringthat the normalized HFR sample has a third lepton. Ifthere are no events satisfying this requirement, then weextrapolate from either neighboring dimuon or trileptoncontrol regions with sufficient statistics. For example,we have no HFR data in the trilepton signal region. Weestimate the HF background there by extrapolating fromthe low-ET/ region, where we have trilepton HFR events.For the extrapolation we use the dimuon ET/ distribution,using the fact the ET/ distribution is similar for dimuonand trilepton events. We verify this fact with the use ofMC-simulated bb/cc events.

For the determination of the systematic uncertainty as-sociated with the HF-estimation method, we re-estimatethe HF background by redefining the HFR dataset usingeither a requirement on the number of silicon detectorhits for the muon that has large impact parameter (atleast two silicon hits), and/or applying a requirement onthe impact parameter significance (|d0|/δ|d0| > 5). Thesecuts favor HF events but reduce our HFR dataset statis-tics. The HF-estimation method systematic uncertaintyis about 25% in the signal region.

Although the HF normalization is extracted from theinclusive analysis sample, with dimuon mass greater than10.5 GeV/c2 (to avoid the Υ resonances) and no addi-tional ET/ or jet multiplicity requirements, the agreementof our HF predictions in both event yields and kinematicdistributions for all our dimuon and trilepton control re-gions is excellent, as we show in Section VII.

V. SUSY SIGNAL SCENARIOS

This analysis is a generic search for trilepton eventsin which we focus on minimizing the SM background.We nevertheless consider two mSUGRA [37] SUSY signalscenarios, “SIG1” and “SIG2”, defined by the value of the

9

)2Dimuon Mass (GeV/c0 20 40 60 80 100 120 140

)2N

um

ber

of

Eve

nts

/(1.

5 G

eV/c

1

10

210

310

CDF data

Total Background

HF

Fakes

)2Dimuon Mass (GeV/c0 20 40 60 80 100 120 140

)2N

um

ber

of

Eve

nts

/(1.

5 G

eV/c

1

10

210

310

Opposite-Charge Dimuons

FIG. 3: Fit of HF+DY+fakes dimuon mass distribution to the observed data for opposite-charge dimuons. The HF normaliza-tion is the only free parameter of the fit. The blue (light gray) filled histogram is the HF and the red (dark gray) is the fakes.The thick line represents the total background, which is almost exclusively DY, HF, and fakes at the opposite-charge dimuonlevel. The hatched areas indicate the total uncertainty on the prediction.

)2Dimuon Mass (GeV/c0 5 10 15 20 25 30 35 40 45

)2N

um

ber

of

Eve

nts

/(1.

5 G

eV/c

0

200

400

600

800

1000 CDF data

Total Background

HF

Fakes

)2Dimuon Mass (GeV/c0 5 10 15 20 25 30 35 40 45

)2N

um

ber

of

Eve

nts

/(1.

5 G

eV/c

0

200

400

600

800

1000

Same-Charge Dimuons

FIG. 4: Fit of HF+DY+fakes dimuon mass distribution to the observed data for same-charge dimuons. The HF normalizationis the only free parameter of the fit. The blue (light gray) filled histogram is the HF and the red (dark gray) is the fakes. Thethick line represents the total background, which is constituted almost exclusively by HF and fakes for same-charge dimuonpairs. The hatched areas indicate the total uncertainty on the prediction.

10

common sfermion mass (m0) and common gaugino mass(m 1

2

) at unification scale, the trilinear coupling (A0), the

ratio of the two Higgs fields vacuum expectation values(tanβ), and the sign of the higgsino mixing parameter(sign(µ)):

• SIG1: m0=100 GeV/c2, m 1

2

=180 GeV/c2, A0=0,

tanβ=5, µ > 0. The expected cross section σ(pp→χ±

1 χ02) times the branching ratio B to leptons is

σ × B = 0.642 × 0.22 pb. The cross section wasobtained using the next-to-leading order calcula-tion of prospino [38] and the branching ratio us-ing pythia. The corresponding chargino and light-est neutralino masses would be 116 GeV/c2 and 65GeV/c2, respectively.

• SIG2: m0=74 GeV/c2, m 1

2

=168 GeV/c2, A0=0,

tanβ=3, µ > 0. The expected cross section timesthe branching ratio to leptons is σ×B = 1.023×0.5pb, as given by prospino and pythia. The cor-responding chargino and lightest neutralino masseswould be 103 GeV/c2 and 57 GeV/c2, respectively.

These two signal scenarios serve as benchmarks of pos-sible SUSY signal and were used for the optimization ofthe minimum ET/ requirement in the signal region, whichis set at 15 GeV [39]. The mass spectrum of the super-symmetric particles was obtained with isajet [40] andthe events are generated with pythia. The SIG1 sce-nario leads to three-body decays (Fig. 2a,b) of the light-est chargino (χ±

1 ) and the next-to-lightest neutralino (χ02)

with branching ratios to electrons and muons suppressed,due to the low branching ratio of the gauge bosons to lep-tons. On the other hand, the SIG2 scenario leads exclu-sively to two-body decays (Fig. 2c,d) of both gauginos tosleptons, with χ±

1 decaying always to a final-state tau lep-ton (produced from a stau decay). Our analysis is moresensitive to SIG2, due to the higher cross section and ourability to select events with low momentum final-stateleptons, originating from tau decays.

VI. SYSTEMATIC UNCERTAINTIES

The sensitivity of our search to signals of new physicsand the significance of a potential excess of events areinfluenced by the uncertainties on our background esti-mates. Because we perform a counting experiment, weconcentrate on the uncertainties on the expected numberof background and signal events. The event-yield system-atic uncertainty is naturally different for MC-simulatedand CDF-data-estimated physical processes. We firstdiscuss the systematic uncertainty on the MC-estimatedbackgrounds and SUSY signals and then we treat the sys-tematic uncertainty on the CDF-data-based backgroundfrom HF and fake leptons.

The sources of systematic uncertainty in the signal re-gion, with their effect on signal and MC-estimated back-ground event yields are:

• the luminosity uncertainty (6%) [41, 42],

• the lepton-identification scale factors uncertainty(∼ 10%),

• the trigger efficiency uncertainty (∼ 1%),

• the jet-energy scale uncertainty (∼ 1%) [27]; thissource of systematic uncertainty is responsible formigrating events from one control or signal regionto another, since variations in jet energies affectboth the corrections to the ET/ and the jet multi-plicity,

• the PDF uncertainty (1%-2%) [32].

• the uncertainty from the theoretical cross-sectionsestimates (5-12% depending on the process) [35,36],

• the uncertainty on the initial- and final-state QCD-induced radiation (ISR/FSR) [43], which has aneffect of 4% and 12% for background and signalMC samples, respectively, and

• the uncertainty induced from the limited MC statis-tics: for the SIG2 MC it is ∼ 2% for the dimuonsand ∼ 6% for the trileptons; for the standard-modelbackground MC it is ∼ 3% for the dimuons and∼ 40% for the trileptons (the latter mainly due tothe DY+γ limited MC statistics).

All of the above sources of systematic uncertainty arecorrelated among the different physics processes (DY, di-boson, tt), with the exceptions of the cross section sys-tematic uncertainties and the MC samples’ statistical un-certainties. Still, the sources of systematic uncertaintiesare uncorrelated with each other and the respective un-certainties are summed in quadrature with each other togive the total yield uncertainties in the control and signalregions.

The systematic uncertainty associated with the HF-estimation method consists of a part that is anti-correlated with the DY+fakes systematic uncertainty(because the HF weights are given by the fit of theDY+fakes+HF to the observed data, and a varied levelof DY+fakes affects these weights) and an uncorrelatedpart (from the fit uncertainty of about 2-4% for the fixedDY+fakes level and from the HF-estimation methodsystematic uncertainty, as described in Section IVB2).The correlated DY+HF+fakes systematic uncertainty isabout 22%. The fake-lepton uncertainty is set to a con-servative maximum-envelope 50% level, which is deter-mined by studying different jet-triggered CDF samples[33]. For the total systematic uncertainty of the pre-dicted SM event yield in all control regions we take intoaccount all correlations among physics processes. Foreach source of systematic uncertainty affecting the MCsamples, we vary all MC samples (including DY) in a cor-related manner and redo the fit of DY+fakes+HF to theobserved data to extract a new HF estimation. The total

11

TABLE I: The dimuon and trilepton event-yield systematicuncertainties for the backgrounds in the signal region. Theuncertainties are summed based on the contributions of theseparate backgrounds taking into account all correlations.The upper part of the table shows the MC-related system-atic uncertainties whereas the lower part shows the system-atic uncertainties for the CDF-data-estimated backgrounds.The uncertainties due to the MC statistics are not shown.

Source Dimuons TrileptonsElectron scale factors – ±2%Muon scale factors ±8% ±5%

Luminosity ±3% ±2%Trigger efficiency ±0.5% ±0.2%

PDF ±2% ±1%ISR/FSR ±2% ±1%

Theoretical cross sections ±3% ±2%Jet-energy scale ±0.5% ±0.02%Total MC syst. ±9% ±6%Fakes estimation ±8% ±25%HF estimation ±5% ±2%

Total (with correlations) ±10% ±24%

TABLE II: The dimuon and trilepton event-yield systematicuncertainties in the signal region, for the SIG1 and SIG2SUSY scenarios.

Source Dimuons TrileptonsElectron scale factors – ±6%Muon scale factors ±11% ±15%

Luminosity ±6% ±6%Trigger efficiency ±0.9% ±0.5%

PDF ±1% ±1%ISR ±12% ±12%

Theoretical cross sections ±10% ±10%Jet-energy scale ±0.3% ±0.6%MC statistics ±2% ±6%

Total ±20% ±24%

variation gives us the total effect of the systematic uncer-tainty. The same procedure is followed when we includethe fake-lepton estimation uncertainty and its effect onHF due to the above fit.

The effect of the systematic uncertainties on the back-ground and SUSY signal expected event yields in the sig-nal region can be found in Tables I and II respectively.

VII. CONTROL REGIONS

We investigate control regions defined by the dimuonmass, ET/ , and jet multiplicity, as shown in Fig. 5. Over-all, 22 dimuon and trilepton control regions are defined.Most control regions we investigate are naturally SM-dominated with little expectation of SUSY signal. LowET/ and Mµµ regions are dominated by the HF back-

ground, whereas the 76 < Mµµ < 106 GeV/c2 region isalmost exclusively populated with Z bosons. The 5 GeVgap in the ET/ cuts between the signal and the controlregions ensures that the low ET/ control regions contain anegligible amount of signal. We compare the SM event-yield predictions with observed events in the control re-gions (along with kinematic plots) before looking at thesignal region.

We present here a Z boson resonance control region(“Control z”), a low ET/ control region (“Control a”),and three control regions (“Control b, c, and d”) thatresult from the inversion of one of the three signal regionrequirements at a time [dimuon mass (Mµµ), or ET/ , orjet multiplicity (Njets) respectively]. In region z, we re-quire that the muons have opposite charge and that thedimuon mass lie between 76 and 106 GeV/c2. We usethis control region for validating the luminosity, the trig-ger efficiencies, and muon-identification scale factors. Inregion a, we require that ET/ < 10 GeV and Mµµ > 10.5GeV/c2. This region is used for verifying our knowl-edge of HF and fake-lepton backgrounds. In region b,we require ET/ > 15 GeV, dimuon mass within the Z-mass region, and low jet multiplicity (at most one jet).This region helps us verify our background prediction ina low-yield region as most Z events are characterized bylow ET/ . In region c, we require ET/ < 10 GeV, exclu-sion of the Z mass region, Mµµ > 15 GeV/c2, and lowjet multiplicity. This region along with region a are theones with the highest population of HF events. In regiond, we require ET/ > 15 GeV, exclusion of the Z mass re-gion, Mµµ > 15 GeV/c2, and high jet multiplicity (morethan one jet). This region is expected to be the mostsensitive to tt production. We finally study the dimuonevents with all signal-region kinematic cuts applied, butbefore the requirement for a third lepton. This is a crit-ical control region as the trilepton signal is a subset ofthis region.

Table III shows the expected and observed number ofdimuon events in our control regions, and Table IV showsthe expected and observed number of trilepton events.After requiring the presence of a third electron or muon,only control regions z, a and c are populated with ex-perimental data. Region z trilepton event yields establishour understanding of the electron fakes, since the thirdelectron in Z boson events is almost exclusively a non-prompt electron. On the other hand, trilepton regionsz and c confirm our understanding of the HF and fakebackgrounds for trileptons. Figs. 6 and 7 show thedimuon mass and ET/ distributions for the dimuon con-trol regions. The agreement between observed data andprediction in the control regions is satisfactory, both inevent yields and kinematic distributions.

VIII. SIGNAL REGION RESULT

After observing satisfactory agreement between experi-mental data and SM predictions in both the dimuon and

12

jets(if N >1) jets(if N >1)Control D

Control A

Control D

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10

15

Control Z76 10610.5 15

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M

(GeV)

µµ (GeV/c )2

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FIG. 5: The control and signal regions used in our analysis are defined in the dimuon mass vs. ET/ plane, with the extrarequirement of low (≤ 1) or high (> 1) jet multiplicity. In this paper we show results for the control regions that result fromthe inversion of one of the three main kinematic selections (dimuon mass, missing transverse energy, and jet multiplicity), withthe addition of a Z-mass control region (Control z) and a low-ET/ control region (Control a). The control regions above aredefined for low jet multiplicity, unless otherwise stated.

TABLE III: Expected and observed dimuon event yields, in all control regions and the signal region. The expected SUSY signalevent yield is for the SIG2 mSUGRA scenario. Combined statistical and systematic uncertainties are shown and correlationsamong sources of systematic uncertainty are included. The signal region without a requirement for a third lepton is a dimuoncontrol region.

Region DY HF Fakes Diboson tt Total SM expected SUSY expected Observed

Control z 6419 ± 709 - 10 ± 11 2.4 ± 0.2 1.18 ± 0.14 6433 ± 712 0.30 ± 0.07 6347Control a 14820 ± 2242 9344 ± 1612 2294 ± 1148 1.03 ± 0.09 0.12 ± 0.03 26459 ± 1429 0.9 ± 0.2 26295Control b 217 ± 25 - 9 ± 7 1.7 ± 0.2 0.27 ± 0.05 227 ± 26 0.5 ± 0.1 253Control c 5770 ± 1043 2238 ± 384 466 ± 234 0.49 ± 0.07 0.02 ± 0.01 8474 ± 857 0.7 ± 0.2 8205Control d 7.8 ± 1.5 9 ± 4 0.3 ± 0.3 0.21 ± 0.07 4.1 ± 0.4 22 ± 5 1.8 ± 0.4 23

Signal Reg. 169 ± 30 90 ± 20 49 ± 25 6.5 ± 0.4 0.96 ± 0.11 315 ± 37 17 ± 3 297

TABLE IV: Expected and observed trilepton event yields, in all control regions and the signal region. The expected SUSY signalevent yield is for the SIG2 mSUGRA scenario. Combined statistical and systematic uncertainties are shown and correlationsamong sources of systematic uncertainty are included.

Region DY HF Fakes Diboson tt Total SM expected SUSY expected Observed

Control z 0.2 ± 0.2 - 2.5 ± 1.2 0.26 ± 0.06 - 3 ± 1 0.06 ± 0.01 4Control a 0.3 ± 0.2 6 ± 3 7.6 ± 3.8 0.25 ± 0.08 - 14 ± 4 0.08 ± 0.02 16Control b - - 0.2 ± 0.1 0.094 ± 0.009 - 0.3 ± 0.1 0.10 ± 0.03 0Control c 0.2 ± 0.2 3 ± 2 2 ± 1 0.10 ± 0.06 - 5 ± 2 0.06 ± 0.02 8Control d - - 0.02 ± 0.01 0.003 ± 0.002 0.011 ± 0.008 0.03 ± 0.01 0.04 ± 0.02 0

Signal Reg. - 0.06 ± 0.04 0.2 ± 0.1 0.15 ± 0.06 - 0.4 ± 0.1 1.7 ± 0.4 1

trilepton control regions, we look at the CDF data inthe trilepton signal region. We observe one event con-taining three muons (trimuon event). The event is char-acterized by low track activity and three well-identifiedmuons that are produced within ∼ 40 degrees in φ. Twoof the muons are energetic, with transverse momenta of45 and 21 GeV/c, and the third one is a soft muon with

pT of 8 GeV/c. Table V shows the main properties ofthis event. It is interesting to note the close values of allthree dimuon masses. The event includes one hadronicjet and two energy clusters of mostly electromagnetic en-ergy with transverse energy of ∼ 41, ∼ 9, and ∼ 4 GeVrespectively. The jet and the muons originate from thesame and only high-quality primary vertex. If the elec-

13

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FIG. 6: Dimuon mass and ET/ distributions for the SM background in the dimuon control regions z (a,b), a (c,d), and b (e,f).The background histograms are stacked. The CDF data are indicated by points with error bars.

tromagnetic energy clusters correspond to real photons,the event would also be interesting in the gauge-mediatedsupersymmetry breaking (GMSB [44]) scenario, wherethe lightest neutralino decays to a photon and a grav-itino, which is the LSP. In that case, the final leptonicsignature of the chargino-neutralino production would bethree leptons, two photons, and ET/ .

Fig. 8 shows where the one trimuon event observed inthe signal region appears in the expected distributions ofkinematic variables for the signal and the backgrounds.Kinematic distributions include the three-dimensionalopening angle between the leading muons, ∆ϕ. Figs.9 and 10 show the transverse and lego detector displays,

respectively, for this trimuon event. The Poisson proba-bility to see one event or more, when we expect 0.4±0.1,is 32.6%.

It is interesting also to interpret this event in the con-text of a search only for trimuon events. The dibosonbackgrounds remain, but the large source of fakes in thedimuon+e sample is reduced. The total trimuon back-ground estimation is 0.16 ± 0.04 events. The Poissonprobability to observe one event or more, when we ex-pect 0.16 ± 0.04, is 14.7%. We conclude that our eventyield is statistically consistent with the SM prediction,noting that most of the kinematics of the event - espe-cially the three-dimensional opening angle of the leading

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FIG. 7: Dimuon mass and ET/ for the SM background in the dimuon control regions c (a,b), d (c,d), and dimuon signal region(e,f). The background histograms are stacked. The CDF data are indicated by points with error bars.

TABLE V: Observed trimuon event properties.

Kind of muons CMUP - CMX - CMXpT of muons (GeV/c) 45.0, 21.1, 7.8

η of muons -0.2, -0.9, 0.8φ of muons (deg.) 359, 321, 340

Isolation of muons (GeV) 2.4, 0.2, 1.1Charge of muons -1, 1, -1

Dimuon masses (GeV/c2) 29.3(1&2), 21.7(1&3), 25.7(2&3)Transverse mass (muon+ET/ ) 86.4, 51.4, 34.23-d ∆ϕ(leading muons) (deg.) 46.3

ET/ (GeV) 43.8ET/ φ (deg.) 205.6

Number of Jets 1ET of jet (GeV) 41.1

η of jet -1.6φ of jet (deg.) 102.9

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FIG. 8: Kinematic variables for the SM background and the SIG2 SUSY signal, in the trilepton signal region. The backgroundhistograms are stacked; the signal histogram is not. The CDF data are indicated by points with error bars.

16

=45 GeV/cTµp

=8 GeV/cTµp

=21 GeV/cTµp

=41 GeVTjetE

=44 GeVTE

FIG. 9: The trimuon event in the transverse view of the cen-tral CDF detector. Tracks with transverse momenta above1 GeV/c are shown.

-3

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0100

200300

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ET(GeV)

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FIG. 10: The trimuon event in the η − φ view. Calorimetertransverse energies above 1 GeV are shown. The longer barscorrespond to the track momenta of the three muons (highφ). The calorimeter energy depositions E1 and E2 are mainlyelectromagnetic and could be associated with two photons.

muons ∆ϕ - are consistent with new physics expectation,as can be seen in Fig. 8.

We have combined the results of this analysis withother CDF trilepton analyses to set exclusion limits inseveral models. For mSUGRA with no slepton mixing,we set a lower limit for the chargino mass of 129 GeV/c2,which corresponds to an upper limit in σ × B of about0.25 pb at the 95% confidence level [22].

IX. ACKNOWLEDGMENTS

We thank the Fermilab staff and the technical staffsof the participating institutions for their vital contribu-tions. This work was supported by the U.S. Departmentof Energy and National Science Foundation; the Italian

Istituto Nazionale di Fisica Nucleare; the Ministry ofEducation, Culture, Sports, Science and Technology ofJapan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A P Sloan Foundation; the Bundesministeriumfur Bildung und Forschung, Germany; the Korean Sci-ence and Engineering Foundation and the Korean Re-search Foundation; the Science and Technology FacilitiesCouncil and the Royal Society, UK; the Institut Nationalde Physique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Ministe-rio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and theAcademy of Finland.

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