Search for anomalous production of events with two photons and additional energetic objects at CDF

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Search for Anomalous Production of Events with Two Photons and Additional

Energetic Objects at CDF

T. Aaltonen,24 J. Adelman,14 B. Alvarez Gonzalezv,12 S. Ameriodd,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 J. Asaadi,54 W. Ashmanskas,18

A. Attal,4 A. Aurisano,54 F. Azfar,43 W. Badgett,18 A. Barbaro-Galtieri,29 V.E. Barnes,49 B.A. Barnett,26

P. Barriaff ,47 P. Bartos,15 G. Bauer,33 P.-H. Beauchemin,34 F. Bedeschi,47 D. Beecher,31 S. Behari,26

G. Bellettiniee,47 J. Bellinger,60 D. Benjamin,17 A. Beretvas,18 A. Bhatti,51 M. Binkley,18 D. Bisellodd,44

I. Bizjakjj ,31 R.E. Blair,2 C. Blocker,7 B. Blumenfeld,26 A. Bocci,17 A. Bodek,50 V. Boisvert,50 D. Bortoletto,49

J. Boudreau,48 A. Boveia,11 B. Braua,11 A. Bridgeman,25 L. Brigliadoricc,6 C. Bromberg,36 E. Brubaker,14

J. Budagov,16 H.S. Budd,50 S. Budd,25 K. Burkett,18 G. Busettodd,44 P. Bussey,22 A. Buzatu,34 K. L. Byrum,2

S. Cabrerax,17 C. Calancha,32 S. Camarda,4 M. Campanelli,36 M. Campbell,35 F. Canelli14,18 A. Canepa,46

B. Carls,25 D. Carlsmith,60 R. Carosi,47 S. Carrillon,19 S. Carron,18 B. Casal,12 M. Casarsa,18 A. Castrocc,6

P. Catastiniff ,47 D. Cauz,55 V. Cavaliereff ,47 M. Cavalli-Sforza,4 A. Cerri,29 L. Cerritoq,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

K. Chungo,18 W.H. Chung,60 Y.S. Chung,50 T. Chwalek,27 C.I. Ciobanu,45 M.A. Ciocciff ,47 A. Clark,21 D. Clark,7

G. Compostella,44 M.E. Convery,18 J. Conway,8 M.Corbo,45 M. Cordelli,20 C.A. Cox,8 D.J. Cox,8 F. Crescioliee,47

C. Cuenca Almenar,61 J. Cuevasv,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’Orsoee,47 C. Deluca,4 L. Demortier,51

J. Dengf ,17 M. Deninno,6 M. d’Erricodd,44 A. Di Cantoee,47 G.P. di Giovanni,45 B. Di Ruzza,47 J.R. Dittmann,5

M. D’Onofrio,4 S. Donatiee,47 P. Dong,18 T. Dorigo,44 S. Dube,53 K. Ebina,58 A. Elagin,54 R. Erbacher,8

D. Errede,25 S. Errede,25 N. Ershaidatbb,45 R. Eusebi,54 H.C. Fang,29 S. Farrington,43 W.T. Fedorko,14 R.G. Feild,61

M. Feindt,27 J.P. Fernandez,32 C. Ferrazzagg,47 R. Field,19 G. Flanagans,49 R. Forrest,8 M.J. Frank,5 M. Franklin,23

J.C. Freeman,18 I. Furic,19 M. Gallinaro,51 J. Galyardt,13 F. Garberson,11 J.E. Garcia,21 A.F. Garfinkel,49

P. Garosiff ,47 H. Gerberich,25 D. Gerdes,35 A. Gessler,27 S. Giaguhh,52 V. Giakoumopoulou,3 P. Giannetti,47

K. Gibson,48 J.L. Gimmell,50 C.M. Ginsburg,18 N. Giokaris,3 M. Giordaniii,55 P. Giromini,20 M. Giunta,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,33 O. Gonzalez,32 I. Gorelov,38 A.T. Goshaw,17 K. Goulianos,51 A. Greseledd,44

S. Grinstein,4 C. Grosso-Pilcher,14 R.C. Group,18 U. Grundler,25 J. Guimaraes da Costa,23 Z. Gunay-Unalan,36

C. Haber,29 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 R.F. Harr,59 M. Hartz,48 K. Hatakeyama,5 C. Hays,43 M. Heck,27 J. Heinrich,46 M. Herndon,60

J. Heuser,27 S. Hewamanage,5 D. Hidas,53 C.S. Hillc,11 D. Hirschbuehl,27 A. Hocker,18 S. Hou,1 M. Houlden,30

S.-C. Hsu,29 R.E. Hughes,40 M. Hurwitz,14 U. Husemann,61 M. Hussein,36 J. Huston,36 J. Incandela,11 G. Introzzi,47

M. Iorihh,52 A. Ivanovp,8 E. James,18 D. Jang,13 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. Katom,42 R. Kephart,18 W. Ketchum,14 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,58

L. Kirsch,7 S. Klimenko,19 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. Kuhr,27 N.P. Kulkarni,59 M. Kurata,56

S. Kwang,14 A.T. Laasanen,49 S. Lami,47 S. Lammel,18 M. Lancaster,31 R.L. Lander,8 K. Lannonu,40 A. Lath,53

G. Latinoff ,47 I. Lazzizzeradd,44 T. LeCompte,2 E. Lee,54 H.S. Lee,14 J.S. Lee,28 S.W. Leew,54 S. Leone,47

J.D. Lewis,18 C.-J. Lin,29 J. Linacre,43 M. Lindgren,18 E. Lipeles,46 A. Lister,21 D.O. Litvintsev,18 C. Liu,48

T. Liu,18 N.S. Lockyer,46 A. Loginov,61 L. Lovas,15 D. Lucchesidd,44 J. Lueck,27 P. Lujan,29 P. Lukens,18

G. Lungu,51 J. Lys,29 R. Lysak,15 D. MacQueen,34 R. Madrak,18 K. Maeshima,18 K. Makhoul,33 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. Martink,22 M. Martınez,4 R. Martınez-Balların,32 P. Mastrandrea,52 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

C. Mesropian,51 T. Miao,18 D. Mietlicki,35 N. Miladinovic,7 R. Miller,36 C. Mills,23 M. Milnik,27 A. Mitra,1

G. Mitselmakher,19 H. Miyake,56 S. Moed,23 N. Moggi,6 M.N. Mondragonn,18 C.S. Moon,28 R. Moore,18

M.J. Morello,47 J. Morlock,27 P. Movilla Fernandez,18 J. Mulmenstadt,29 A. Mukherjee,18 Th. Muller,27 P. Murat,18

M. Mussinicc,6 J. Nachtmano,18 Y. Nagai,56 J. Naganoma,56 K. Nakamura,56 I. Nakano,41 A. Napier,57 J. Nett,60

C. Neuz,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 K. Osterberg,24 S. Pagan Grisodd,44

2

C. Pagliarone,55 E. Palencia,18 V. Papadimitriou,18 A. Papaikonomou,27 A.A. Paramanov,2 B. Parks,40

S. Pashapour,34 J. Patrick,18 G. Paulettaii,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 K. Potamianos,49

O. Poukhov∗,16 F. Prokoshiny,16 A. Pronko,18 F. Ptohosi,18 E. Pueschel,13 G. Punziee,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. Rimondicc,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 B. Rutherford,18

H. Saarikko,24 A. Safonov,54 W.K. Sakumoto,50 L. Santiii,55 L. Sartori,47 K. Sato,56 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. Scribanoff ,47 F. Scuri,47 A. Sedov,49 S. Seidel,38 Y. Seiya,42 A. Semenov,16 L. Sexton-Kennedy,18

F. Sforzaee,47 A. Sfyrla,25 S.Z. Shalhout,59 T. Shears,30 P.F. Shepard,48 M. Shimojimat,56 S. Shiraishi,14

M. Shochet,14 Y. Shon,60 I. Shreyber,37 A. Simonenko,16 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,18 S. Somalwar,53 V. Sorin,4

P. Squillaciotiff ,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 J.S. Suh,28 A. Sukhanov,19 I. Suslov,16 A. Taffardf ,25 R. Takashima,41 Y. Takeuchi,56 R. Tanaka,41

J. Tang,14 M. Tecchio,35 P.K. Teng,1 J. Thomh,18 J. Thome,13 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. Totaroii,55 S. Tourneur,45 M. Trovatogg,47 S.-Y. Tsai,1 Y. Tu,46 N. Turiniff ,47 F. Ukegawa,56

S. Uozumi,28 N. van Remortelb,24 A. Varganov,35 E. Vatagagg,47 F. Vazquezn,19 G. Velev,18 C. Vellidis,3

M. Vidal,32 I. Vila,12 R. Vilar,12 M. Vogel,38 I. Volobouevw,29 G. Volpiee,47 P. Wagner,46 R.G. Wagner,2

R.L. Wagner,18 W. Wagneraa,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 H. Wolfe,40 T. Wright,35 X. Wu,21 F. Wurthwein,10 A. Yagil,10 K. Yamamoto,42

J. Yamaoka,17 U.K. Yangr,14 Y.C. Yang,28 W.M. Yao,29 G.P. Yeh,18 K. Yio,18 J. Yoh,18 K. Yorita,58 T. Yoshidal,42

G.B. Yu,17 I. Yu,28 S.S. Yu,18 J.C. Yun,18 A. Zanetti,55 Y. Zeng,17 X. Zhang,25 Y. Zhengd,9 and S. Zucchellicc6

(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, ccUniversity 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, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany28Center for High Energy Physics: Kyungpook National University,Daegu 702-701, Korea; Seoul National University, Seoul 151-742,

Korea; Sungkyunkwan University, Suwon 440-746,

3

Korea; Korea Institute of Science and Technology Information,Daejeon 305-806, Korea; Chonnam National University, Gwangju 500-757,

Korea; Chonbuk National University, Jeonju 561-756, Korea29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720

30University of Liverpool, Liverpool L69 7ZE, United Kingdom31University College London, London WC1E 6BT, United Kingdom

32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

34Institute of Particle Physics: McGill University, Montreal, Quebec,Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia,

Canada V5A 1S6; University of Toronto, Toronto, Ontario,Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

35University of Michigan, Ann Arbor, Michigan 4810936Michigan State University, East Lansing, Michigan 48824

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia38University of New Mexico, Albuquerque, New Mexico 87131

39Northwestern University, Evanston, Illinois 6020840The Ohio State University, Columbus, Ohio 4321041Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan43University of Oxford, Oxford OX1 3RH, United Kingdom

44Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, ddUniversity of Padova, I-35131 Padova, Italy45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 1910447Istituto Nazionale di Fisica Nucleare Pisa, eeUniversity of Pisa,

ffUniversity of Siena and ggScuola Normale Superiore, I-56127 Pisa, Italy48University of Pittsburgh, Pittsburgh, Pennsylvania 15260

49Purdue University, West Lafayette, Indiana 4790750University of Rochester, Rochester, New York 14627

51The Rockefeller University, New York, New York 1002152Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,

hhSapienza 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,

I-34100 Trieste, iiUniversity of Trieste/Udine, I-33100 Udine, Italy56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 0215558Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 4820160University of Wisconsin, Madison, Wisconsin 53706

61Yale University, New Haven, Connecticut 06520(Dated: January 3, 2014)

We present results of a search for anomalous production of two photons together with an electron,muon, τ lepton, missing transverse energy, or jets using pp collision data from 1.1-2.0 fb−1 ofintegrated luminosity collected by the Collider Detector at Fermilab (CDF). The event yields andkinematic distributions are examined for signs of new physics without favoring a specific model ofnew physics. The results are consistent with the standard model expectations. The search employsseveral new analysis techniques that significantly reduce instrumental backgrounds in channels withan electron and missing transverse energy.

PACS numbers: 13.85Rm; 13.85Qk; 18.80.-j; 14.80.Ly

∗Deceased†With visitors from aUniversity of Massachusetts Amherst,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, fUniversity 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, jUniversity Col-lege Dublin, Dublin 4, Ireland, kUniversity of Edinburgh, Edin-burgh EH9 3JZ, United Kingdom, lUniversity of Fukui, Fukui

4

I. INTRODUCTION

Over the last twenty years, the rapid pace of develop-ments in phenomenology and model-building has left ex-perimentalists at the collider energy frontier with a widearray of new physics scenarios to investigate [1]. We arealso assured that the number of models which have notyet been described is large. Since each search requiressubstantial resources, only a few new physics scenarioscan be the focus of dedicated efforts. We address thisproblem by performing broad searches in available datasamples for any discrepancy with the standard model(SM) [2] in event yields or kinematic distributions. Whilethis approach is not optimized for any particular scenario,it could possibly increase the chance of an unpredicteddiscovery.

In this article we investigate a sample of data col-lected by the CDF II detector in pp collisions at

√s =

1.96 TeV at the Fermilab Tevatron. We restrict our-selves to a “baseline” sample with two isolated, cen-tral (0.05<|η|<1.05) photons (γ) with ET>13 GeV [8].We then select subsamples which also contain at leastone more energetic, isolated and well-identified objector where two photons are accompanied by large miss-ing transverse energy (E/T ). The additional object maybe an electron (e), muon (µ), or τ lepton (τ). The E/Tis calculated from the imbalance in the energy of visibleparticles projected to the plane transverse to the beams.The integrated luminosity for each subsample varies from1.1 to 2.0 fb−1.

The γγ+X (X=e/µ, τ , and E/T ) signatures are presentin many new physics scenarios beyond the SM. Examplesinclude models with the gauge-mediated supersymmetrybreaking (GMSB) [3], extended Higgs sector [4], techni-color models [5], 4th generation fermions [6], and theorieswith large extra dimensions [7].

The CDF collaboration has previously performed asearch for anomalous production of two photons and anadditional energetic object (E/T , e, µ, τ , γ, jets, and b-quarks) in 85 pb−1 of the Tevatron Run I data [9]. Apartfrom the observation of a single eeγγE/T candidate event,the results were consistent with the SM predictions. The

City, Fukui Prefecture, Japan 910-0017 mKinki University, Higashi-Osaka City, Japan 577-8502 nUniversidad Iberoamericana, MexicoD.F., Mexico, oUniversity of Iowa, Iowa City, IA 52242, pKansasState University, Manhattan, KS 66506 qQueen Mary, Univer-sity of London, London, E1 4NS, England, rUniversity of Manch-ester, Manchester M13 9PL, England, sMuons, Inc., Batavia, IL60510, tNagasaki Institute of Applied Science, Nagasaki, Japan,uUniversity of Notre Dame, Notre Dame, IN 46556, vUniversity deOviedo, E-33007 Oviedo, Spain, wTexas Tech University, Lubbock,TX 79609, xIFIC(CSIC-Universitat de Valencia), 56071 Valen-cia, Spain, yUniversidad Tecnica Federico Santa Maria, 110v Val-paraiso, Chile, zUniversity of Virginia, Charlottesville, VA 22906aaBergische Universitat Wuppertal, 42097 Wuppertal, Germany,bbYarmouk University, Irbid 211-63, Jordan jjOn leave from J. Ste-fan Institute, Ljubljana, Slovenia,

eeγγE/T event sparked considerable theoretical interest,because this signature is very rare in the SM and theevent’s topology is consistent with that of a decay of apair of new heavy particles. In Run II, both the CDF [10]and D0 [11] collaborations searched for production ofγγ+E/T events in the context of GMSB models using datacorresponding to 0.20 fb−1 and 1.1 fb−1 of integrated lu-minosity, respectively. A search for anomalous produc-tion of γγ+e/µ events with energetic central photons andleptons (Eγ,e

T >25 GeV and pµT>25 GeV/c) in 0.93 fb−1 ofdata was performed by the CDF collaboration as a partof a broader signature-based search for new physics inl + γ +X (l = e, µ and X = γ, l, E/T ) events [12]. Othersignatures involving two photons were studied in CDFsearches reported in Ref. [13–15]. The current model-independent analysis is improved upon previous diphotonsearches both in terms of refined experimental techniquesand of amount of data analyzed. It also probes a widerkinematic range compared to the CDF analyses reportedin Ref. [12] and Ref. [15].This paper is organized as follows. It begins with a de-

scription of the CDF II detector and the baseline dipho-ton sample. Then, each γγ+X (X=e/µ, τ , and E/T )subsample is discussed in separate sections where we de-scribe the definition of the subsamples, the calculationof the SM predictions, and the comparison of the dataand the predictions. The details of several techniquesare postponed to appendices.

II. DETECTOR OVERVIEW

The CDF II detector is a cylindrically symmetric ap-paratus designed to study pp collisions at the FermilabTevatron. The detector has been described in detail else-where [16]; only the detector components that are rel-evant to this analysis are briefly discussed below. Themagnetic spectrometer consists of tracking devices insidea 3-m diameter, 5-m long superconducting solenoid mag-net which provides an axial magnetic field of 1.4 T. A setof silicon microstrip detectors (L00, SVX, and ISL) [17–19] and a 3.1-m long drift chamber (COT) [20] with 96layers of sense wires measure momenta and trajectories(tracks) of charged particles in the pseudorapidity re-gions of |η|<2 and |η|<1 [8], respectively. Surroundingthe magnet coil is the projective-tower-geometry sam-pling calorimeter, which is used to identify and measurethe energy and position of photons, electrons, jets, andE/T . The calorimeter consists of lead-scintillator electro-magnetic and iron-scintillator hadron compartments andit is divided into a central barrel (|η|<1.1) and a pairof “end plugs” that cover the region 1.1<|η|<3.6. Thecentral calorimeter is composed of towers with a segmen-tation of ∆η × ∆φ ≃ 0.1 × 15o. The energy resolutionof the central electromagnetic calorimeter for electronsis σ(ET )/ET = 13.5%/

√ET (GeV) ⊕ 1.5% [21], while

the energy resolution of the central hadron calorimeterfor charged pions that do not interact in the electromag-

5

netic section is σ(ET )/ET = 50%/√ET (GeV)⊕3% [22].

In the plug calorimeter, the segmentation varies from∆η × ∆φ ≃ 0.1 × 7.5o for 1.1<|η|<1.8 to ∆η × ∆φ ≃0.6 × 15o for |η|=3.6. The corresponding plug elec-tromagnetic and hadron calorimeter energy resolutionsare σ(E)/E = 14.4%/

√E(GeV) ⊕ 0.7% and σ(E)/E =

74%/√E(GeV) ⊕ 4%, respectively [23]. The additional

system in the central region is used for identificationand precise position measurement of photons and elec-trons. Multiwire proportional chambers with cathode-strip readout (the CES system) are located at the depthof six radiation lengths (near shower maximum) in thecentral electromagnetic calorimeter. Cathode strips andanode wires, with a channel spacing between 1.5 cm and2 cm, running along the azimuthal (strips) and the beamline (wires) direction give location and two-dimensionalprofiles of the electromagnetic showers. The position res-olution of the CES is 2 mm for a 50 GeV photon. Theelectromagnetic compartments of the calorimeter are alsoused to measure the arrival time of particles deposit-ing energy in each tower [24]. Muons from collisions aswell as cosmic rays are identified using systems whichare located outside the calorimeters: the central muondetector (CMU) and the central muon upgrade detec-tor (CMP) in the pseudorapidity region of |η|<0.6, andthe central muon extension (CMX) for the pseudorapid-ity region of 0.6<|η|<1.0 [25]. The CMU system usesfour layers of planar drift chambers and detects muonswith pT>1.4 GeV/c. The CMP system, located behinda 0.6 m thick steel absorber outside the magnetic re-turn yoke, consists of an additional four layers of planardrift chambers and detects muons with pT>2.2 GeV/c.The CMX detects muons with pT>1.4 GeV/c using fourto eight layers of drift chambers, depending on the po-lar angle. A system of Cherenkov luminosity counters(CLC) [26], located around the beam pipe and inside theplug calorimeters, is used to measure a number of in-elastic pp collisions per bunch crossing, and thereby theluminosity.The online event selection at CDF is done by a three-

level trigger [27] system with each level providing a ratereduction sufficient to allow for processing at the nextlevel with minimal deadtime. The Level-1 uses customdesigned hardware to find physics objects based on a sub-set of the detector information. The Level-2 trigger con-sists of custom hardware to do a limited event reconstruc-tion which can be processed in programmable processors.The Level-3 trigger uses the full detector information andconsists of a farm of computers that reconstruct the dataand apply selection criteria similar to the offline require-ments.

III. DATA SELECTION AND EVENT

RECONSTRUCTION

The search for anomalous production of γγ + E/T andγγ + τ events is performed with data corresponding to

2.0±0.1 fb−1 of luminosity integrated from the beginningof Run II. The search for anomalous γγ + e/µ eventsutilizes a smaller dataset of 1.1±0.1 fb−1 of integratedluminosity. The online (trigger) requirements and of-fline selection criteria that are common to all three finalstates are discussed below. Additional requirements ofeach analysis are explained separately.

The inclusive γγ events are selected online by a three-level trigger that requires two isolated electromagnetic(EM) clusters with Eγ

T>12 GeV (diphoton-12 trigger)or two electromagnetic clusters with Eγ

T>18 GeV andno isolation requirement (diphoton-18 trigger). A de-tailed description of diphoton triggers can be found inAppendix A1. The triggered γγ candidate events arethen subjected to the offline selection. Each event is re-quired to have two central EM clusters (photon candi-dates) inside a well-instrumented region of the calorime-ter (approximately 0.05<|η|<1.05) with ET>13 GeV.For each photon candidate, the transverse shower pro-file in the CES and the amount of energy leaked into thehadron calorimeter must be consistent with those of asingle electromagnetic shower. We distinguish photonsfrom electrons by making sure that no high-pT chargedtrack points to the EM cluster. Both photon candidatesare also required to be isolated energy clusters in thecalorimeter in order to suppress background due to jets.More details of the standard photon identification criteriacan be found in Appendix A2. To reduce contaminationdue to cosmic-ray, beam-related, and other non-collisionbackgrounds, the event must contain a well-reconstructedvertex, formed by tracks, with |z|<60 cm. If multiple ver-tices are reconstructed, the vertex with the largest

∑pT

of the associated tracks is selected. Unless noted other-wise, the transverse energy of all calorimeter objects iscalculated with respect to this primary vertex. Finally,the arrival time of both photon candidates, corrected foraverage path length, has to be consistent with the ppcollision time. It should be pointed out that due to thephoton timing requirements, we are only sensitive to newphysics processes where photons are produced in decaysof new particles with small lifetime (<1 ns).

Inclusive γγ events satisfying the above criteria formthe baseline γγ signal sample used in all three analyses.This sample consists of real γγ events (approximately30%), jet-γ (45%) and jet-jet (25%) [28] events whereone or both jets are misidentified as a photon. (An ob-ject misidentified as a photon is referred to as a “fake”photon.) The γγ + e/µ, γγ + τ , and γγ + E/T candidateevents are then selected from the base signal sample byrequiring additional objects of interest or significant E/T .We also select a control sample of γγ events by applyingless stringent photon identification requirements as dis-cussed in Appendix A2. To avoid an overlap with thesignal sample, at least one photon candidate from thecontrol sample must fail the standard photon cuts. Thecontrol sample is ideal for testing our analysis techniquesbecause it has a similar event topology, but is dominatedby background events (the fraction of real γγ events in

6

it is approximately 5%).Our baseline signal and control γγ samples consist

of 31,116 and 42,708 events, respectively, in data cor-responding to 2.0 fb−1 of integrated luminosity.

IV. SEARCHES FOR ANOMALOUS

PRODUCTION OF γγ +X EVENTS

In this Section, we describe in detail three separatesearches for anomalous production of γγ + e/µ, γγ + τ ,and γγ + E/T events. All analyses use the same baselineγγ samples and utilize the same definitions of the addi-tional objects and kinematic variables: electrons, muons,τ leptons, jets, soft unclustered energy, E/T , and HT . TheHT is defined as a scalar sum of E/T and ET of all identi-fied photons, leptons, and jets. The detailed descriptionsof these objects can be found in Appendices A 3-A 8.

A. The γγ + e/µ Final State

We search for anomalous production of events contain-ing two photons and at least one additional electron ormuon in data corresponding to 1.1±0.1 fb−1 of integratedluminosity. The events of interest are derived from theγγ baseline sample described in Section III. The electronidentification criteria are similar to those for the photonexcept that an electron candidate must have an energetictrack pointing to the EM cluster. The momentum, p, ofthis track has to be consistent with the energy depositedin the EM calorimeter. The electron identification re-quirements are described in detail in Appendix A3.A well-reconstructed COT track is identified as a muon

candidate if it is matched to hit segments (stubs) in thecentral muon detectors, and its energy deposition pat-tern in the EM and HAD calorimeters is consistent withthat left by a minimum ionizing particle. Details on themuon identification requirements can be found in Ap-pendix A4.The selected γγe and γγµ events must have at least

one electron or muon candidate with EeT>20 GeV and

pµT>20 GeV/c, respectively. We compare the observednumber of events and kinematic distributions in the datawith those from our SM background predictions. Back-grounds for the γγe and γγµ signatures of new physicsinclude:

1. The SM production of Z→l+l− and W→lν in as-sociation with two photons (Zγγ, Wγγ), wherephotons are radiated from either the initial statequarks, charged electroweak boson (W ), or thefinal–state leptons.

2. Backgrounds due to misidentified particles (fakephotons or leptons)

(a) electrons misidentified as photons (e.g., Zγevents),

(b) jets misidentified as photons (e.g, Wγ+ jet orZγ + jet events),

(c) jets misidentified as leptons (mostly γγ candi-date events with an additional jet).

We describe below how these background contributionsare estimated.The SM Zγγ and Wγγ contributions are estimated

fromMonte Carlo (MC) simulation. The MC samples aregenerated using the leading-order (LO) matrix-elementgenerator madgraph [29]. The output of madgraph

is fed into pythia [30] to carry out parton fragmenta-tion, simulation of the underlying event and additionalpp interactions in the same bunch crossing, as well asinitial- and final-state radiation. The output of pythiais then processed through the geant-based detector sim-ulation [31] followed by the same reconstruction pro-gram as that for the data. To account for an imper-fect modeling of the CDF-II detector, the MC predic-tions are corrected for small differences (1-10%) in photonand lepton identification and trigger efficiences betweendata and MC. In addition, the LO cross sections pre-dicted by madgraph are scaled to the next-to-leading-order (NLO) cross sections according to the K-factors inRef. [32]. These K-factors are functions of the dileptonmass and ET of the highest-ET photon, and their valuesrange from 1.36 to 1.62 with an average of ∼1.4 for thekinematic range of Zγγ and Wγγ production. The un-certainty for this background prediction includes statisti-cal uncertainty due to the finite size of MC samples, 6%systematic uncertainty on the measured integrated lumi-nosity, and 7% systematic uncertainty on the Zγγ andWγγ cross sections due to uncertainties in the factoriza-tion and renormalization scales and parton distributionfunctions (PDF) [33].The rest of the background contains at least one

misidentified object. Fake photons can arise from thehard bremsstrahlung of electrons in the detector mate-rial, inefficient electron-track reconstruction, or decays ofπ0, η0, or K0

s in jets. Although these background sourcesyield real photons in the final state, they are referred toas ”fake” in this analysis, to be distinguished from thephotons possibly produced by new exotic particles. Thenumber of γγ + l (l = e, µ) events where at least oneof the photons is faked by an electron is estimated fromthe lγ + e data (collected with the diphoton triggers).We obtain the prediction by applying a e→γ misidenti-fication probability as a function of the ET of electron(about 2.7% and 1.5% for electrons with ET =20 GeVand 40 GeV, respectively) to the selected lγ + e events.More details about this misidentification probability andits uncertainty are included in Appendix B1. To esti-mate the number of γγ + l events where at least one ofthe photons is a misidentified jet, we select the lγ + jetdata collected with inclusive lepton triggers and multi-ply them by a jet→γ misidentification probability as afunction of the jet’s ET (about 0.2% and 0.04% for jetswith ET =13 GeV and >50 GeV, respectively). The de-

7

scription of the jet→γ misidentification probability andits associated uncertainty can be found in Appendix B 2.Also note that both lγ + e and lγ + jet samples maycontain events with fake leptons.The last source of background is events with two real

photons and a fake lepton from the direct diphoton pro-duction with additional jets. The number of “dipho-ton + fake lepton” events is obtained by applying ET -dependent misidentification probabilities from Ref. [34]to the events with two photon candidates and an ob-ject which may fake a lepton. These objects are jets forelectrons and isolated tracks for muons. The probabil-ity for a jet (isolated track) with ET (pT )=50 GeV tofake a central electron (muon) is ∼0.01% (∼1%). Detailsof the misidentification probabilities and their uncertain-ties are discussed in Appendix B3. According to earlierstudies [28], only 29%±4% of observed diphotons are realdiphoton events. In order to avoid duplication with thefake photon contribution estimated above, the number of“diphoton + fake lepton” events is multiplied by the realdiphoton fraction (29%±4%), which gives the number of“real γγ + fake lepton” events.The fake photon signature can also be produced as a

result of the bremsstrahlung of cosmic muons as theypass through the calorimeters. However, the probabilityfor a real photon event to overlap with such a cosmicevent is found to be very small: 1.5×10−8 (see Ref. [28]).Therefore, the cosmic backgrounds are negligible in theγγe and γγµ searches.Table I lists the expected and observed numbers of

γγe and γγµ events for EγT > 13 GeV. At this stage

of event selection, we observe three γγe events and zeroγγµ events. The leading background in the γγe chan-nel is due to events where at least one of the photonsis a misidentified electron. The leading background inthe γγµ channel is the electroweak production of Zγγevents. Figures 1–2 show several important kinematicdistributions, including invariant mass, electron and pho-ton ET , E/T , jet multiplicity, and HT from data and thepredicted backgrounds before applying the final selection,the silicon-track rejection (described next).

TABLE I: Summary of the predicted and observed numbersof γγe and γγµ events before applying silicon-track rejection.The systematic uncertainty includes uncertainty due to MCstatistics, uncertainties in the data luminosity, predicted crosssections, and the misidentification probabilities.

Source electron muonZγγ 0.90 ± 0.09 0.55 ± 0.05Wγγ 0.17 ± 0.02 0.09 ± 0.01

lγ + e→γ 5.14 ± 0.68 0.02 ± 0.02lγ + jet→γ 0.48 ± 0.31 0.13 ± 0.09Fake l+γγ 0.13 ± 0.05 0.004 ± 0.004

Total 6.82 ± 0.75 0.79 ± 0.11Data 3 0

TABLE II: Summary of the predicted and observed numbersof γγe and γγµ events after applying silicon-track rejection.The systematic uncertainty includes uncertainty due to MCstatistics, uncertainties in the data luminosity, predicted crosssections, and the misidentification probabilities.

Source electron muonZγγ 0.82 ± 0.08 0.50 ± 0.05Wγγ 0.15 ± 0.02 0.08 ± 0.01

lγ + e→γ 2.26 ± 0.46 0.004 ± 0.004lγ + jet→γ 0.44 ± 0.26 0.12 ± 0.08Fake l+γγ 0.12 ± 0.05 0.004 ± 0.004

Total 3.79 ± 0.54 0.71 ± 0.10Data 1 0

The dominant source of background in the γγe searchare γ + ee events where one of the electrons is misre-constructed as a photon. An electron may lose its trackand be reconstructed as a photon because of catastrophicbremsstrahlung in the detector material in front of theCOT. However, such an electron often leaves a few hitsin the silicon detector and can be partially recoveredby a special tracking algorithm (see Appendix A2 andRef. [35] for more details). We further compare the dataand background prediction after removing events whereat least one of the photons is matched to this type ofelectron track (silicon-track rejection). The silicon-trackrejection suppresses ∼80% of fake photons from the elec-tron bremsstrahlung for Eγ

T>45 GeV (see Fig. 12 fromAppendix B3) while it has only ∼1% inefficiency for realphotons. Once this procedure is applied, the observednumber of γγe events is reduced to one. The final back-ground predictions after the silicon-track rejection can befound in Table II.

The robustness of our background estimation tech-nique is validated in the following three ways. First, weuse an independent method to measure the misidenti-fication probabilities. Instead of counting electrons thatsatisfy standard central-electron criteria, we use the num-ber of electrons that satisfy photon-like electron criteriain the e→γ fake rate denominator (see Appendix B1).The difference in the prediction of fake photons from eeγevents is ∼4-11%. Second, we cross-check if the eeγ data(to which the e→γ fake rate is applied) contain signifi-cant number of fake electrons. We fit data with a com-bined likelihood of multiple electron identification vari-ables, where the signal shapes are obtained from electronsin Z decays and the background shapes are obtained fromthe sample enriched with fake electrons. The purity ofelectrons is estimated to be 97±2%. In addition, we com-pare the yields of eeγ and µµγ events in data and thosepredicted by Zγ madgraph MC. We divide the ratio ofdata to MC yields in the muon channel by the same ratioin the electron channel. If the eeγ events contain signif-icant amount of fake electrons, the double ratio will beinconsistent with unity. The double ratio is found to be

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FIG. 1: Kinematic distributions of the γγe events from the SM (dashed line) and total (solid line) background predictions aswell as the three events observed in the data (marker). The total backgound includes SM and fake contributions. The grayboxes indicate the uncertainty in background determination. Each photon is required to have an ET>13 GeV. Distributionsfrom the top left to the bottom right are: a) three-body invariant mass; b) invariant mass of two photons; c) invariant massof each electron-photon pair; d) ET of each photon; e) ET of the electron; f) HT , scalar sum of E/T and ET of all identifiedphotons, electrons, and jets; g) E/T ; and h) number of jets with ET>15 GeV.

1.10±0.15. Third, we examine the background estimatein larger samples, where either one photon and one elec-tron (eγ) or one photon, one electron, and one jet (eγj)events are required. The numbers of eγ and eγj eventsin data are consistent with those from the backgroundpredictions within one standard deviation.

To summarize, we do not observe any evidence foranomalous production of γγe and γγµ events.

B. The γγ + τ Final State

We search for events with two photons and ahadronically-decaying τ lepton in data corresponding to2.0 fb−1 of integrated luminosity. These events are asubset of the baseline diphoton sample (see Section III)with at least one τ lepton candidate identified using thetight requirements and passing ET >15 GeV (see Ap-

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FIG. 2: Kinematic distributions of the γγe events from the SM (dashed line) and total (solid line) background predictions. Thetotal backgound includes SM and fake contributions. The gray boxes indicate the uncertainty in background determination.We observe zero events in the data. Each photon is required to have an ET>13 GeV. Distributions from the top left to thebottom right are: a) three-body invariant mass; b) invariant mass of two photons; c) invariant mass of each muon-photon pair;d) ET of each photon; e) pT of the muon; f) HT , scalar sum of E/T and ET of all identified photons, muons, and jets; g) E/T ;and h) number of jets with ET>15 GeV.

pendix A5). We select 34 γγ + τ candidate events.We consider two sources of backgrounds: the SM pro-

duction of W→τν or Z→ττ with photons and γγ eventswith jets misidentified as τ leptons. Other backgroundsare negligible.The electroweak backgrounds are estimated from Wγ

and Zγ madgraph [29] MC simulation. The LO orderpredictions are multiplied by the appropriate next–to–leading–order K-factors described in Section IVA and

Ref. [32]. We find that these electroweak events withreal leptons are dominated by events with at least onereal photon, so we do not consider the case where bothphotons are misidentified jets. The simulation predictsthe background from the cases of two real photons or onereal with one fake photon to be 2.2±0.8 events, where theuncertainty comes from MC statistics.

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fake), and jets, where one of the jets is misidentified as aτ lepton. To estimate this background, we select eventswith two photons and a jet identified as “loose” τ lep-ton candidate (see Appendix A5) and apply the jet→τmisidentification probability (see Appendix B 4). Sincethe misidentification probability is different for jets orig-inated by quarks or by gluons, and the ratio of quark jetsto gluon jets here may be different from the one in thesample used to derive the jet→τ misidentification prob-ability, we investigate a correction for the different typesof jets in our sample. The probability for a quark jet tofake a τ lepton is three times larger than the probabil-ity for a gluon jet. The process becomes more complexbecause a photon candidate may also be a misidentifiedjet, and the probability for a quark jet to fake a photonis ten times larger than for a gluon jet. We use pythia

MC samples of diphotons, inclusive single photons anddijets to investigate the quark and gluon content of ourdata sample. Previous studies [28] have determined thatthe baseline diphoton sample has approximately 30% realdiphoton events, 45% events with a real photon and a jetmisidentifed as a photon, and 25% events with two jetsmisidentified as photons. The simulations indicate thatthe quark–to–gluon ratio is significantly higher in thecase of one real photon and one fake photon (80% quarks)than either of the other cases (approximately 30% in di-jet events and 40% in events with two real photons) andneeds to be corrected for. We account for this effect byusing two methods. In the first method, we simply applythe jet→τ misidentification rate and then make a cor-rection for the difference in the average quark–to–gluonratio in the sample. In the second method, we allow forthe possibility that quark jets will preferentially become

misidentified photons, leaving the remaining jets to be-come misidentified taus. This method yields our reportedcentral result, and the variation between the methods in-dicates a 13% systematic uncertainty which is added tothe 20% systematic uncertainty in the misidentificationprobability.

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FIG. 4: The kinematic distributions in γγ+τ candidate events(marker) and the SM backgrounds (histogram): a) ET of τlepton candidate; b) E/T ; c) number of jets with ET>15 GeV;d) HT , scalar sum of the transverse energies of photons, τlepton candidate, jets, and E/T . The gray boxes indicate theuncertainty in background determination.

The misidentified τ background is 44±10 events andthe total background estimate is 46±10 events, consis-tent with the 34 observed γγ + τ candidate events. Weperform three checks of the methodology by predictingthe size of γγ + τ sample where the two photons are se-lected with the relaxed criteria (γγ control sample de-scribed in Section III) or with one of the photons inthe forward region (1.1<|η|<2.0). The predictions forall control samples are consistent with the observations.Figures 3-4 show several important kinematic distribu-tions for the selected γγ + τ candidate events and thepredicted SM background. These distributions includethe diphoton invariant mass, ET of a τ lepton candidate,E/T , jet multiplicity, and HT . No excess is found abovethe SM background.In summary, we do not observe any evidence for the

anomalous production of γγ + τ events.

C. The γγ + E/T Final State

We search for the anomalous production of two pho-tons and large missing transverse energy (E/T ) in data

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FIG. 5: The E/T distribution in all γγ candidate events fromthe baseline sample. The data (marker) is compared with thetotal background prediction (solid line with the gray bandrepresenting the total uncertainty). The total backgroundprediction is a sum (shown by the stacked histograms) ofthe QCD, electroweak (dashed line), and non-collision (dash-dotted line) backgrounds.

corresponding to 2.0 fb−1 of integrated luminosity. Thesubsample of γγ + E/T events is derived from the base-line diphoton sample described previously in Section IIIand in Appendix A2. The missing transverse energy isdefined as an energy imbalance in the calorimeter (seedetailed description of E/T in Appendix A7) and it isan experimental signature of neutrinos or new particlesthat do not interact electromagnetically or strongly withthe detector material. The E/T , however, can be mim-icked by a simple energy misreconstruction in SM events.Fluctuations in jet energy measurements are the mostcommon source of such fake E/T . Figure 5 shows the E/Tdistribution in the γγ baseline sample. This figure illus-trates that events with fake E/T are not only the domi-nant background in the region up to E/T∼40 GeV, butthey also have a significant contribution even to the tailof E/T distribution. A better separation between eventswith real and fake E/T can be achieved if a significanceof the measured E/T is considered rather than its abso-lute value. The E/T -significance is a dimensionless quan-tity based on the energy resolution of jets and soft un-clustered particles. It also takes into account the eventtopology as shown in Appendix C. As it is demonstratedin Fig. 6, the E/T -significance distributions have very dif-ferent shapes in events with fake and real E/T : exponen-tially falling (solid line) and almost flat shapes, respec-tively. Thus, the E/T -significance is an efficient tool inseparating such events. We study γγ + E/T events whichpass three a priori E/T -significance requirements: E/T -significance>3, 4, and 5. This choice of cut values has

a straightforward motivation. If the γγ sample were onlycomposed of events with fake E/T due to energy misrecon-struction in the calorimeter, then we would select 0.1%,0.01%, and 0.001% of the total number of events by re-quiring E/T -significance>3, 4, and 5, respectively. On theother hand, studies with MC Wγ→eν + γ sample indi-cate that the E/T -significance>3 (E/T -significance>5) cutis ∼100% (∼90%) efficient for events with real E/T>35GeV (see Fig. 7).

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FIG. 6: The E/T -significance distribution in all γγ candidateevents from the baseline sample. The data (marker) is com-pared with the total background prediction (solid line withthe gray band representing the total uncertainty). The to-tal background prediction is a sum (shown by the stackedhistograms) of the QCD, electroweak (dashed line), and non-collision (dash-dotted line) backgrounds. The straight solidline represents the expected E/T -significance distribution if allγγ candidate events were to have fake E/T due to the mea-surement fluctuations in the calorimeter (see Appendix C formore details).

We consider three major sources of background forthe γγ + E/T signature: QCD (γγ, jγ, and jj wherej=jet→γfake) events with large fake E/T due to energyloss or mismeasurement in the calorimeter, electroweak(EWK) processes with real E/T from neutrinos, and non-collision events with fake photons and E/T . Each of thesesources is discussed below in the order of their impor-tance. All of the background estimation techniques aretested on a control sample of “loose” diphoton eventsdescribed in Section III and in Appendix A2.Significant losses or fluctuations in energy measure-

ments in the inclusive γγ sample, which can lead toconsiderable values of fake E/T , happen only in a smallfraction of events. However, the large production crosssections of QCD processes make them one of the largestbackgrounds. We distinguish three types of QCD back-grounds: events with energy mismeasurement due tocalorimeter energy resolution effects (QCD type-1); γγ

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candidate events with a wrong choice of the primary in-teraction vertex (QCD type-2); and γγγ events whereone of the photon candidates is lost in the calorimetercracks (QCD type-3).

The QCD type-1 background estimate is based ona E/T -resolution model (metmodel) described in Ap-pendix C. For each γγ data event, we generate tenpseudoexperiments to simulate fake E/T and calculate itssignificance given the event kinematics. In each pseudo-experiment, we smear the energies of jets and soft un-clustered particles using appropriate resolutions. Thedifference between the smeared and measured energyof the object is taken as its individual contribution tothe total fake E/T . We predict the QCD backgrounddue to energy mismeasurements by counting the num-ber of pseudoexperiments that pass our E/T -significancerequirements divided by the number of pseudoexperi-ments per event. Kinematic distributions from thesepseudoexperiments are then used as QCD backgroundtemplates for data. The systematic uncertainty (23%for E/T -significance>3, 47% for E/T -significance>4, and130% for E/T -significance>5) is evaluated by comparingthe metmodel expectations obtained with the defaultparameters to predictions obtained by varying each pa-rameter by one standard deviation (±1 σ). These param-eters and associated sources of systematic uncertaintiesare discussed in Appendix C. The statistical and sys-tematic uncertainties are added in quadrature to obtainthe total uncertainty. The predictions for the QCD type-1 background and their associated uncertainties can befound in Table III.

The background contribution due to γγ candidateevents with mis-assigned primary vertex (QCD type-2)cannot be directly estimated by the metmodel because

the energy resolution parameterization does not includethis effect. The vertex misassignment occurs when a γγpair [36] is produced by a hard scattering interaction thatoverlaps with another interaction producing a vertex withthe highest

∑pT of tracks. As a consequence of the

wrong vertex choice, the ET of both photon candidatesare incorrectly calculated, thus leading to fake E/T . Al-though the effect is small, it can occasionally result ina large fake E/T , for example, when two vertices are farapart and the photons are sufficiently energetic. We cor-rect for these mismeasurements by recalculating the ET

of photons with respect to the vertex which gives thesmallest value of E/T . This procedure is verified to bevalid for events with no intrinsic E/T . It is also tested insimulated Wγ→eνγ events [38] and data eγ events withE/T>20 GeV. The selection of eγ events is discussed inAppendix A 9. The effect is found to be small: after theprocedure is applied, the number of simulated and dataevents with E/T > 20 GeV is reduced by 1% and 2%, re-spectively. In some fraction of events, however, the hardinteraction completely fails to produce a reconstructedvertex and the vertex re-assignment cannot fix fake E/T .Since the metmodel cannot account for this contribu-tion, we employ a method based on a combination ofdata and Monte Carlo simulation to obtain the predic-tions. For this purpose, we use pythia γγ events [30]passed through the detector simulation [31]. These MCevents also include additional interactions in the samebunch crossing that are modeled according to the lumi-nosity profile in data. We select only events where thehard scattering interaction resulting in a γγ pair does notproduce a reconstructed vertex, and the primary vertexis created by tracks from an overlapping additional in-teraction. We will refer to such events as “no vertex” γγ

13

events. The MC sample of “no vertex” events is normal-ized to the number of such events in real data (4.8±0.4%of the baseline γγ events). We then apply the standardanalysis procedure to the sample and obtain the fractionof “no vertex” events in MC passing our E/T -significancecuts. The systematic uncertainties on the QCD type-2background contribution include the MC statistical un-certainty (12%-24%), the uncertainty on the normaliza-tion factor (10%), the uncertainty due to the jet energyscale (7-8%), and the MC-data differences in the met-

model parameterization (40%). The predictions for theQCD type-2 background and their associated uncertain-ties can be found in Table III.

The γγγ events are produced at a very low rate com-pared to that of γγ events. However a probability oflosing a photon in calorimeter cracks is ∼10%, so thatthe probability of losing one of the candidate photonsin a tri-photon event is as large as ∼30%. These events(QCD type-3) could reconstruct as γγ + E/T events. Toreduce this background, we reject events if the E/T vectorpoints along the direction (within |∆φ|<0.3) of a nar-row jet [39] located close to the calorimeter cracks atη∼0 and |η|∼1.1. The remaining contribution of theQCD type-3 events is estimated using a large inclusivepythia γγ MC sample. We select reconstructed tri-photon events (Eγ1,2

T >13 GeV and Eγ3T >7 GeV) in MC

and data. The numbers of reconstructed γγγ candidatesgive us the MC-to-data normalization factor. To obtainan estimate of the remaining QCD type-3 background,we select pythia tri-photon events at the generator level(before detector simulation), apply the standard analysisprocedure to these events, and multiply the result by thenormalization factor described above. The systematicuncertainties for this background prediction is due to thefollowing sources: 1) MC statistical uncertainty (24%-33%); 2) uncertainty on the normalization factor (19%);3) uncertainty due to MC-data differences in the met-

model parameterization (10%-44%); 4) jet energy scaleuncertainty (10%-11%). The predictions for all sourcesof QCD backgrounds and their associated uncertaintiescan be found in Table III.

Electroweak processes involving W→lν andZ→νν/τ+τ− are the most common source of largereal E/T in pp collisions. There are three ways theseprocesses can produce a γγ + E/T signature (listed inthe order of importance): 1) Wγ and Zγ events withone real and one fake photon; 2) Wγγ and Zγγ eventswhere both photons are real; 3) W + jet, Z→τ+τ−, andZ + jet events where both photon candidates are fakephotons. We estimate the EWK backgrounds by usingW/Z + γ [38] (for 1) and 2)) and inclusive W/Z [40] (for3)) Monte Carlo events passed through the detector sim-ulation. We consider all three leptonic decay modes ofW and Z bosons. To avoid an overlap between W/Z + γand W/Z samples, we remove pythia W/Z events wherereconstructed photons are matched to generated photonsoriginating from initial/final state radiation (ISR/FSR)of quarks or leptons. The MC-based predictions for

the EWK backgrounds are then multiplied by a scalefactor that diminishes possible data-MC differencesand cancels out many of the systematic uncertainties(e.g., trigger efficiencies, acceptance and photon IDefficiencies, K-factors, modeling of ISR/FSR in MC,uncertainties in parton distribution functions, jet energyscale uncertainty, and luminosity uncertainty). Thisscale factor is obtained by comparing eγ + E/T events(see Appendix A9) in data and MC. It is defined as theratio of numbers of data and MC eγ events satisfying allanalysis requirements. The resulting EWK backgroundpredictions and the corresponding uncertainties can befound in Table III. The total uncertainties includes theMC statistical uncertainties (3.5-4.4%) and the MC-to-data normalization factor uncertainties (5.4-6.1%).The last uncertainty includes statistical uncertaintiesfrom data and MC eγ + E/T samples and systematicuncertainties associated with the purity of the e+γ datasample and difference between the E/p-cut efficiency(see Appendix A9) in data and MC. From Table III,one can see that the EWK processes are the dominantsource of background when E/T -significance>4. We findthat 59-63% (30-40%) of the total EWK backgroundfor the γγ + E/T signature comes from the electron(τ lepton) decay channels of W and Z bosons. Notethat the E/T -significance cuts are rather efficient forevents with large real E/T : for example, 84% and 68%of W+γ→eν+γ events pass the E/T -significance>3 andE/T -significance>5 requirements, respectively.

The last remaining source of background is non-collision events where both photons and E/T are fake.These events may either be caused by cosmic rays (CR)or beam halo (BH) muons depositing energy in thecalorimeter. CR events are suppressed by requiring theEM timing of both photon candidates (T1 and T2) tobe consistent with the collision time: |T1,2|<6.7 ns and|T1−T2|<4.1 ns (more details are given in Appendix A2).BH events are removed by the topological cuts based onthe distinct energy deposition pattern of BH muons trav-eling along the beam pipe. More details about CR andBH rejection cuts can be found in Appendix A2. Thenumber of remaining BH events is estimated from thenumber of identified BH candidates and known rejectionpower of the BH cuts. The background contribution dueto CR events is estimated based on the number of theseevents in the 30 ns< T1,2 <120 ns EM timing windowand known efficiency of the cosmic rejection cuts (seeAppendix A2 and Ref. [41]). The total prediction fornon-collision backgrounds can be found in Table III. Theuncertainty for this estimate is dominated by the statis-tics in the samples of identified BH and CR events.

The results of the search are presented in Ta-ble III. The total expected SM background for threeE/T -significance cuts (E/T -significance>3, 4, and 5) is71.7±7.5, 39.0±3.1, and 30.4±2.4 events, respectively.These predictions agree well with the observed numbersof data events: 82, 31, and 23. We also examine vari-ous kinematic distributions in data and SM backgrounds

14

TABLE III: The results of the search for anomalous production of γγ + E/T events. The data is compared to the backgroundpredictions for three values of the E/T -significance cut. The quoted uncertainties include the effect of limited MC statistics aswell as systematic uncertainties.

E/T -significance>3.0 E/T -significance>4.0 E/T -significance>5.0EWK 35.4±2.2 29.9±2.0 25.9±1.9

QCD type-1 28.1±6.8 3.6±1.8 0.6±0.8QCD type-2 4.4±2.0 2.5±1.0 1.5±0.7QCD type-3 2.9±1.0 2.2±1.0 1.6±1.0Non-Collision 0.9±0.3 0.8±0.3 0.8±0.3

Total 71.7±7.5 39.0±3.1 30.4±2.4Data 82 31 23

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for E/T -significance>3 and E/T -significance>5. Figures 8and 9 show the E/T , leading photon ET , HT , and Mγγ

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FIG. 9: The kinematic distributions for γγ+E/T candidate events with E/T -significance>5: a) E/T , the missing transverse energy;b) ET of leading photon candidate; c) HT , the scalar sum of the transverse energies of photons, jets, and E/T ; and d) invariantmass, Mγγ , of two photons. In all figures, the data (marker) is compared with the total background predictions (solid line withthe gray band representing the total uncertainty). The total background prediction is a sum (shown by the stacked histograms)of the QCD and electroweak (dashed line) backgrounds. The non-collision background is too small to be visible on a plot withlinear scale.

lustrates multiplicities and ET distributions of extra jetsand electrons in selected events. We observe good agree-ment between data and predicted background shapes forall studied kinematic distributions that are expected tobe sensitive to production of new particles.In summary, we have searched for anomalous produc-

tion of γγ +E/T events in data corresponding to 2.0 fb−1

of integrated luminosity. No significant deviations fromthe SM background predictions are observed.

V. CONCLUSIONS

We performed a model-independent search for anoma-lous production of two photons with an electron, muon,τ lepton, or large missing transverse energy. The anal-

ysis of a γγ+e/µ signature was performed using datacorresponding to 1.1 fb−1 of integrated luminosity. Af-ter final selection, we observed one γγ+e candidate eventand zero γγ+µ events, in agreement with the expectedbackground of 3.79±0.54 and 0.71±0.10 events, respec-tively. The kinematic properties of the γγ+e event wereconsistent with the SM predictions. The silicon-track re-jection technique applied in this search allows for morethan 60% reduction in the bremsstrahlung background(the dominant background in the electron channel) andhas a promising potential for future searches with theγ+e+X signature.

The search for new physics in γγ+τ was based on datacorresponding to 2.0 fb−1 of integrated luminosity. Weobserved 34 data events, in good agreement with the ex-pected background of 46±10 events. The kinematic dis-

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for events with E/T -significance>3; and d) the electron ET for events with E/T -significance>3. In all figures, the data (marker)is compared with the total background prediction (solid line with the gray band representing the total uncertainty). The totalbackground prediction is a sum (shown by the stacked histograms) of the QCD, electroweak (dashed line), and non-collision(dash-dotted line on figures a) and b) only) backgrounds.

tributions of the selected events did not reveal any devi-ations from the SM predictions.

The study of the γγ+E/T signature was performedusing data from 2.0 fb−1 of integrated luminosity.The events of interest were selected based on the E/T -significance, rather than a fixed E/T -cut. This methodproved to be very effective in rejecting events with fakeE/T , while remaining sensitive to new physics processeseven with moderate values of E/T (E/T∼20-40 GeV).We selected 82, 31, and 23 data events with the E/T -significance greater than 3, 4, and 5, respectively. Theseresults are consistent with the expected SM backgroundof 71.7±7.5, 39.0±3.1, and 30.4±2.4 events, respectively.The examined kinematic distributions for the observedevents with E/T -significance greater than three and five

are in a good agreement with the predicted backgroundshapes. The metmodel developed as part of the γγ+E/Tsearch was also successfully applied to suppress multijetbackground with fake E/T in the first observation of vec-tor boson pairs in a final state with two jets and E/T atthe Tevatron [42]. Finally, the reported in this papermodel-independent analysis was later used as a basis fora search for supersymmetry with gauge-mediated break-ing in γγ+E/T events [43]. The data samples used in thesetwo analyses have a 60% overlap.

In summary, no significant deviations from the stan-dard model were observed in the numbers of recordedevents and their kinematic properties in signatures withtwo photons and an additional electron, muon, τ lepton,or large E/T . We also did not observe any new eeγγ+E/T

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candidate events, similar to the one reported in Ref. [9].With improved analysis techniques and up to 20 timesmore data compared to the previous searches [9]-[11], thismodel-independent search is substantially more sensitiveto new physics.

VI. 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 ItalianIstituto Nazionale di Fisica Nucleare; the Ministry ofEducation, Culture, Sports, Science and Technology ofJapan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A.P. Sloan Foundation; the Bundesministeriumfur Bildung und Forschung, Germany; the World ClassUniversity Program, the National Research Foundationof Korea; the Science and Technology Facilities Coun-cil and the Royal Society, UK; the Institut National dePhysique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Minis-terio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and theAcademy of Finland.

Appendix A: Definitions

1. Diphoton Triggers

There are two diphoton paths in the CDF three-leveltrigger: the first path requires two isolated electromag-netic (EM) clusters with ET>12 GeV (diphoton-12),and the second path requires two electromagnetic clus-ters with ET>18 GeV and has no isolation requirement(diphoton-18). The transverse energy of clusters is calcu-lated with respect to the nominal center of the detectorat z=0 cm. The trigger requirements at each level arebriefly described below.At Level-1, events with two towers with EM

ET>8 GeV each are required. For each trigger tower,the amount of energy in the hadronic compartment of thecalorimeter (EHAD) has to be consistent with that of anelectromagnetic object. A trigger tower consists of twoadjacent towers in the same calorimeter wedge, so thatthe granularity is approximately ∆η ×∆φ ≃ 0.2× 15o.The Level-2 requirements are different for the two trig-

gers. The diphoton-12 trigger selects events if there aretwo isolated clusters (seeds) with EM ET>10 GeV each.The isolation (ISO) energy is calculated as a sum of thetransverse energy in nine towers surrounding the seedtower according to five preset patterns. The ISO energyin each of the patterns has to be less than 3 GeV or 15%of the seed energy, whichever is larger. The diphoton-18

trigger requires two towers with EM ET>16 GeV eachat Level-2.The events are fully reconstructed at Level-3. At this

level, for both triggers, the energy profile at the showermaximum (χ2

CES) of each photon candidate has to beconsistent with that of a single photon. The diphoton-12trigger selects events with two isolated photon candidateswith ET>12 GeV. The isolation energy at the level-3 iscalculated as the sum of ET in all towers (except for pho-

ton towers) within the cone of ∆R =√∆η2 +∆φ2 < 0.4

centered around the photon candidate. This ISO energyhas to be less than 2 GeV or 10% of the photon energy,whichever is larger. The diphoton-18 trigger has no iso-lation requirement and accepts events with two photoncandidates with ET>18 GeV. Table IV gives a summaryof all trigger requirements for events with EM objects inthe central calorimeter.

2. Photon Identification

Photon candidates have to satisfy strict (also re-ferred to as “tight”) photon identification requirements.The EM cluster has to be located inside the well–instrumented region of the CES chamber, away from theφ-boundary of a calorimeter tower [44]. The energy de-position pattern in both transverse profiles at CES hasto be consistent with that of an electromagnetic object.The ratio of the energy measured in the hadron (HAD)calorimeter to the EM energy, EHAD/EEM, has to sat-isfy EHAD/EEM<0.055+0.00045×Eγ requirement. Todistinguish photons from electrons, no high-pT chargedtrack should point into the cluster (Ntrack≤1 with trackpT<1.0+0.005×ET). The main sources of ”fake” photonsare π0 and η0 produced in jets. These mesons are usu-ally produced in association with other particles. To re-duce this contamination from jets, the photon candidatemust be isolated in the calorimeter and tracking cham-ber. To calculate the calorimeter isolation (cal-ISO), theET deposited in the calorimeter towers within the cone of∆R < 0.4 around the EM cluster is summed, and the ET

due to the EM cluster is subtracted. The cal-ISO is thencorrected for the photon’s energy leakage into towers inthe neighboring wedge and for the contribution from mul-tiple interactions in the same bunch crossing. The trackisolation (track-ISO) is calculated as

∑pT of tracks in-

side a cone ∆R<0.4 and satisfying |zvertex-ztrack|<5 cm.Both cal-ISO and track-ISO must be consistent with theamount of energy expected from the underlying event.In addition to calorimeter and tracking isolation, thereshould be no other significant energy (ET of 2nd CEScluster) deposited in the CES chamber containing thephoton candidate. Table V provides a summary of thephoton identification requirements described above.We obtain the γγ control sample by selecting events

where two photon candidates pass relaxed (“loose”) pho-ton identification requirements, but at least one of themfails the “tight” cuts. The main difference between

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TABLE IV: Summary of the diphoton trigger requirements.

Trigger Level Diphoton-12 Diphoton-18EM ET > 8 GeV same

Level-1 EHAD/EEM < 0.125 sameNcluster = 2 same

EM ET > 10 GeV EM ET > 16 GeVLevel-2 EHAD/EEM < 0.125 same

EISOT < 3 GeV or EISO

T /ET < 0.15 N/ANcluster = 2 same

EM ET > 12 GeV EM ET > 18 GeVLevel-3 EHAD/EEM < 0.055 + 0.00045×E/GeV if E < 200 GeV same

EISOT < 2 GeV or EISO

T /ET < 0.1 N/Ashower profile: χ2

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TABLE V: Summary of the standard (“tight”) and relaxed (“loose”) photon identification requirements for the signal andcontrol γγ samples, respectively.

Cuts “Tight” photon ID “Loose” photon ID

EγT ≥ 13 GeV same

Shower profile in CES: χ2 ≤20 same

EHAD/EEM ≤0.055+0.00045×E/GeV ≤0.125cal-ISO ≤0.1×ET if ET<20 GeV or ≤0.15×ET if ET<20 GeV or

≤2.0 GeV+0.02×(ET − 20 GeV) ≤3.0 GeV+0.02×(ET − 20 GeV)track-ISO ≤ 2.0 GeV+0.005 ×ET ≤ 5 GeVNtracks in cluster ≤ 1 sametrack pT if Ntracks = 1 ≤1.0 GeV+0.005×ET ≤0.25×ET

ET of 2nd CES ≤0.14×ET if ET<18 GeV no cutcluster ≤2.4 GeV+0.01×ET if ET≥18 GeV

“loose” and “tight” photon requirements is in the amountof allowed isolation energy (see Table V). The resultingγγ control sample is dominated by jet− γ and jet− jetevents where one or both photon candidates are faked byjets. The fraction of real γγ events in the control sampleis only 5%.

In addition to the photon identification requirementsdescribed above, we also apply cuts to remove contam-ination from non-collision sources. Muons produced inthe beam halo are known to fake a photon signature [41].These energetic muons travel parallel to the beam pipeand deposit energy in many towers of one wedge, consis-tent with a minimum ionizing particle. When the muonundergoes energetic bremsstrahlung, it may also createone or two fake photon candidates. Probability for a sin-gle photon BH event to overlap with a collision event witha photon candidate is very low. Therefore, events withboth fake photons from one muon are a dominant sourceof the BH background. We use this fact to suppresssuch BH events. We reject events if ∆φγγ<0.524 radand if there are more than two hadronic and four cen-tral electromagnetic towers above 0.1 GeV threshold [45].The efficiency of these requirements for collision eventsis estimated with data Z→e+e− events and found to be∼100%. The rejection power of the cuts for beam halo

events is found to be 90.4%±0.2%, as estimated using avery pure sample of beam halo events with two photoncandidates located in the same calorimeter wedge. Thecriteria used to select this sample are discussed in detailin Ref. [41].

Muons from cosmic rays may also bremsstrahlung inthe calorimeter and create fake photon candidates. Tosuppress these events, we use different approaches fordata collected before and after the timing system in theEM calorimeter [24] was installed. In the first 0.44 fb−1

of integrated luminosity for which the EM timing is notavailable, we reject events if there is a segment of hits(“stub”) in the muon drift chambers within a cone of30o around the direction of any of the photon candidatesthat is not linked to a track in the COT (trackless muonstub). This requirement rejects approximately 85% ofcosmic rays and is approximately 98% efficient for γγevents. In data from the later 1.6 fb−1 of integrated lu-minosity for which the EM timing is available, we rejectevents if one of the photon candidates has arrival time|T1,2|>4σT or two photons have |∆T | = |T1−T2|>4σ∆T ,where σT=1.67 ns and σ∆T=1.02 ns are the timing reso-lutions obtained by studying the EM timing of electronsfrom Z→e+e− events [46]. These EM timing require-ments reject 99.4% of cosmic rays, while they are 99.9%

19

efficient for prompt γγ events.Another source of fake photons is electrons from elec-

troweak processes which are misreconstructed as promptphotons. This occurs when either an electron undergoesa catastrophic bremsstrahlung in the detector materialin front of the COT or when its track does not get re-constructed. In both cases, electrons usually leave a fewhits in the silicon detectors and their tracks can be par-tially recovered by a special tracking algorithm [35]. Thisalgorithm looks for silicon hits along two helix curvesconnecting vertex and EM cluster positions. The helixcurvature is uniquely defined by the EM cluster ET , andtwo curves correspond to a positive and negative chargehypotheses. If any of the photon candidates is matchedto such a track, we reject the event. This technique isused in the γγ + e/µ and γγ + E/T searches and it is re-ferred to as the “silicon track rejection” in the main text.

3. Electron Identification

We select electrons using the CDF standard criteria.An electron is characterized by a narrow shower in theelectromagnetic calorimeter and a matching track (eitherin the COT or silicon detector) originating from the pri-mary vertex. The transverse EM energy, EEM

T , must begreater than 20 GeV. The EHAD/EEM ratio has to be lessthan 0.055. The lateral energy distribution of the showermust be consistent with that for an electron. Candi-dates are required to be isolated in the calorimeter andto contain at least 90% of the total transverse energywithin a cone of ∆R=0.4. For an electron detected inthe central region (|η|<1.05), the matching track is re-quired to be well reconstructed by the COT and havepT>10 GeV/c. The ratio of the electron energy to trackmomentum, E/p, must be less than 2.0. Electrons fromphoton conversions are suppressed by rejecting the can-didates which have an oppositely-charged track with asmall separation in the xy-plane and a minimal differ-ence in the polar angle. For an electron detected in theforward region (1.2<|η|<2.0), the matching track is re-quired to have a minimum of three hits measured in thesilicon detector. We do not apply further requirements onthe forward matching tracks because fewer measurementsper track are available and the momentum measured inthe forward region is not as reliable as that measured inthe central region. More details of electron identificationcan be found in Ref. [47].

4. Muon Identification

We select muons using the CDF standard criteria. Amuon is characterized by a well-reconstructed COT trackwhich is matched to track segments (stubs) in the cen-tral muon detectors, and an energy deposition in the EMand HAD calorimeters consistent with a minimum ion-izing particle. The pT , measured either with the COT

only, or with the COT and the silicon detector if the sil-icon hits are available, must be greater than 20 GeV/c.Two types of muons are selected: CMUP (|η|<0.6) andCMX (0.6<|η|<1.0). The CMUP muon candidate re-quires a match between the track and the stubs in theCMU and CMP detectors. The CMX muon candidaterequires a match to a muon stub in the CMX detector.In order to reduce the background from cosmic rays orhadrons which decay in flight, we require the track to beconsistent with originating along the beamline. Cosmicmuons are further suppressed via their back-to-back tracktopology and asynchronous timing measured in the COT.More details on the muon identification can be found inRef. [47].

5. Tau-Lepton Identification

The τ lepton has a ∼18% branching fraction for decaysinto an electron or muon, with neutrinos. When thisoccurs, the event would be categorized in the e/µ finalstate and addressed in that study. In the τ lepton searchwe address only the hadronic decay modes.To identify the hadronic decays of τ leptons [48], we re-

quire a narrow cluster of one or three tracks and calorime-ter energy. This cluster must be consistent with a τ lep-ton in several ways, inconsistent with an electron, andisolated from other nearby calorimeter energy.The clustering begins with a single tower with

ET>6 GeV. Up to five more towers may be added to thecluster if they are adjacent and have ET>1 GeV. At leastone high-quality track with pT>6 GeV/c must be associ-ated with the cluster. This track defines the origin pointof the τ lepton. The cone subtending an angle of θsigfrom the track direction defines the signal region wherethe τ lepton decay products are expected. This angleis fixed to be 0.17 at low τ lepton ET and is smaller forET>30 GeV, shrinking to 0.05 at ET=100 GeV, allowingfor greater rejection as the τ lepton decay products be-come highly collimated. A second cone given by θ<0.52defines an isolation annulus. The calorimeter and theshower maximum detector are used to define π0 candi-dates in the τ lepton signal cone and the isolation annu-lus. To reject electrons some hadronic energy, consistentwith the observed signal-cone tracks, is required.The τ lepton four-vector is defined by the total four-

vector of the tracks and π0 candidates in the signal cone.If the calorimeter cluster energy is significantly greaterthan this sum, the calorimeter cluster energy is used in-stead. The “visible” mass of the τ lepton is found as themagnitude of this total four-vector.We define two levels of τ lepton identification: a

“loose” identification (used in studies and backgroundtechniques) and the standard or “tight” identification,used for the signal region search.Apart from the selection included in the reconstruction

as described above, the loose identification requires onlyET>15 GeV. The tight selection also requires visible τ

20

lepton mass less than 1.8 GeV, total track pT in the iso-lation cone less than 1.0 GeV, π0 ET in the isolation coneless than 0.6 GeV, and one or three tracks in the signalcone, with total charge of ±1.

6. Jets

We reconstruct jets by using the cone clustering algo-

rithm [49] with a cone radius R =√∆φ2 +∆η2 =0.4.

Identified photons and electrons are removed from a listof jets. The jet energy is corrected for a non-linearity ofthe detector response and for contributions due to under-lying event and multiple interactions in the same bunchcrossing [50]. Unless otherwise stated, we only considerjets with ET>15 GeV and |η|<3.0.

7. Missing Transverse Energy and HT

The missing transverse energy, E/T , is defined as an en-ergy imbalance in the calorimeter and it is a signature ofneutrinos or new particles that do not interact with thedetector material. The E/T is calculated from all calorime-ter towers with ET>0.1 GeV in the region |η|<3.6 accord-

ing to ~E/T = −∑i EiT~ni where ~ni is a unit vector that

points from the interaction vertex to the ith calorimetertower in the transverse plane. To improve resolution andreduce the number of events with large fake E/T , we ap-ply corrections to the E/T to account for a non-linearity ofthe detector response for jets with ET>15 GeV and forpresence of reconstructed muons, which do not deposittheir total energy in the calorimeter.One of the global kinematic characteristics of any hard

scattering process is the total transverse energy of finalproducts, HT . We define HT for each event as a sum ofthe transverse energies of all identified objects: photons,electrons, muons, visible energy of τ leptons, jets, andE/T . According to many theoretical models, new physicsis expected to appear at large energy scales and mayreveal itself in an anomalous rate of events with largevalues of HT .

8. Unclustered Energy

The activity due to the underlying event and additionalinteractions in the same bunch crossing is characterized

by the soft unclustered energy,

soft∑ET . We calculate

soft∑ET for each event by taking the difference between

the total transverse energy in the event and transverseenergies of all reconstructed photons, electrons, and jets:soft∑

ET =

all∑ET −

∑Ejet

T −∑

EγT −

∑Eele

T .

9. The eγ Events in γγ + E/T Analysis

We use inclusive eγ events to obtain a data/MC nor-malization factor for the MC-based estimate of the EWKbackgrounds in the search for anomalous production ofγγ+E/T events. To minimize differences between eγ andγγ samples, we obtain the eγ events in data and MC byusing the same diphoton triggers (for data) and analy-sis selection procedures as used to derive our γγ baselinesample. In this selection, we treat an electron as a pho-ton (i.e., we apply the same cuts as in Table V) with onlyone exception that we also require the presence of a trackpointing to an EM cluster. This track must satisfy the0.8<E/p<1.2 requirement where E is the energy of theEM cluster and p is the track momentum. All additionaltracks must pass the cuts listed in Table V.

Appendix B: Fake Rates

1. The e → γ Fake Rate

Electrons may be misidentified as signal photons dueto hard bremsstrahlung in the detector material, inef-ficiency of track reconstruction, or collinear final stateradiation (FSR). We measure the misidentification prob-ability, P(e→γ), using Drell-Yan Z/γ∗ events. TheP(e→γ) is defined as the ratio of the number of recon-structed Z/γ∗→eγ events to the number of reconstructedZ/γ∗→ee events. The ET dependence of P(e→γ) is ob-tained from the simulation. The overall normalizationis scaled by the ratio of data–to–MC probabilities mea-sured at ET=40-50 GeV, around the Z peak. The elec-trons have been selected using two types of identifica-tion: 1) standard central-electron criteria in Section A 3,2) photon-like electron criteria in Section A9. The resultfrom identification-1 has been used in the γγe and γγµsearches, while the result from identification-2 has beenused in the cross-checks of γγe, γγµ, and γγE/T searches.The P(e→γ) for identification-1, before (P(e→γ)B) andafter (P(e→γ)A) applying silicon-track rejection, is mea-sured with the data and MC Drell-Yan samples and pa-rameterized as a function of the electron ET (in GeV):

P(e → γ)B = SB · (e−2.991−0.045·ET + 0.007), (B1)

P(e → γ)A = SA · P(e → γ)B · (1 − ǫ(ET )), (B2)

where SB and SA are the data to MC scaling factors:

SB = 1.08± 0.09,

SA = 1.32± 0.20,

and the ǫ(ET ) is the efficiency of silicon-track rejectionmeasured with the Drell-Yan MC:

ǫ(ET ) = 0.405 · 2√π

∫ ∞

z

e−t2dt (B3)

z = 0.086 · (24.711− ET )

21

(a) Before silicon-track rejection

(GeV)TElectron E20 30 40 50 60 70 80

rat

e / 4

GeV

γ →

e

0.00

0.01

0.02

0.03(a) Before silicon-track rejection(a) Before silicon-track rejection (b) After silicon-track rejection

(GeV)TElectron E20 30 40 50 60 70 80

rat

e / 4

GeV

γ →

e

0.00

0.01

0.02

0.03(b) After silicon-track rejection(b) After silicon-track rejection

FIG. 11: Probability for a CDF standard central electron to be misidentified as a standard central photon as measured in theDrell-Yan MC, before (a) and after (b) applying the silicon-track rejection. The misidentification probabilities (points) areparameterized as a function of electron ET at the parton level. The gray boxes indicate the systematic uncertainties in eachET bin due to the uncertainties on fit parameters.

(GeV)TElectron E20 30 40 50 60 70 80

mat

chin

g ef

ficie

ncy

(%)

/ 4 G

eVγ

e-

0

10

20

30

40

50

60

70

80

90

100

FIG. 12: Efficiency for an electron reconstructed as a CDFstandard central photon to be matched to the silicon-electrontrack, as a function of electron ET at the parton level, mea-sured in the Drell-Yan MC. The gray boxes indicate the sys-tematic uncertainties in each ET bin due to the uncertaintieson fit parameters.

The electron ET at the parton level is further trans-lated to the photon ET at the reconstruction level us-

ing a simulation study. Figure 11 shows the P(e→γ)B

and P(e→γ)A measured in the Drell-Yan MC, withoutdata–to–MC scaling factors applied. Figure 12 shows theǫ(ET ). The average P(e→γ)B is about 1.5% with an 11%fractional uncertainty, and the averageP(e→γ)A is about0.4% with a 17% fractional uncertainty. The uncertain-ties come from the limited size of Z data sample whichdetermines the data–to–MC scaling factor, the variationof fitting methods which determines the number of Zcandidates, and the difference between results measuredin the diphoton and inclusive electron triggers.

2. The jet → γ Fake Rate

Hadrons in jets, such as π0, η0, and K0s , may decay

into multiple photons. The segmentation of the CDFEM calorimeter is not sufficiently small to separate thesephotons and the standard reconstruction algorithm willreconstruct these hadron daughters as a single photoncandidate. The probability to misidentify a jet as a signalphoton, P(jet→γ), has been measured in Ref. [32], usingdata collected with inclusive jet triggers. The P(jet→γ)is defined as the number of identified photon candidatestimes the fake-photon fraction (FQCD) and divided by thenumber of jets. The fraction FQCD is required becausethe identified photon candidates in the jet data will con-tain real photons not relevant to the fake rate. Ref. [32]has determined FQCD statistically by combining the fol-lowing information: (a) the lateral shower shape mea-sured in the wire and strip chamber (CES), (b) the extra

22

energy in a cone of ∆R=0.4 around the photon candidate(cal-ISO) measured in the calorimeters, and (c) the con-version rate measured in the central preshower detector.The P(jet→γ) is parameterized as a function of the ET

of jet (in GeV) and found to be:

P(jet → γ) = 10−3 · (e2.397−0.153·ET (jet) + 0.404). (B4)

The fake photon ET is smaller than the original jet ET

because the fake photon is often accompanied by otherparticles from that jet. The translation of the jet ET tothe photon ET has been studied using simulations andis represented by a Gaussian distribution with a meanof 0.937 and a width of 0.048. The P(jet→γ) is about0.2% at Eγ

T =13 GeV and 0.04% for EγT>50 GeV, with a

systematic uncertainty ranging from 50% to 200%. Thesources of systematic uncertainties include: the differ-ences between the methods for determining FQCD, thedifferences of results when using a loose photon candi-date as the fake denominator, variation of the mixtureof quark jets and gluon jets, and variation of fragmenta-tion model in the simulation which changes the Gaussianfunction of ET translation.

3. The jet → e/µ Fake Rate

Hadrons in jets may be misidentified as electrons dueto inelastic charge exchange or the production of an ener-getic conversion electron. The inelastic charge exchangein the EM calorimeter, π−p→π0n or π+n→π0p, resultsin a track in the COT due to the π± and an EM showerin the calorimeter due to the photons from π0 decay.The combination of a charged track and an EM showergives a fake electron candidate. Hadrons can also de-cay into muons before interacting with calorimeter (e.g.,K+→µ+νµ) or pass through the calorimeter into themuon chamber (punch-through) with minimal interac-tion and give fake muon candidates. The probability tomisidentify a jet as an electron or a muon, P(jet→e, µ),has been measured in Ref. [34], using data collectedwith inclusive jet triggers. P(jet→e, µ) is defined asthe ratio of the number of identified electron/muon can-didates to the number of “fakeable” objects (denomi-nator). The fakeable object is a jet with uncorrectedET>4 GeV for central electrons, a jet with uncorrectedET>15 GeV for forward electrons, and an isolated trackwith pT>4 GeV/c and minimal extra energy in the coneof ∆R=0.4 for muons. A track is considered to be iso-lated if the total ET of calorimeter towers within the coneof ∆R<0.4 around the track is less than 4 GeV or lessthan 10% of track’s momentum. The misidentificationprobabilities, parameterized as a function of the jet ET

(in GeV), for the electrons are:

P(jet → ecentral) = 0.00013 + e−7.940−0.194·ET (jet),(B5)

P(jet → eforward) = 0.00032+ 0.000012 · ET (jet).(B6)

The translation of the jet ET to the electron ET hasbeen studied using simulations. The ratio of electron ET

(GeV)TTau-lepton E0 20 40 60 80 100 120 140

P(lo

ose

tau

(jet)

mis

id a

s ta

u)

0

0.01

0.02

0.03

0.04

0.05

0.06

Trigger SampleTower>5 GeV

>20 GeVTJet E>50 GeVTJet E>70 GeVTJet E

FIG. 13: The solid line represents the probability for objectspassing loose τ lepton ID cuts to also pass tight τ leptonID cuts (jet → τ fake rate) as a function of τ lepton ET ,with the overlapping regions removed. The dashed lines arethe systematic uncertainties on the jet → τ fake rate (±1standard deviation).

to jet ET is represented by a Gaussian distribution witha mean of 0.89 and a width of 0.06. The misidentificationprobabilities, parameterized as a function of the track pT(in GeV/c), for the muons are:

P(track → µCMUP) = 0.00086 + 0.00017 · pT (µ), (B7)P(track → µCMX) = 0.00082 + 0.00020 · pT (µ). (B8)

Since the misidentification probabilities were measuredup to ET=50 GeV and pT=50 GeV/c and the misidenti-fication probabilities are expected to reach a plateau, weassign a constant value to all misidentification probabili-ties for ET≥50 GeV and pT≥50 GeV/c. The P(jet→e, µ)averages ≈0.01% for central electrons, ≈0.04% for for-ward electrons, and ≈1.0% for central muons, with a 50%systematic uncertainty estimate provided by the varia-tion of results measured in different jet triggers.

4. The jet → τ Fake Rate

The probability of a quark or gluon jet to be misrecon-structed as an hadronically–decaying τ lepton is mea-sured and then applied to a sample of jets to estimatethe number of fake τ leptons we expect in that sample.We measure this misidentification rate in a sample of

inclusive jet triggers [51], using only the energy clustersfor which the trigger is fully efficient. This jet samplehas a negligible fraction of real τ leptons because the

23

rates for W/Z→τ+X and c/b→τ+X processes are verysmall compared to the jet production rates. Therefore,the measurement of the misidentification rate is straight-forward. We identify all loose and tight τ leptons (SeeSection A5) and measure the rate by dividing the num-ber of tight τ leptons by the number of loose τ leptonsas a function of the τ -candidate ET .We check the misidentification rate by using it to pre-

dict various distributions in the jet samples. We comparethe number of τ leptons observed and predicted as a func-tion of the first, second and third jet ET , the event totalenergy, the underlying event energy, the number of jets,the number of interactions in the event, and the distancethe nearest jet. The only notable discrepancy is the casewhere the τ lepton is close to a second jet, where the jet’senergy tends to spoil the τ lepton’s isolation and reducethe fake rate. We include this effect in the applicationof the misidentification rate. The assigned systematicuncertainty of 20% accounts for any other discrepancies.The resulting function is shown in Fig. 13.Finally, we identify the primary source of each jet in

inclusive pythia MC jet samples by searching for thehighest-ET parton consistent with the jet direction. Wethen measure the misidentification rate in quark andgluon jets separately. We find the rate for gluon jetsis approximately three times smaller than the rate forquark jets, which have a higher probability to fragmentto a few energetic particles.

Appendix C: The E/T Resolution Model

A major sources of background in the γγ + E/T finalstate is diphoton candidate events with significant fakeE/T due to energy mismeasurement in the calorimeter.Given the large production rates for QCD processes (γγ,γ-jet, and jet-jet), fluctuations in energy measurementscan result in a considerable fraction of such events. Wepredict the shape of this fake E/T and calculate its signif-icance on an event–by–event basis by means of the E/Tresolution model denoted as metmodel.The metmodel is based on a simple assumption that

fluctuations in energy measurements of jets, soft unclus-tered particles from the underlying event, and multipleinteractions are the dominant sources of fake E/T . There-fore, the individual contributions of each of these compo-nents to fake E/T can be modeled, on average, by smearingtheir energies according to the corresponding energy reso-lution functions. Jets are the dominant source of fake E/Tbecause they are collimated sprays of energetic particlesin a certain direction and may have large measurementfluctuations in that direction. The unclustered energy,on the other hand, tends to be uniformly spread in thecalorimeter. Therefore, the portion of E/T due to thissource is usually small and mostly results in a smear-ing of the jet component of fake E/T . Taking into accountthe above considerations and for reasons of simplicity, wemodel only the fake E/T due to mismeasurements of jets

(GeV)yTE

-40 -20 0 20 40

Eve

nts/

3 G

eV

1

10

210

310

410 1/2<12 GeVTEΣ<1/210 GeV a)

)1/2 (GeVTEΣ2 4 6 8 10 12 14 16 18

(G

eV)

σ

2

3

4

5

6

7

8

9

b)

FIG. 14: Example of the fake E/T parameterization due tounclustered energy. Figure a) shows a two-Gaussian fit of theE/T

y distribution for pythia γγ events from one of the bins

in√

∑

ET . Figure b) demonstrates how a width, σ, of the

leading Gaussian depends on the√

∑

ET . On both plots,points are pythia data and curves are the fit functions.

and all soft unclustered energy (rather than individualunclustered particles).

The E/T resolution due to the soft unclustered energy isstudied in the γγ control sample (see Appendix A2) andZ/γ∗→e+e− events with 85 GeV/c2<Mee<97.5 GeV/c2.We fit distributions of x and y components of the E/T forevents without jets, Njet(ET>15 GeV)=0, in small bins

of√∑

ET , with a sum of two Gaussian distributions.

24

We assume that both Gaussian distributions have thesame mean, but different widths (σ and scale×σ, respec-tively). From the individual fits of E/T

x and E/Ty distribu-

tions, we obtain the mean, σ, scale, and relative normal-ization, Norm, of two Gaussians for each bin of

√∑ET

(bin size is 2 GeV1

2 ). The parameters are then fitted by

simple polynomial functions of z=√∑

ET : p0 + p1z forσ and the scale, p0+p1z

2 for the mean, and Norm = p0.These functions provide a parameterization of the unclus-tered energy contribution into the x and y componentsof the fake E/T in the event. The default set of param-eters is obtained from the γγ control sample. We alsouse the results of fits in the data Z→e+e− sample asan alternative set of parameters to study the associatedsystematic uncertainties. Figure 14 demonstrates an ex-ample of the E/T

yresolution parameterization due to the

unclustered energy in pythia γγ events. Distributionsfor both x and y components of E/T look essentially iden-tical to those shown in Fig. 14. We also do not observeany large difference in the parameterization of the E/T res-olution due to unclustered energy between Z/γ∗→e+e−

and “loose” γγ events in data as well as between dataand MC.

To account for contributions from jets into the fake E/T ,we obtain the jet energy resolution, JER, as a function ofjet energy and pseudorapidity, E and η. For this purpose,we use pythia samples of dijet and Z−jet events passedthrough the geant-based detector simulation. In theseevents, we reconstruct jets before (hadron jet) and after(detector jet) the detector simulation by using the samecone clustering algorithm at both levels. The jet energyresolution is then defined as a ratio of the detector (Edet)and hadron level (Ehad) jet energies, JER=Edet/Ehad-1,for hadron and detector jets with pT>3 GeV/c that arematched within a cone of R(φ, η)<0.1. Unlike the energybalance in dijet and Z-jet events, this definition of JERis mostly sensitive to detector effects and allows us to sig-nificantly minimize the dependence of resolution on theeffects of initial and final state radiation. However, westill compare the dijet and Z-jet balance in data and MCto make sure that the simulation adequately describes theresolution. We fill JER histograms for jets in 5 GeV binsin jet energy and ∆η=0.2 bins in pseudorapidity. We fitthese histograms by a linear combination of Gaussian andLandau functions of x, where x=−JER/(1 + JER) en-sures stable fits in the entire range of jet energies. Exam-ples of fits for one particular η-bin can be found in Fig. 15.These plots illustrate that our fit function successfullydescribes the jet energy resolution in a wide range of jetenergies. It is also important to mention that the samefit function is used for all η-bins. From the individual fitsfor each (Ejet,η)-bin, we obtain a relative normalization,C, and parameters of a Gaussian (mean and σ) and Lan-dau (mean and σ) fits. These parameters are plotted asa function of Ejet for each η-bin, and fit with the follow-ing functions: σ=

√p0/E + p1; mean=p0 + p1E + p2/E;

and C=(p0 + p1√E)/E + p2. This provides a smooth

parameterization of JER for all reconstructed jets with

Ejet>3 GeV and |η|<3.6.

-1had/EdetE-1 -0.5 0 0.5 1

Eve

nts/

0.03

-110

1

10

210

310<25 GeVdet20 GeV<E

|<0.6η0.4<| a)

-1had/EdetE-1 -0.5 0 0.5 1

Eve

nts/

0.03

-110

1

10

210

310<405 GeVdet400 GeV<E

|<0.6η0.4<| b)

FIG. 15: Examples of jet energy resolution (JER) fits usinga linear combination of Gaussian and Landau functions ofx=−JER/(1 + JER) where JER = Edet/Ehad − 1 for twodifferent jet energy bins: a) 20 GeV<Edet<25 GeV and b)400 GeV<Edet<405 GeV.

We predict the shape of fake E/T based on the energyresolution functions described above. For each event, weproduce a probability distribution function, P(E/T ), of allpossible values of the fake E/T by smearing the energiesof jets and unclustered energy according to these objectsindividual resolution functions in a large number of pseu-doexperiments. Then, we sum up these individual P(E/T )distributions for all events to obtain a shape of the pre-dicted fake E/T due energy mismeasurements in our data

25

sample. Technical details of how we generate P(E/T ) aregiven below. An example of this P(E/T ) distribution forone of the γγ baseline sample events can be found inFig. 16. The method is validated in MC samples withand without intrinsic E/T . Figure 17 demonstrates thatthe metmodel successfully predicts the shape of E/T -distributions in pythia γγ and pythia Z→e+e− eventswith fake E/T . The technique is also cross-checked byperforming the entire analysis with the data γγ controlsample and data Z→e+e− sample.The P(E/T ) distribution for a given event can be ob-

tained using a large number of pseudoexperiments. Foreach pseudo-experiment, we start by forming a list of alljets with ET>3 GeV and |η|<3.0 in this event and thensmear their energies according to JER(Ejet, η) describedabove. If the smeared jet energy, Esmear

T , is above the15 GeV threshold, we calculate the contribution of that

jet into the fake E/T : ~E/Tjet,i

= ~ET − ~EsmearT . Therefore,

the metmodel should account for a correlation betweenthe directions of E/T and jets. Then, we re-calculate theunclustered energy based on Esmear

T of all jets to avoiddouble-counting when one of the jets with ET<15 GeVhas Esmear

T >15 GeV. For the next step, we randomlygenerate the expected x and y components of the E/T con-tribution due to the unclustered energy deposited in thecalorimeter. This procedure also accounts, on average,for effects of energy resolution of photons and electronsas well as residual effects of the wrong vertex choice. Fi-nally, we take a vector sum of all individual E/T compo-nents due to the soft unclustered energy and each of thejets with Esmear

T >15 GeV to obtain the final predictionof the fake E/T .The metmodel is not designed to predict the exact

value of the fake E/T in each event. Instead, it provides

a two-dimensional probability density function, P( ~E/T ),for values of the fake E/T which could arise from energy

mismeasurements in the calorimeter. This P( ~E/T ) can beused to determine a significance of the observed E/T in agiven event according to the following formula:

E/T -significance = − log10

(1−

∫ ~w

0

P(~z)d~z

), (C1)

where ~z is the generated fake ~E/T and ~w is the observed~E/T . The E/T -significance defined by Eq. C1 correctlytakes into account all of the correlations between jets andthe observed E/T . However, the method has one signifi-cant drawback since it requires generating a large numberof pseudoexperiments (e.g., >106 pseudoexperiments forE/T -significance=6). To overcome this problem, we takea simplified path of calculating an upper limit on theE/T -significance (“raw” E/T -significance) according to the

formula:

E/T -significance = − log10(PjetsPuncl), (C2)

Puncl =∏

i=x,y

(1−

∫ ui

−ui

P iuncl(u)du

),

ui = E/Tx, E/T

y,

Pjets =

jets∏

i,vi>0

∫ vi

−1

Pi(v)dv ×jets∏

i,vi<0

(1−

∫ vi

−1

Pi(v)dv

)

vi = E/T /(EiT cos∆φi),

where Px,yuncl(u) is the probability density function for

unclustered energy contribution to E/T resolution (illus-trated in Fig.14a), Pi(v) is the probability density func-tion for jet energy resolution (shown in Fig.15), Ei

T

is the transverse energy of the i-th jet, and cos∆φi

is the azimuthal angle between that jet and measuredE/T . The “raw” E/T -significance obtained from Eq. C2 isthen calibrated to have a simple shape defined a pri-ori: dN/dx=Nevnt·ln(10.0)·10−x, where x is the E/T -significance and Nevnt is the number of events in a sam-ple. The shape of the E/T -significance has one importantproperty: if all events in a data sample were to haveonly fake E/T , then Nevnt · 10−cut events would pass arequirement E/T -significance>cut. This property makesit very easy to calibrate the E/T -significance by meansof pseudoexperiments. In each pseudo-experiment, weobtain a randomly generated value of E/T . Then wecalculate the significance of this generated E/T as if itwere measured E/T . We repeat this procedure for allevents in the data sample and obtain the significancedistribution for pseudoexperiments. Finally, an adjust-ment factor is derived for each bin of the distribu-tion so that the corrected E/T -significance satisfies theN(E/T -significance>cut)=Nevnt · 10−cut requirement.

The systematic uncertainties associated with the met-model predictions are evaluated by comparing the re-sults obtained with the default set of parameters topredictions obtained with the metmodel parameterschanged by one standard deviation (±σ). In total, tensources of the systematic uncertainties are considered: 1)difference in the unclustered energy parameterization ofthe E/T resolution for γγ control and Z→e+e− events;2) uncertainties on four parameters of the unclusteredenergy parameterization; 3) uncertainties on five param-eters of the JER parameterization. The correlations be-tween these parameters are also taken into account. Thestatistical uncertainty that depends on the number ofpseudoexperiments per event and the systematic uncer-tainty are added in quadrature to obtain the total uncer-tainty.

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et al., arXiv:hep-ph/9906224; S. Ambrosanio et

26

(GeV)TE0 10 20 30 40 50 60

Eve

nts

/ 2 G

eV

-410

-310

-210

-110

1

10

210

: Run 194911 Event 694054γγData 1000 pseudo-experiments

a)

-significanceTE0 1 2 3 4 5 6

Eve

nts

/ 0.2

-410

-310

-210

-110

1

10

210b)

FIG. 16: Examples of the generated a) P(E/T ) and b) E/T -significance distributions for one of the signal sample events.

(GeV)TE0 20 40 60 80 100 120

Eve

nts

/ 3 G

eV

-110

1

10

210

310

410

510 γγPythia

syst±METMODEL: pred

a)

(GeV)TE0 20 40 60 80 100 120

Eve

nts

/ 3 G

eV

-110

1

10

210

310

410

510 -e+e→Pythia Z

syst±METMODEL: pred

b)

FIG. 17: Examples of the metmodel predictions for E/T -distributions in pythia a) γγ and b) Z→e+e− events. These eventsdo not have the intrinsic E/T . However, fluctuations in energy measurements can result in the fake E/T as large as 100 GeV.Both distributions are well described by the metmodel predictions in the entire range of the observed E/T .

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